Practice Questions for Business Statistics

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Chapter: Making Inferences about One Population

Contents:

29-1 If 100 random samples of size n were drawn

79-1 find in the table

79-2 percentile of students' distribution

80-1 "students' distribution, 90 percent of the area"

80-2 (XBAR - 16)/(S/SQRT(7))

83-1 T-distributions are spread out

84-2 A t-distribution with 30 d.f. is most similar

86-1 a true statement regarding the comparison of t-distributions

87-2 A t-distribution is used in estimating MU when

88-1 Suppose that we repeatedly draw a random sample

88-2 Obtain the values of the t-distribution

89-1 the value of Student's t that subdivides

92-1 standard normal distribution and a student's distribution are alike

96-1 Since percentiles of the t-distribution approximate those of

148-1 When (for what level of confidence) do we use Z =

148-2 (Z-score) corresponds to the sample mean

154-2 the 95% confidence interval for the appropriate z-score is

155-1 on which test was his performance better

156-1 then P(70.5 < XBAR < 71.3) is approximately

161-1 what is the probability that the mean competency

161-2 The middle 99% points for the distribution of the sample mean

162-1 P(WBAR > 195)

163-1 what are the middle 90%

175-1 Find (approximately) P[XBAR>2]

193-1 the students' personal libraries at this

201-1 whether or not the manufacturing process is operating satisfactorily

215-2 average (mean) height of 9 randomly selected setters

732-1 "Which of the following describes a ""statistical inference""?"

765-2 Standard error of a mean

777-1 MU

1342-1 A pocket calculator enthusiast claims that 80% of all incoming freshmen

1394-1 Establish a 90% confidence interval for the mean speed of cars

1398-1 is 10. The standard error of the mean is

1399-2 "As the sample size (n) increases, the mean of a random sample"

1399-3 In general the sampling distribution of the mean and the distribution

1400-2 Suppose that all possible distinct samples of size n > 30

1401-1 Suppose that all possible distinct samples of size n > 1

1418-1 90% confidence limits corresponding to a

1418-2 the lower confidence limit for a two sided

1419-1 t distribution is usually used instead of the standard normal

1420-2 90% confidence interval for the true percentage of children

1421-1 "MU, which of the following is most precise:"

1421-2 An approximate 95% confidence interval

1425-3 "Other things being equal, the larger the confidence coefficient"

1426-1 An investigation reveals that a confidence interval with

1428-1 percentages of fat in 1 pound packages

1429-1 Construct a 99% confidence interval

1429-2 "1, 2, 3, 4, 5. Construct a 95% symmetric confidence"

1430-2 What kind of table whould you use

1431-2 Determine 95% confidence limits corresponding to a

1433-1 The value you would find in the table to complete the information

1433-2 A 95% confidence interval for the mean

1434-1 interval for the population proportion favoring Senator Claghorn is:

1434-2 "t-statistic, student A uses a confidence coefficient of"

1435-1 What will be the effects of changes

1435-2 "To three decimals, what is the upper limit of"

1438-1 The size of a confidence interval for a mean is affected by

1439-1 The 93% confidence interval for MU is closest to:

1440-1 Consider the following table which gives the deodorants preferred

1441-2 then a 99% confidence interval for p is given by

1443-1 What is the probability that XBAR differs from MU by more than 1?

1443-2 A 95% confidence interval for MU is:

1445-1 The mean weight of a random sample of 16 dogs on the quad

1446-1 "XBAR = 31 and SUM(i = 1, 400)((X(i) - 31)**2) = 1596"

1447-1 "XBAR = 20 and SUM(i = 1, 16)((X(i) - 20)**2) = 960"

1448-2 Eighty percent of a sample of 400 people support candidate B.

1449-1 "8, 11, 9, 17, 12, 15 are a sample of size 6"

1454-1 found that the mean cost (i.e. XBAR) of hospital care for

1455-1 by adding to and subtracting from the sample mean a certain multiple

1455-2 A 90% confidence interval

1456-1 "Given that 99% confidence limits for MU are 42 and 58, "

1457-1 Suppose a psychologist wishes to know the mean IQ of students

1459-1 an approximate 95% confidence interval for MU?

1460-2 Find the 0.95 confidence interval estimate

1461-2 "A parameter is fixed (non-fluctuating), a confidence interval is"

1463-1 contained within approximately how many of these intervals?

1463-2 The sample mean of 225 scores on a math test is 75.

1464-1 the probability of MU falling within a confidence interval

1469-2 Is 113 an acceptable value for MU at a 95% confidence level?

1470-1 The Chamber of Commerce in Miami Beach wishes to estimate

1471-1 estimate the proportion of people in a population who

1471-2 Set up a 90% confidence interval for the area of the plot.

1472-1 John has done an experiment on gallons of water per second

1472-2 500 accounts receivable is selected

1473-1 A survey on consumer finances reports that 33 per cent

1473-3 Use a confidence level of 90%.

1474-2 confidence interval for the proportion of males

1478-1 nine patients on this new diet had observed cholesterol

1478-2 interval for the actual percentage of television viewers

1480-1 voters in Portsmouth indicate that 60%

1481-1 confidence interval for the true mean arm reach of tournament fighters.

1481-2 "Estimate the proportion of ""poverty"" families"

1482-1 Interpret the statistical meaning of this confidence interval.

1483-1 Would your interval have been narrower if SIGMA would have been

1484-1 respond to him based on part a above

1485-1 "their bills for the evening were [$12.50, $10.75, $14.28]"

1486-1 from 0 (no parenting skills deemed successful) to 100

1487-1 A sociologist conducted a study of assertion by

1488-1 "A sample of six male delinquents, aged 16, indicates"

1491-2 Explain why the confidence interval in (b) is approximate.

1495-1 Make a confidence interval statement concerning the proportion of

1499-3 Would you forecast a win for candidate A? Why?

1500-1 Which of the following confidence limits would appear most favorable

1501-1 determine if these limits are consistent with

1509-1 "If (5,8) is a 95% confidence interval for a MU, then the probability"

1509-2 A confidence interval for MU will generally be smaller if

1510-1 As the size of a confidence coefficient (one minus ALPHA)

1510-2 The sample mean lies at the center of the confidence interval for MU.

1511-2 A 95% confidence interval is twice as long as a 90% confidence

1513-3 With any sample size a high level of confidence in an interval

1522-2 What would be the midpoint of an interval estimate of p?

1523-1 the width of the interval can be narrowed by

1547-1 The confidence coefficient is the probability that an unknown parameter

1547-3 If confidence intervals are computed from repeated samples of the same

1548-2 MARGIN OF ERROR

1551-2 The purpose of using a sample and calculating a mean is to

1566-1 will approximate the normal curve if

1566-3 "If we think of how all possible XBAR's are distributed, the"

1568-1 The Central Limit Theorem tells us that:

1568-2 "As the size of the sample, n, increases towards the size of the popu"

1569-1 The Central Limit Theorem

1570-1 The sampling distribution of means of random samples of size n drawn

1572-3 10 hours using the Central Limit Theorem.

1576-1 "According to the Central Limit Theorem, how does a sampling distribu"

1577-1 Define what is meant by the sampling distribution of XBAR for size

1578-1 What is the approximate distribution of Z?

1580-2 The Central Limit Theorem is of most value when we sample from

1581-1 "As the sample size increases, the distribution of the sample mean"

1581-2 The Central Limit Theorem applies to the case of sampling from

1582-2 "the same size, drawn from a severely skewed population, will equal"

1583-2 "According to the Central Limit Theorem, the shape of "

1584-2 "The central limit theorem tells us that, if we take a large sample,"

1585-2 The sampling distribution of XBAR is approximately normal if and only

1691-1 "Other things being equal, a low level of confidence is desirable."

1730-1 ________________ is the process of drawing conclusions about population

1791-3 A proportion is a special case of a mean when you have

1815-1 "variance 36. For samples of size 9, the sampling distribution"

1820-2 "If the population distribution of scores (X) is normally distributed,"

1857-4 Suppose we have sampled (with replacement) from a finite population.

1858-3 A larger mean implies a larger standard deviation.

1859-1 non-normal population with SIGMA**2 = 1 and MU = 0 would have mean

1865-1 "The variance of the sample mean, SIGMA(XBAR)**2, is computed"

1869-1 "Does this imply that one is ""above average"" and the other is ""below"

1869-2 Give an example illustrating that the standard error of a sample

1891-2 Explain how SIGMA differs from SIGMA(XBAR).

1898-1 "For a large sample size, the estimated standard error of the mean is"

1898-2 The standard deviation of the original observations is generally

1901-1 Distributions of population statistics have standard deviations

1905-2 estimator of the variance of the population from which

1927-1 VAR(XBAR) = __________. (sometimes denoted (SIGMA(XBAR))**2).

1928-1 "If the variance of the mean S(XBAR)**2 = 5 and n = 5, what is S**2?"

1951-3 The distribution of XBAR will have a variance equal to the

1959-1 If the random variable X has a normal distribution with mean MU and

1960-2 "In a population with MU = 10 and SIGMA**2 = 64, the standard error"

1962-1 "MU = 5 and SIGMA = 20, the probability that the mean"

1963-2 If independent samples of size 6 are drawn over and over again and

1964-1 The standard error of the mean is another name for the standard

1964-3 "SIGMA(XBAR) changes in what way when n,"

1966-1 S(XBAR) is:

1966-3 "SIGMA(XBAR), is customarily called the:"

1967-1 Find the standard error of the mean for

1968-1 How could you estimate the value of the standard error

1968-2 "as before, but using samples of size 9n"

1969-1 The standard error of the mean

1969-2 Which of the following best describes the standard error of YBAR?

1971-1 Which investigator is apt to obtain a better estimate of the corres

1977-4 "As the sample size increases, the standard error of the mean remains"

1978-1 The standard deviation of the random sampling distribution of the mean

1978-3 "If the sample size is greater than one, the sampling distribution"

1979-3 The standard error of the sample mean increases with the sample

1981-1 The formula SIGMA(XBAR) = SIGMA/SQRT(n) requires the population

2074-2 The standard error of the median is an index of

2074-4 it must be a _________________ distribution.

2103-1 Let MU(X) and SIGMA(X)**2 be the mean and the variance of a

2857-1 A sampling distribution:

2859-1 Which is NOT a characteristic of a (random) sampling distribution

2860-3 We __________ have a complete sampling distribution displayed for us.

2862-4 How does a sampling distribution differ from the distribution of

2866-1 if the sample size is increased nine-fold

2867-3 A sampling distribution could be considered a population.

2889-1 If a population is very large an especially large sample is usually

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Questions:

29-1

    Q:  Which one of the following statements is correct?

        a.  If L and U are the lower and upper limits of a 99% confidence
            interval for MU, then MU varies between L and U with a
            probability of .99.

        b.  If for a sample of 100 students from the registrar's office
            it was found that 95% of these students had dean's list
            averages, then random sampling from the entire student body
            could not possibly have been performed.

        c.  Assuming the population variance is known, then if the sample size
            is doubled, the variance of the distribution of the sample mean of
            a variable would be halved.

        d.  If 100 random samples of size n were drawn and, if, for each,
            a 99% confidence interval for MU was computed, then exactly
            99 of these confidence intervals would contain within their
            limits the true population mean.

        e.  For continuous variables the probabilities P(a < x < b) and
            P(a <= x <= b) are always the same, whereas for discrete
            variables these probabilities are always different.

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79-1

    Q:  A sample of size 16 is taken from a normal population.  Then a 99%
        confidence interval is set up with XBAR = 30 and s = 20.  The value
        you would find in the table to complete the information necessary
        to obtain the interval would be:

        (a)  2.602              (d)  2.947
        (b)  2.326              (e)  2.921
        (c)  2.576              (f)  none of these.

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79-2

    Q:  The first percentile of students' distribution with 24 degrees of
        freedom is:

        (1)  -2.80      (4)  2.49
        (2)  -2.50      (5)  2.50
        (3)  -2.49

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80-1

    Q:  For students' distribution, 90 percent of the area lies between t =
        -1.89 and t = 1.89 if the degrees of freedom are:

        (1)  2            (4)  7
        (2)  3            (5)  8
        (3)  6

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80-2

    Q:  A large normally distributed population has mean 16.  Consider all
        samples of size 7.  The numbers

             (XBAR - 16)/(S/SQRT(7))

        are:

        (a)  normally distributed
        (b)  t distributed with 7 degrees of freedom
        (c)  t distributed with 6 degrees of freedom
        (d)  neither t nor normal

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83-1

    Q:  T-distributions are spread out __________(more or less) than a normal
        distribution with MU = 0, SIGMA = 1.

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84-2

    Q:  A t-distribution with 30 d.f. is most similar to a _____ distribution.

             a.  normal distribution with mean = 1 and variance = 1
             b.  normal distribution with mean = 0 and variance = SIGMA**2
             c.  normal distribution with mean = 0 and variance = 29
             d.  normal distribution with mean = 0 and variance = 1

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86-1

    Q:  Which of the following is a true statement regarding the comparison of
        t-distributions to the standard normal distribution?

        a.  The normal distribution is symmetrical whereas the t-distributions
            are slightly skewed.
        b.  The proportion of area beyond a specific value of t is less than
            the proportion of area beyond the corresponding value of z.
        c.  The greater the df, the more the t-distributions resemble the
            standard normal distribution.
        d.  All of the above.
        e.  None of the above.

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87-2

    Q:  A t-distribution is used in estimating MU when __________ is unknown
        but its use assumes that the sample data ____________________________.

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88-1

    Q:  Suppose that we repeatedly draw a random sample from a normally
        distributed population with a known mean and calculate a value for
        student's t for each sample.

        a.  We will calculate t = (sample mean - _____) / _____

        b.  If each sample consists of 7 elements, the t distribution
            generation will have _____ degrees of freedom.

        c.  Over a large number of trials _____% of the values generated
            will be greater than 1.440.

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88-2

    Q:  Obtain the values of the t-distribution with 8 degrees of freedom that
        subdivide the area under the curve so that 5% is to the left of the
        smaller value and 5% is to the right of the larger value.  Sketch the
        curve of this t-distribution and indicate the areas involved.

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89-1

    Q:  What is the value of Student's t that subdivides the area under
        any Student's t curve so that 50% of the area lies to the right
        of that value?

        What is the corresponding value for a standard normal distribution?

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92-1

    Q:  1)  State two ways in which a standard normal distribution and a
            student's distribution are alike.

        2)  State at least one way in which they differ.

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96-1

    Q:  True or False?  If False, correct it.

        Since percentiles of the t-distribution approximate those of
        the normal distribution if n is greater than 30, this is usually
        considered a good sample size to use.

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148-1

    Q:  When (for what level of confidence) do we use Z = 1.645, for a
        two-sided test or confidence interval?

        a.  90%
        b.  95%
        c.  80%
        d.  100%
        e.  99%

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148-2

    Q:  A random sample of size 25 is taken from a population with mean 7 and
        variance 4.  The sample mean is calculated to be 8.  What value of the
        standard normal random variable (Z-score) corresponds to the sample
        mean?

        a.  25
        b.  1.25
        c.  -1.25
        d.  +2.5
        e.  none of the above

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154-2

    Q:  Consider the following data:

                1, 7, 3, 3, 6, 4

        Assuming this data is drawn from a normal population with mean = MU
        and variance = 6, the 95% confidence interval for the appropriate
        z-score is _____ standard units long.

        a)  5.14    b)  4.90    c)  4.58    d)  4.04    e)  3.92

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155-1

    Q:  The class average on the first midterm was 81 with a standard
        deviation of 9.  The class average on the second midterm was 78
        with a standard deviation of 12.

        If a student got a 93 on each test, on which test was his performance
        better relative to the class?

        A.   First midterm                B.  Second midterm

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156-1

    Q:  The height of male college freshmen has a  normal  distribution  with
        mean  71 inches and standard deviation 3 inches.  If 100 male college
        freshmen are selected at random, and XBAR is  the  average  of  their
        heights, then P(70.5 < XBAR < 71.3) is approximately:

        a) .4525   b) .6732   c) .7938   d) .8413  e) none of these

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161-1

    Q:  Suppose that for a sample of 36 Family  Nurse  Practitioners  (FNP's)
        from  several  similar  type  hospital  clinics,  a  competency score
        ranging from 0 to 100 was derived based on performance at the clinic.
        Suppose  further  that  the  population mean competency score for all
        FNP's was 80 and the population variance was 100.  For the sample of
        36 FNP's, what is the probability that the mean competency score will
        be between 75 and 80?

        a.  .4987   b.  .1915   c.  .5013   d.  .2287   e.  .5115

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161-2

    Q:  Suppose  that  for  a sample of 36 Family Nurse Practitioners (FNP's)
        from several  similar  type  hospital  clinics,  a  competency  score
        ranging from 0 to 100 was derived based on performance at the clinic.
        Suppose further that the  population  mean  competency score  for  all
        FNP's was 80 and the population variance was 100.

        The middle 99% points for the distribution of the sample mean
        competency score described above is (rounded to two decimal places):

        a.  (54.24, 105.76)   b.  (76.12, 83.88)   c.  (56.74, 103.26)
        d.  (75.71, 84.29)    e.  None of these

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162-1

    Q:  Suppose  that  the  weight  (W) of male patients registered at a diet
        clinic has the normal distribution with mean 190  and  variance  100.
        For  a  sample  of  size  25  from the clinic, which of the following
        statements is equivalent to the statement:

                                           P(WBAR > 195)

        where WBAR denotes the mean weight of the sample?

        a.  P(Z < -2.5)        d.  P(Z > 2.5)
        b.  P(Z < 1)           e.  P(Z < 2.5)
        c.  P(Z > -1)

        (Note:  Z is a standard normal random variable.)

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163-1

    Q:  Suppose  that  the  weight  (W) of male patients registered at a diet
        clinic has the normal distribution with mean 190  and  variance  100.
        For  a  sample  of  size  25 from the clinic, what are the middle 90%
        points of the distribution of WBAR where WBAR denotes the mean weight
        of the sample?

        a.  (186.08, 193.92)      d.  (186.71, 193.29)
        b.  (173.55, 206.45)      e.  None of these
        c.  (170.40, 209.6)

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175-1

    Q:  A random sample of size 100 is selected from a population with MU=0
        and SIGMA=20. Find (approximately) P[XBAR>2].

               a.  .0228                         b.  .4207
               c.  .3085                         d.  .1587
               e.  None of the above.

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193-1

    Q:  Suppose the distribution  of  the students' personal libraries at this
        university can be approximated by a normal distribution with mean equal
        to 18.7 and variance equal to 1.08.  If a random sample of  27 students
        is polled, what is the probability that the average size of  their lib-
        raries will be at least 19.3 books?

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201-1

    Q:  A company manufactures cylinders that have a mean 2 inches in
        diameter.  The standard deviation of the diameters of the cylinders
        is .10 inches.  The diameters of a sample of 4 cylinders are
        measured every hour.  The sample mean is used to decide
        whether or not the manufacturing process is operating satisfactorily.
        The following decision rule is applied:  If the mean diameter
        for the sample of 4 cylinders is equal to 2.15 inches or more,
        or equal to 1.85 inches or less, stop the process.  If the
        mean diameter is more than 1.85 inches and less then 2.15
        inches, leave the process alone.
        a.  What is the probability of stopping the process if the
            process average MU, remains at 2.00 inches?
        b.  What is the probability of stopping the process if the
            process mean were to shift to MU = 2.10 inches?
        c.  What is the probability of leaving the process alone if
            the process mean were to shift to MU = 2.15 inches?
            To MU = 2.30 inches?

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215-2

    Q:  Suppose that height of English setter dogs is normally distributed
        with a mean of 30 inches and a known variance of 9.  What is the
        probability that the average (mean) height of 9 randomly selected
        setters will be greater than 31 inches?

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732-1

    Q:  Which of the following describes a "statistical inference"?

        a.  A true statement about a population made by measuring some sample
            of that population.
        b.  A conjecture about a population made by measuring some sample of
            that population.
        c.  A true statement about a sample made by measuring some population.
        d.  A conjecture about a sample made by measuring some population.
        e.  A true statement about a sample made by measuring the entire
            population.

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765-2

    Q:  Define the following term and give an example of its use.
        Your example should not be one given in class or in a handout.

        Standard error of a mean

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777-1

    Q:  Define the following term and give an example of its use.
        Your example should not be one given in class or in a handout.

        MU

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1342-1

    Q:  A pocket calculator enthusiast claims that 80% of all incoming freshmen
        own a pocket calculator.  To investigate this claim a random sample of
        200 incoming freshmen have been interviewed.  Of these 120 own
        calculators.

        a.  Set 90% confidence limits for P1, the true proportion having
            calculators.  (Use ALPHA = .10.)
        b.  Test the enthusiast's claim.

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1394-1

    Q:  A random sample of 64 cars passing a check point on a certain highway
        showed a mean speed of 60.0 mph.  The standard deviation of speeds is
        known to be 15.0 mph.

        a.  Give a point estimate of the population mean speed on this highway.

        b.  Establish a 90% confidence interval for the mean speed of cars on
            this highway.  Interpret the meaning of this interval.

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1398-1

    Q:  A sample of 3600 cases is drawn at random from an infinitely large
        population.  The standard deviation of the population is 10.  The
        standard error of the mean is

        a.  2/15.
        b.  1/6.
        c.  4/5.
        d.  10.
        e.  none of the above.

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1399-2

    Q:  True or False?  If false, correct it.

        As the sample size (n) increases, the mean of a random sample is less
        likely to be near the mean of the population.

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1399-3

    Q:  True or False?  If false, correct it.

        In general the sampling distribution of the mean and the distribution
        of the parent population have exactly the same shape.

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1400-2

    Q:  Suppose we have sampled (with replacement) from a finite population.
        Suppose that all possible distinct samples of size n > 30 have been
        selected and that the mean and variance have been computed for each
        sample.

        Suppose here, that Variance = SUM((X - XBAR)**2/(n - 1)).

        True or False?  If False, correct it.

        The distribution of XBAR will be symmetric.

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1401-1

    Q:  Suppose we have sampled with replacement from a finite
        population.  Suppose that all possible distinct samples
        of size n (where n > 1) have been selected and that the
        mean has been computed for each sample.

        True or false?  If false, correct it.

        The shape of the distribution of XBAR will be the same
        as the shape of the population.

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1418-1

    Q:  A sample of twenty-five observations is taken from a normal popu-
        lation with variance 9.  90% confidence limits corresponding to a
        sample mean of 30 are best represented by:

        (a)  30 +/- 9.00
        (b)  30 +/- .79
        (c)  30 +/- 1.03
        (d)  30 +/- .47
        (e)  30 +/- .99

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1418-2

    Q:  Suppose that a sample of size 16 from a normal distribution with mean
        MU yielded a sample mean of 3.2 and a standard deviation of 4.  For a
        98% confidence level, the lower confidence limit for a two sided in-
        terval for MU is:

        (1)  0.6          (4)  2.555
        (2)  0.62         (5)  5.8
        (3)  2.5

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1419-1

    Q:  To find confidence intervals for the mean of a normal distribution, the
        t distribution is usually used instead of the standard normal distribu-
        tion because:

        (1)  the mean of the population is not known
        (2)  the t distribution is more efficient
        (3)  the variance of the population is usually not known
        (4)  the standard error of the estimate is S/SQRT(n)
        (5)  the sample mean is known.

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1420-2

    Q:  Out of 50 children drawn at random from a large population of
        school children, all but 10 showed need of dental treatment.
        Based on normal approximation, a 90% confidence interval for
        the true percentage of children in that population who need
        dental treatment is:

        (a)  (10.7%, 29.3%)        (d)  (65.4%, 94.6%)
        (b)  (77.1%, 82.9%)        (e)  None of these.
        (c)  (70.7%, 89.3%)

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1421-1

    Q:  In repeated constructions of 95% confidence intervals for a
        population mean, MU, which of the following is most precise:

             a.  MU falls in the interval approximately 95 times out of a
                 100.
             b.  the interval brackets the unknown MU approximately 95 times
                 out of a 100.
             c.  95 out of a 100 populations will have their means in the
                 interval.
             d.  XBAR falls in the interval approximately 95 times out of
                 a 100.
             e.  The interval brackets XBAR approximately 95 times out of
                 a 100.

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1421-2

    Q:  Suppose in a random sample of 9 men, the mean height is found  to  be
        70  inches,  and  suppose  it  is  known that the population standard
        deviation is 3 inches. An approximate 95% confidence interval for the
        population mean height is:

             a.  64 to 76 inches             d.  69 to 71 inches
             b.  67 to 73 inches             e.  none of these
             c.  68 to 72 inches

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1425-3

    Q:  True or False?  If False, correct it.

        Other things being equal, the larger the confidence coefficient (i.e.
        1 - ALPHA), the smaller the confidence interval.

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1426-1

    Q:  True or False?  If False, correct it.

        An investigation reveals that a confidence interval  with  confidence
        coefficient  .95  for the mean extends from 11.2 to 17.5.  This means
        that in about 95 percent of all samples drawn by the same method, the
        sample means will fall between 11.2 and 17.5.

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1428-1

    Q:  Suppose we have a population of percentages of fat in 1 pound packages
        of hamburger.  Suppose these percentages are normally distributed with
        mean 28 and standard deviation 4.  The probability that the mean per-
        centage of a sample of 16 packages is between 26.5 and 29.5 ounces is
        closest to:

        a.  .433
        b.  .134
        c.  .866
        d.  .933
        e.  .067

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1429-1

    Q:  The mean of a sample of 100 items, drawn from an infinite population
        with variance 400, is XBAR = 5.  Construct a 99% confidence interval
        for MU, the mean of the population.

        a.  -.05 to 9.25        b.  2 to 7        c.  -0.30 to 10.20
        d.  -0.5 to 11.2        e.  -0.15 to 10.15

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1429-2

    Q:  A sample of size 5 from a normal population consists of the numbers
        1, 2, 3, 4, 5.  Construct a 95% symmetric confidence interval for
        the mean of the population.

        a.  2.00 - 4.00   b.  1.04 - 4.96   c.  0.00 - 6.00   d.  1.52 - 4.48
        e.  1.85 - 4.15   f.  1.90 - 4.10   g.  0.50 - 5.50   h.  0.95 - 5.05

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1430-2

    Q:  In a survey study on the incidence of depression in a population
        of psychiatric hospital administrators, scores on a depression
        measure were obtained from 86 respondents.  The observed mean
        score was 62, with a standard deviation of 16.  What kind of
        table whould you use in constructing a 99% confidence interval
        for the mean depression score?

        a.  Chi square
        b.  Kendall's tau
        c.  binomial probabilities
        d.  student's t
        e.  other (specify):

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1431-2

    Q:  A sample of twenty-five observations is taken from a normal population
        with variance 4.  Determine 95% confidence limits corresponding to a
        sample mean of 20.

        (a)  20 +/- .4             (c)  20 +/- .32
        (b)  20 +/- 8              (d)  20 +/- .8

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1433-1

    Q:  A  sample  of  size 26 is taken from a normal population.  Then a 95%
        confidence interval is set up with XBAR = 30 and s = 20.   The  value
        you  would find in the table to complete the information necessary to
        obtain the interval would be:

        a.  2.064
        b.  2.060
        c.  1.711
        d.  1.708
        e.  1.960

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1433-2

    Q:  Nine men with a genetic condition that causes obesity entered a weight
        reduction program.  After four months the statistics of weight loss were
        XBAR = 11.2, S = 9.0.   A 95%  confidence  interval for the mean of the
        population of which this is a sample (assuming normality and randomness)
        is:

        a.  11.2 +/- 1.96(3)
        b.  11.2 +/- 1.86(3)
        c.  11.2 +/- 2.262(3)
        d.  11.2 +/- 2.306(3)
        e.  11.2 +/- 2.306(9)/SQRT(8)

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1434-1

    Q:  A political pollster is hired to estimate the proportion of voters in
        favor of Senator Claghorn.  He takes a sample of 400 and finds 56% of
        the voters favor the Senator.  A 95% confidence interval for the true
        population proportion favoring Senator Claghorn is:

        (a)  .56 +/- 1.96SQRT((.56)(.44))
        (b)  .44 +/- 1.96SQRT((.56)(.44)/400)
        (c)  .56 +/- 1.96SQRT((.44)(.56)/400)
        (d)  .56 +/- 1.64SQRT((.56)(.44)/400)
        (e)  none of the above.

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1434-2

    Q:  In finding confidence intervals for the mean of a  normal  population
        by  using  a  t-statistic, student A uses a confidence coefficient of
        0.95  while  student  B  uses  0.99.   Which  one  of  the  following
        statements is true about the length of the confidence intervals found
        by A and B?  (The length of the  confidence  interval  is  the  upper
        limit minus the lower limit).

        (1)  B's interval will always be smaller than A's interval
        (2)  B's interval will usually be smaller than A's interval
        (3)  B's interval will always be larger than A's interval
        (4)  B's interval will usually be larger than A's interval
        (5)  There is no way of knowing which of the intervals will be larger.

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1435-1

    Q:  For a certain normally distributed population, the value of the standard
        deviation is known, but the value of the mean is unknown.  What will
        be the effects of changes in sample size and in the confidence
        coefficient on the length of the confidence interval estimate of the
        population mean?

        a.  Increasing sample size increases the length, given a fixed
            coefficient.
        b.  Increasing the confidence coefficient decreases the length
            given a fixed sample size.
        c.  Increasing sample size decreases the length, given a fixed
            coefficient.
        d.  None of the above

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1435-2

    Q:  A random sample of 625 boxes taken from the output of a box making
        machine was inspected for flaws.  It was found that 500 of the boxes
        were free from flaws.  To three decimals, what is the upper limit of
        the 0.99 confidence interval estimate of the proportion of
        acceptable boxes being produced?

        a.  .8 + 1.96*SQRT(.16/625)
        b.  .8 + 2.576*(.16/625)
        c.  .8 + 1.96*(.16/625)
        d.  .8 + 2.576*SQRT(.16/625)

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1438-1

    Q:  The size of a confidence interval for a mean is affected by changes in
        which of the following?

        a.  The size of the sample
        b.  The confidence coefficient
        c.  The variance of the sample
        d.  b and c only
        e.  a, b, and c

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1439-1

    Q:  The strength of elevator cables are to be measured.  Let
        X = strength of a cable, and assume X is normal with mean
        MU and variance SIGMA**2, both unknown.  A sample of 89
        straps is taken, with results XBAR = 31 and S**2 = 89.

        The 93% confidence interval for MU is closest to:

        (a)  31 +/- (2.11)*SQRT(89)            (b)  31 +/- (1.60)*(1.0)
        (c)  31 +/- (1/SQRT(89))               (d)  31 +/- 1.81
        (e)  31 +/- (1.80)*(89/SQRT(89))

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1440-1

    Q:  Consider the following table which gives the deodorants preferred
        by samples of lacrosse and soccer players.

                            Brand X    Brand Y
                            ------------------
        lacrosse players   |  20    |    30
        --------------------------------------
        soccer players     |  10    |    40
        --------------------------------------

        1.  Now let PI(1) be the proportion of all lacrosse players who
            prefer Brand X.  An 80% confidence interval for PI(1) would
            use a table value closest to:

            A.  1.28      B.  1.10      C.  1.50      D.  1.70      E.  1.90


        2.  An 80% confidence interval for PI(1) would then be closest to:

            A.  (1/5) +/- (1.28)(SQRT((4/25)(1/100)))
            B.  (2/5) +/- (1.28)(SQRT((6/25)(1/50)))
            C.  (2/3) +/- (1.1)(SQRT((2/9)(1/30)))
            D.  (1/5) +/- (1.5)(SQRT((4/25)(1/50)))
            E.  (2/5) +/- (1.7)(SQRT((6/25)(1/100)))

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1441-2

    Q:  A poll of 100 students revealed that 50 were in favor of returning
        to the semester system.  If p is the proportion of all U.C.D. stu-
        dents in favor of semesters, then a 99% confidence interval for p
        is given by

        (a)  .5 +/- .098            (d)  .5 +/- .135
        (b)  .5 +/- .112            (e)  .5 +/- .141
        (c)  .5 +/- .129

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1443-1

    Q:  A sample of size 36 is taken from a population with unknown mean
        MU and standard deviation SIGMA = 3.

        What is the probability that XBAR differs from MU by more than 1?

        (a)  .3413    (b)  .9544    (c)  .0228    (d)  .4772    (e)  .0456

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1443-2

    Q:  A sample of size 36 is taken from a population with unknown mean
        MU and standard deviation SIGMA = 3.

        A 95% confidence interval for MU is:

        (a)  XBAR +/- 1.96(1/2)      (d)  MU +/- 1.64(XBAR)
        (b)  XBAR +/- 1.96           (e)  MU +/- 1.96(SIGMA)
        (c)  XBAR +/- 1.64(1/4)

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1445-1

    Q:  The mean weight of a random sample of 16 dogs on the quad is 58 lbs.
        with a sample standard deviation of 8 lbs.  A 95% confidence interval
        for the mean weight of dogs on the quad is:

        a)  58 +/- (1.96*2)    b)  58 +/- (2.13*2)    c)  58 +/- (1.96*4)
        d)  58 +/- (1.75*2)    e)  58 +/- (2.33*4)

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1446-1

    Q:  A sample of size 400 is taken from a large population, yielding

             XBAR = 31 and SUM(i = 1, 400)((X(i) - 31)**2) = 1596

        The 95% confidence interval for the mean is:

        (a)  [30.88, 31.12]          (d)  [30.84, 31.16]
        (b)  [30.80, 31.19]          (e)  [30.76, 31.24]
        (c)  [30.75, 31.25]

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1447-1

    Q:  A sample of size 16 is taken from a normally distributed population,
        yielding:

             XBAR = 20 and SUM(i = 1, 16)((X(i) - 20)**2) = 960

        The 95% confidence interval for the mean of this population is:

        (a)  [15.8, 24.3]          (d)  [17.1, 22.9]
        (b)  [15.6, 24.4]          (e)  [16.4, 23.6]
        (c)  [16.2, 23.8]

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1448-2

    Q:  Eighty percent of a sample of 400 people support candidate B.
        The 95% confidence interval for the proportion of people who
        support B is nearest:

        A. [.768, .832]  B. [.761, .839]
        C. [.775, .825]  D. [.790, .810]

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1449-1

    Q:  If the observations:  8, 11, 9, 17, 12, 15 are a sample of size 6
        from a normal population with a mean = MU and a variance = 24, then
        a 95% confidence interval for MU has confidence limits

        a.  12   +/- 3.92
        b.  11.5 +/- 3.92
        c.  12   +/- 5.142
        d.  11.5 +/- 5.142
        e.  none of these

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1454-1

    Q:  Suppose for a random sample of 16 hospitals in North Carolina, it was
        found  that  the  mean cost (i.e. XBAR) of hospital care for recovery
        from acute myocardial  infarction  (MI)  was  $15000  with  a  sample
        standard  deviation of $1200.  Then a 99% confidence interval for the
        mean cost of recovery for all hospitals in North Carolina would  have
        the following limits (rounded to nearest whole numbers):

        a.  (14116, 15884)  b.  (14123,15876)  c.  (14225, 15775)
        d.  (14227, 15773)  e.  none of these

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1455-1

    Q:  The  limits  of  a  95%  confidence  interval for the mean MU of some
        population, whose variance SIGMA**2 is assumed known,  are  found  by
        adding  to and subtracting from the sample mean a certain multiple of
        the standard error. For a sample size of 36, the multiplier described
        in the previous sentence is:

              a.  1.645
              b.  1.6896
              c.  2.0301
              d.  1.96
              e.  None of these

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1455-2

    Q:  Suppose that a sample of sixteen heights yielded  a  sample  mean  of
        75.1  inches and a sample variance of 9.0.  A 90% confidence interval
        (rounded to two decimal places) for  the  true  mean  height  of  the
        population has which of the following limits:

        a.  (73.79, 76.41)         d.  (71.16, 79.04)
        b.  (73.87, 76.33)         e.  None of these
        c.  (74.09, 76.11)

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1456-1

    Q:  Given that 99% confidence limits for MU are 42 and 58, which of
        of the following could be 95% confidence limits?

             a.  43 and 57
             b.  41 and 59
             c.  41 and 57

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1457-1

    Q:  Suppose a psychologist wishes to know the mean IQ of students in a
        given high school.  25 students were sampled and the sample mean was
        103.  The sample standard deviation was 12.  Which of the following
        is a 90% confidence interval for the mean IQ for all students?

        a.  98.9 - 107.1
        b.  97.6 - 108.3
        c.  98.0 - 108.0
        d.  94.5 - 111.5
        e.  none of these

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1459-1

    Q:  In a sample of size 400 we found XBAR=10 and S**2=100.  Which of the
        following is an approximate 95% confidence interval for MU?

               a.  (.2, 19.8)                  b.  (-9.8, 9.8)
               c.  (8.04, 11.96)               d.  (9.02, 10.98)
               e.  (-.98, .98)

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1460-2

    Q:  A sample of size 25 was taken from a normal population whose standard
        deviation SIGMA is believed to be 20.  The sample data produced a mean
        XBAR of 57.5  Find the 0.95 confidence interval estimate for the popu-
        lation mean MU.

        a)  18.3 to 96.7
        b)  49.66 to 65.34
        c)  50.9 to 64.1
        d)  53.5 to 61.5
        e)  55.93 to 59.07

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1461-2

    Q:  A parameter is fixed (non-fluctuating), a confidence interval is

        a.  also fixed.
        b.  equal to + or - one standard deviation.
        c.  variable from sample to sample.
        d.  either fixed or variable depending on sample size.
        e.  None of the above.

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1463-1

    Q:  We know the mean MU of a population.  Suppose 1,000 samples of size n
        are  drawn  from  this  population.  For each sample we compute a 90%
        confidence interval  for  MU.   We  would  expect  the  mean  of  the
        population  would  NOT  be contained within approximately how many of
        these intervals?

        a.  0
        b.  10
        c.  100
        d.  900
        e.  Impossible to tell.

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1463-2

    Q:  The  sample  mean  of  225  scores on a math test is 75.  Find the 95
        percent confidence interval for the mean of the population,  assuming
        that SIGMA(X) = 7.

        a.  72.5 - 77.5
        b.  74.1 - 75.9
        c.  73.2 - 76.8
        d.  73.8 - 76.2
        e.  None of the above.

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1464-1

    Q:  In a 95% confidence interval for the mean,

        a.  if many samples are drawn, YBAR will fall within the confidence
            interval 95% of the time.

        b.  the probability of YBAR falling within a confidence interval
            computed from one sample is .95.

        c.  the probability of MU falling within a confidence interval compu-
            ted on one sample is .95.

        d.  if many samples are drawn, the computed confidence intervals will
            contain MU 95% of the time.

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1469-2

    Q:  The following values of "Y" represent a random sample from
        some population -- 115, 110, 112, 113, 111, 107, 110, 106, 112.

        (a)  Construct a 95% confidence interval for the population mean.

        (b)  Is 113 an acceptable value for MU at a 95% confidence level?

        (c)  Construct a 99% confidence interval for the population mean.

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1470-1

    Q:  The Chamber of Commerce in Miami Beach wishes to  estimate  the  mean
        expenditures  per tourist per visit in that city.  A random sample of
        one-hundred tourists has been selected for investigation, and it  has
        been  found  that the mean expenditures of the sample was $800.00 per
        tourist per visit.  It  is  known  that  the  standard  deviation  of
        expenditures for all tourists is $120.00.

        Construct a 95 percent confidence interval for the true mean expendi-
        ture per tourist.  Interpret your result.

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1471-1

    Q:  It is wanted to estimate the proportion of people in a population who
        have English ancestors.  Make a 95% interval estimate assuming that a
        random sample of 100 people has 21 of English descent in it.

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1471-2

    Q:  A plot of land is surveyed by 25 student surveyors with the
        following results:

        YBAR = 7.25 acres     [SUM(i=1,25)(Y(i)-YBAR)**2]/[25] = .01660

        Set up a 90% confidence interval for the area of the plot.

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1472-1

    Q:  John has done an experiment on gallons of water per second that flow in
        a sewer main in the city.  He makes 16 measurements  of  this  flow and
        finds that their average is 100 and their variance is 9.   Find  a  98%
        confidence interval for the mean flow.

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1472-2

    Q:  A random sample of 500 accounts receivable is selected from the 4,032
        accounts that a firm has, and the sample mean is found to be
        $242.30.  The sample standard deviation is computed to be $3.20.
        Set up a .99 confidence interval estimate of the population mean.
How do you interpret the meaning of this interval?

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1473-1

    Q:  A survey on consumer finances reports that 33 per cent of a sample
        of 2,600 spending units expected good times during the next 12 months.
        Assume that a simple random sample was used in the study.  Set up a
        .95 confidence interval estimate of the population proportion of
        spending units expecting good times.

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1473-3

    Q:  Compute a confidence interval for the mean, given XBAR = 24, n = 25,
        and SIGMA(XBAR) = 2.  (Use a confidence level of 90%.)

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1474-2

    Q:  Out of the random sample of 360 full time students on the River
        Campus, 225 were male and 135 were females.  Obtain a 99% con-
        fidence interval for the proportion of males among the full time
        student body.

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1478-1

    Q:  A new diet for the reduction of cholesterol is introduced.  In order to
        test this procedure, nine patients on this new diet had observed choles-
        terol levels of:

             patient        cholesterol        patient        cholesterol

                1               240               6               220
                2               290               7               190
                3               220               8               230
                4               250               9               200
                5               260

        XBAR = 210    S**2 = SUM(([X(i) - 210]**2)/8) = 950    S = 30.9

        Assume cholesterol levels are normally distributed.

        Construct a 99% confidence interval for MU with XBAR = 210.

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1478-2

    Q:  In a random sample of 200 television viewers in a certain area, 95
        had seen a certain controversial program.  Construct a 0.99 confi-
        dence interval for the actual percentage of television viewers in
        that area who saw the program.

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1480-1

    Q:  The results of an imaginary random sample of 30 registered
        voters in Portsmouth indicate that 60% of the voters favor
        Henry Kissinger for president.
        Set 95% confidence limits for this sample result.

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1481-1

    Q:  A sample of size 9 is used to estimate the mean arm reach of
        fighters in a certain tournament.  Arm reach (inches) for all fighters
        in the tournament is known to be normally distributed with a variance
        4 inches squared.  If the sample mean is 35 inches, establish a 95%
        confidence interval for the true mean arm reach of tournament fighters.

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1481-2

    Q:  A random sample of 100 families in a large city showed 20 with annual
        earnings that placed them in a "poverty" category.  Estimate the pro-
        portion of "poverty" families in the  city  using  a  90%  confidence
        interval.

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1482-1

    Q:  A  light bulb manufacturer desires to determine the mean life time of
        the light bulbs in the most recent batch produced.  Available  are  25
        light bulbs to be tested. For these bulbs, the average lifetime is 72
        hours (i.e. XBAR = 72). From previous experience  it  is  known  that
        each  batch  produced  bulbs  according to a normal distribution with
        standard deviation of 15 hours.

             a.  Construct a 99% confidence interval for the mean MU of the
                 batch.
             b.  Interpret the statistical meaning of this confidence interval.

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1483-1

    Q:  a)  Find a 95% confidence interval for MU from a sample of 9 where
            XBAR = 12 and s = 1, and interpret the interval.

        b)  Would your interval have been narrower if SIGMA would have been
            known to be 1?

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1484-1

    Q:  Taking a random sample from its very extensive files, a water company
        finds that the amount owed in 16 delinquent accounts have  a mean  of
        $16.35 and a standard deviation of $4.56.

        a.  Use these values to construct a .98 confidence interval for the
            average amount owed on all delinquent accounts.

        b.  If Mr. Blackwater, the company president, claims the delinquent
            accounts have a population mean of $19.01, how could you quickly
            respond to him based on part a above (also after explaining that
            you were using a 2% ALPHA level)?

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1485-1

    Q:  You are interested in the amount of discretionary funds available to
        male patrons of a disco.  A random sample of three patrons indicates
        that their bills for the evening were [$12.50, $10.75, $14.28].  Esti-
        mate with 90% confidence the mean amount spent by patrons at this disco.

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1486-1

    Q:  A researcher assigns each of his interviewers a list of 7 families,
        drawn randomly from a region, to be interviewed.  Each interviewer
        is instructed to administer a successful parenting scale SPS to each
        parent in his sample.  The SPS scores, X(i), are defined as ranging
        from 0 (no parenting skills deemed successful) to 100 (successful
        parenting skills consistently and skillfully applied).  The first
        interviewer returned with the following scores for his seven female
        respondents (i.e., mothers).  Based on this sample, estimate the
        mean SPS for females in Region I with 90% confidence:

            [X(i)] = [75, 62, 48, 50, 55, 62, 69]
                 S = 9.856

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1487-1

    Q:  A sociologist conducted a study of assertion by having one of her top
        students, after appropriate training, note the number of assertive acts
        performed in a day by each of 10 randomly selected coeds, producing the
        following sample of data, in acts per day:  [5,3,10,6,4,9,5,5,7,5].
        Estimate with 90% confidence the mean number of assertive acts per day
        performed by the coeds.
        SUM(X(i)) = 59
        XBAR = 5.9
        S    = 2.18

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1488-1

    Q:  A sample of six male delinquents, aged 16, indicates that they have the
        following number of delinquent acts recorded on their police record:
        [5, 3, 3, 4, 3, 5].  Estimate, with 90% confidence, the mean number of
        such acts recorded on the records of the universe of subjects (i.e., 16
        year-old delinquent males in Gotham City).
        SUM(X(i)) = 23
          S = 0.983

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1491-2

    Q:  In a random sample of 100 flashlight batteries, the average useful life
        was 22 hours and the sample standard deviation was 5 hours.

        (a)  Estimate MU, the average life of all batteries of the type
             sampled.

        (b)  Determine an approximate 99% confidence interval for MU.

        (c)  Explain why the confidence interval in (b) is approximate.

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1495-1

    Q:  In a recent survey of Democrats in the Congress, 30% favored Senator
        Kennedy of Massachusetts as the party's top presidential candidate
        at this time, while the remaining 70% was divided up among numerous
        other potential candidates.  The results were reported accurate to
        within +/- 10% with 95% confidence.

        Make a confidence interval statement concerning the proportion of
        Democrats in the Congress who preferred Senator Kennedy at the time
        of the survey.

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1499-3

    Q:  A TV network reports that their survey based on 200 randomly
        selected voters indicates:
              .60 favor candidate A
              .40 favor candidate B
              Margin of Error (95%) for the difference = .14.

        Would you forecast a win for candidate A? Why?

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1500-1

    Q:  Suppose that you are interested in an election and the latest
        poll indicates:
        Your candidate:  36% of the vote
        Leading opponent:  40% of the vote
        Suppose also that the poll indicates no uncommitted voters.
        Which of the following confidence limits would appear most favorable
        to your candidate?  Why?
        a.  difference = 4% +/- 1%, 1 - ALPHA = .99
        b.  difference = 4% +/- 10%, 1 - ALPHA = .99
        c.  difference = 4% +/- 10%, 1 - ALPHA = .80

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1501-1

    Q:  A brewery producing beer has a number of specifications for quality.
        Among these standards is the requirement that the degree of hop like
        flavor should be a value of 8.0.

        The production of the brewery consists of a large number of batches.
        It's possible for differences to arise  between batches,  so we will
        regard each batch as a different population.   We will  consider the
        hoppiness of each batch as a normally distributed variable with mean
        and variance unknown.

        From each batch you  can remove 6 samples for hoppiness.   For  each
        batch you are to:

            a.  set confidence limits for the batch (population) mean, MU;
            b.  determine if these limits are consistent with the require-
                ment that hoppiness is a value of 8.0.

        1.  Outline the procedure to be followed in setting confidence limits
            where the probability of the interval calculated including MU is:

                a.  90%
                b.  99%

        2.  Apply the procedure outlined to this set of sample values:  13,
            11, 9, 14, 8, 11.  Is this sample data consistent with the speci-
            fication of hoppiness = 8.0 when the probability level used is:

                a.  90%
                b.  99%

        3.  Do these results suggest any weakness in the procedure used?  If
            so, what?

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1509-1

    Q:  True or false?  If false, explain why.

        If (5,8) is a 95% confidence interval for a MU, then the probability
        that MU lies in the interval is .95.

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1509-2

    Q:  True or false?  If false, correct it.

        A confidence interval for MU will generally be smaller if a confidence
        coefficient equals .90 than if this coefficient equals .95.

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1510-1

    Q:  True or False?  Explain.

        As the size of a confidence coefficient (one minus ALPHA) is
        increased, the width of the corresponding confidence interval
        will tend to increase.

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1510-2

    Q:  True or False?  If False, correct it.

        The sample mean lies at the center of the confidence
        interval for MU.

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1511-2

    Q:  True or False?  If False, correct it.

        A 95% confidence interval is twice as long as a 90% confidence
        interval.

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1513-3

    Q:  True or false? If false, explain why.

             With any sample size a high level of confidence in an interval
             estimate may be obtained.

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1522-2

    Q:  We are interested in the proportion (p) of voters in a  community
        that would  favor  a  school  issue to be settled by a referendum.  A
        random sample of size 225 from the community indicated that 65% were in
        favor. What would be the midpoint of an interval estimate of p?

        a.   .03
        b.  1.96
        c.  p
        d.  Insufficient information to obtain correct result.
        e.  Sufficient information but correct result is not given.

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1523-1

    Q:  In  interval  estimation  of  a  population  mean,  the  width of the
        interval can be narrowed by

        a.  increasing n.
        b.  lessening the confidence level (e.g., .99 to .90).
        c.  reducing the magnitude of SIGMA(X).
        d.  all of the above.
        e.  none of the above.

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1547-1

    Q:  True or False?  If false, correct it.

        The confidence coefficient is the probability that an unknown parameter
        has a certain value.

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1547-3

    Q:  True or False?  If False, correct it.

        If confidence intervals are computed from repeated samples of the same
        size, in the long run they will cover the unknown parameter in the same
        percentage of cases as the confidence coefficient.

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1548-2

    Q:  Define the following term and give an example of its use.
        Your example should not be one given in class or in a handout.

        MARGIN OF ERROR

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1551-2

    Q:  The purpose of using a sample and calculating a mean is to

           a.  find the average for the sample
           b.  determine the dispersion of the sample
           c.  estimate the mean of the population
           d.  estimate sample size

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1566-1

    Q:  The distribution of means of all possible samples of the same size (n)
        drawn from a population will approximate the normal curve if
            a.  the n is large enough
            b.  the population is large
            c.  the population is symmetrical
            d.  the mean of each sample equals the mean of the population
            e.  none of the above is correct.

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1566-3

    Q:  If we think of how all possible XBAR's are distributed, the mean and
        variance of those observations are

        a.  MU(X) and SIGMA(X)
        b.  zero and SIGMA(X)
        c.  MU(X) and ((SIGMA(X))**2)/SQRT(n)
        d.  MU(X) and ((SIGMA(X))**2)/n
        e.  none of these.

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1568-1

    Q:  The Central Limit Theorem tells us that:

        a)  the shape of all sampling distributions of sample means are nor-
            mally distributed.
        b)  the mean of the distribution of sample means is less than the mean
            of the parent population.
        c)  the standard deviation of the distribution of sample means is the
            same as the standard deviation of the population.
        d)  all of the above are true.
        e)  none of the above are true.

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1568-2

    Q:  As the size of the sample, n, increases towards the size of the popu-
        lation, the value of the standard error of the mean,  SIGMA(XBAR),
        approaches:

        a)  zero
        b)  one
        c)  SIGMA
        d)  SIGMA/SQRT(n)
        e)  None of the above are correct.

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1569-1

    Q:  The Central Limit Theorem

        a.  says that YBAR approaches MU(Y) as sample size increases.
        b.  says that s(Y) approaches SIGMA(Y) as sample size increases.
        c.  says that both a and b will occur.
        d.  refers to a matter other than those stated above.

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1570-1

    Q:  The sampling distribution of means of random samples of size n  drawn
        from some population will approach normality

        a.  only if the parent population is normally distributed and if n
            is large.

        b.  only if the parent population is normally distributed regardless
            of the value of n.

        c.  if n is large regardless of the shape of the parent population
            distribution.

        d.  regardless of the value of n and regardless of the shape of the
            parent population distribution.

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1572-3

    Q:  The  mean  of  a random  sample of size n = 36  is used to  estimate the
        sample mean of a very  large  population  of  means  which  has standard
        deviation SIGMA = 25 hours.  Find the probability  that the sample  mean
        will be "off" either  way  by  less  than  10  hours  using the  Central
        Limit Theorem.

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1576-1

    Q:  According to the Central Limit Theorem, how does a sampling distribu-
        tion of means change as sample size increases?  Of what significance
        is this change (are  these  changes) in telling you how accurately a
        sample mean will estimate a population mean?

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1577-1

    Q:  The scientific rationale for statistical inferences about population
        means relies on a set of three propositions which we have called the
        Central Limit Theorem.  These propositions give us information about,
        respectively, the mean, standard deviation, and shape of a sampling
        distribution of XBAR.

        A.  Define what is meant by the sampling distribution of XBAR for size
            25 samples.

        B.  According to the Central Limit Theorem, what relationship will
            necessarily exist between the mean of this sampling distribution
            and the mean of the population?

        C.  According to the Central Limit Theorem, what relationship will
            necessarily exist between the standard error of the mean
            (SIGMA(XBAR)) and the standard deviation of the population?

        D.  Based on your answer in C, explain how a confidence interval
            estimate of MU will be affected by:

              1)  an increase in the size of the sample selected
              2)  an increase in the variability of the population from
                  which the sample is selected.

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1578-1

    Q:  If X(1), X(2),...X(n) are n(n > 30) independent and identically
        distributed random variables and

                Z = (XBAR - MU(XBAR))/SQRT(VAR(XBAR))

        a.)  What is the approximate distribution of Z?

        b.)  MU(Z) = _________________________.

        c.)  VAR(Z) = _______________________.

        d.)  Why is the central limit theorem of fundamental importance
             to statistics?

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1580-2

    Q:  True or false?  If false, explain why.

        The Central Limit Theorem is of most value when we sample from a
        normal distribution.

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1581-1

    Q:  True or False?  If False, correct it.

        As the sample size increases, the distribution of the sample mean
        approaches a normal distribution.

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1581-2

    Q:  True or False?  If False, correct it.

        The Central Limit Theorem applies to the case of sampling from a
        normal distribution as well as other cases.

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1582-2

    Q:  True or False?  If False, correct it.

        The mean of the distribution of means of all possible random samples
        of the same size, drawn from a severely skewed population, will equal
        the population mean.

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1583-2

    Q:  Determine if the following is true or false and explain why.

        According to the Central Limit Theorem, the shape of the sampling
        distribution of XBAR (given that n = 30) will be normal, whether
        or not the shape of the population is normal.

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1584-2

    Q:  True or False?  If false, explain why.

        The central limit theorem tells us that, if we take a large sample,
        the sample values will follow an approximate normal distribution.

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1585-2

    Q:  True or False?  If False, correct it.

        The sampling distribution of XBAR is approximately normal if and only
        if the population is normally distributed.

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1691-1

    Q:  True or False?  If False, correct it.

        Other things being equal, a low level of confidence is desirable.

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1730-1

    Q:  ________________ is the process of drawing conclusions about population
        characteristics from the facts given by a sample.  It is generalization
        from the specific to the general.

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1791-3

    Q:  True or false?

             A proportion is a special case of a mean when you have a
             dichotomous population.

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1815-1

    Q:  Consider simple random sampling from a normal distribution with mean
        18 and variance 36.  For samples of size 9, the sampling distribution
        for the sample mean has mean and variance equal to:

        a.  2 and 12 respectively
        b.  18 and 4 respectively
        c.  18 and 12 respectively
        d.  2 and 4 respectively
        e.  none of these

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1820-2

    Q:  If the population distribution of scores (X) is normally distributed,
        then the sampling distribution of XBAR will be distributed

        a.  normally only if n is large.
        b.  normally for any given sample size if the sample is randomly
            selected.
        c.  normally if XBAR is large.
        d.  Not enough information is given to determine the characteristics
            of the distribution.
        e.  There is sufficient information but the correct answer is not
            given.

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1857-4

    Q:  Suppose we have sampled (with replacement) from a finite population.
        Suppose that all possible distinct samples of size n (where n > 1)
        have been selected and that the mean and variance have been computed
        for each sample.  (Suppose here, that the variance =
        (SUM((X-XBAR)**2))/(n-1).)

        True or false?  If false, correct it.

        The distribution of XBAR will have a mean equal to MU.

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1858-3

    Q:  True or False?  If False, correct it.

        A larger mean implies a larger standard deviation.

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1859-1

    Q:  True or False?  If False, correct it.

        The means of two hundred  random  samples  each  of  size  4  from  a
        non-normal  population  with  SIGMA**2 = 1 and MU = 0 would have mean
        approximately 0 and standard deviation approximately .5.

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1865-1

    Q:  A population is such that MU = 10, and SIGMA(X)**2 = 9.  A
        simple random sample of size 10 is taken and XBAR is computed.
        The variance of the sample mean, SIGMA(XBAR)**2, is computed
        to be:

        (a)  9        (b)  .9        (c)  .6        (d)  .36

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1869-1

    Q:  You are the parent of two children that have been given an IQ
        test that purports to be a sampling of the intellect.  One child
        receives a score of 99 and the other receives 101.  You know,
        of course, that the IQ is based on 100 as average or 'normal'.
        Does this imply that one is "above average" and the other is "below
        average"?  Explain.

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1869-2

    Q:  Give an example illustrating that the standard error of a sample
        difference ought to be reported along with the sample difference.

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1891-2

    Q:  Explain how SIGMA differs from SIGMA(XBAR).

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1898-1

    Q:  True or False?  If False correct it.

        For a large sample size, the estimated standard error of the mean is
        generally larger than the sample standard deviation obtained from a
        random sample of the same size.

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1898-2

    Q:  True or False?  If False, correct it.

        The standard deviation of the original observations is generally
        larger than the standard deviation of all possible sample means.

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1901-1

    Q:  True or false?  If false, explain why.

           Distributions of population statistics have standard deviations
           while distributions of sample statistics have standard errors.

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1905-2

    Q:  What is the value of the usual (unbiased) estimator of the variance
        of the population from which the random sample composed of the values
        5, 10, and 3 came?

        a.  85.33
        b.  13.00
        c.   8.67
        d.   6.00
        e.   none of the above

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1927-1

    Q:  Let X be a random variable with the following probability
        distribution:

                  P(X = 0) = .4
                  P(X = 1) = .3
                  P(X = 2) = .2
                  P(X = 3) = .1

        A sample of 5 values is taken from a population with the above
        probability distribution.  The sample is:

              X(1) = 0    X(2) = 1    X(3) = 0
              X(4) = 3    X(5) = 2

        VAR(XBAR) = __________.  (sometimes denoted (SIGMA(XBAR))**2).

        Estimated variance of XBAR, ((S(XBAR))**2) = __________.

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1928-1

    Q:  A. If the sample standard deviation S = 3 and n = 3, what is S(XBAR)**2?

        B. If the variance of the mean S(XBAR)**2 = 5 and n = 5, what is S**2?

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1951-3

    Q:  Suppose we have sampled (with replacement) from a finite
        population.  Suppose that all possible distinct samples
        of size n (where n > 1) have been selected and that the
        mean has been computed for each sample.

        True or false?  If false, correct it.

        The distribution of XBAR will have a variance equal to the
        population variance.

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1959-1

    Q:  If the random variable X has a normal distribution with mean  MU  and
        variance  SIGMA**2,  which  one of the following statements gives the
        most accurate information about  the  sampling  distribution  of  the
        sample mean XBAR?

            (1)  XBAR is often close to SIGMA regardless of the sample size.
            (2)  As the sample size decreases, XBAR is closer to MU.
            (3)  As the sample size decreases, the variability of the distri-
                 bution of XBAR about MU increases.
            (4)  The errors (XBAR - MU) are both positive and negative regard-
                 less of the sample size.
            (5)  XBAR becomes less than SIGMA**2 as the sample size increases.

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1960-2

    Q:  In a population with MU = 10 and SIGMA**2 = 64, the standard error
        of XBAR for a sample size of 16 is:

        a.  -1.25
        b.   0.5
        c.   2
        d.   4
        e.   16

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1962-1

    Q:  If random samples of size 25 are drawn from a normal population for
        which MU = 5 and SIGMA = 20, the probability that the mean of a ran-
        dom sample will be less than zero is:

        (1)  .1056          (4)  .3944
        (2)  .2119          (5)  .8944
        (3)  .2881

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1963-2

    Q:  Suppose Y is a continuous random variable (now assumed to be normally
        distributed) with MU = 138 and SIGMA**2 = 126.  If independent samples
        of size 6 are drawn over and over again and YBAR is calculated for
        each sample, then:

        a.  the mean of YBAR is 138 and the standard deviation of YBAR is 21.

        b.  the mean of YBAR is 138 and the standard deviation of YBAR is
            square root of 21.

        c.  the mean of YBAR is 21.

        d.  the variance of YBAR is 21.

        e.  b and d.

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1964-1

    Q:  The standard error of the mean is another name for the standard
        deviation of:

        a.  a sample
        b.  a population
        c.  the sampling distribution of any statistic
        d.  the sampling distribution of the mean
        e.  none of the above

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1964-3

    Q:  SIGMA(XBAR) changes in what way when n, the sample size, increases?

        a.  it increases
        b.  it stays the same
        c.  it decreases
        d.  it is 0
        e.  it is 1

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1966-1

    Q:  S(XBAR) is:

             a.  the standard error of the mean
             b.  the standard deviation of the sampling distribution of XBAR
             c.  an estimate of the standard error of the mean
             d.  the standard deviation of the sampling distribution of X
             e.  none of these

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1966-3

    Q:  The standard deviation for the sampling distribution of sample means,
        SIGMA(XBAR), is customarily called the:

        a)  coefficient of variation for sample means.
        b)  sampling error for means.
        c)  standard deviation for the mean.
        d)  standard error of the mean.
        e)  all of the above are correct.

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1967-1

    Q:  Find the standard error of the mean for a distribution where samples of
        size 36 are taken from a population with a mean MU = 100 and a standard
        deviation SIGMA = 18.

        a)  0.5      b)  2.0      c)  3.0      d)  18.0
        e)  None of the above are correct.

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1968-1

    Q:  A sample of 100 cases is drawn, and  values  of  YBAR  and  s(Y)  are
        computed  on  the sample.  The population mean and standard deviation
        are unknown. How could you estimate the value of the  standard  error
        of the mean, SIGMA(YBAR), in this situation?

        a.  Use [SUM(Y(i)**2)]/[n-1]
        b.  Use [SIGMA(Y)**2]/[SQRT(n-1)]
        c.  Use [s(Y)]/[SQRT(n)]
        d.  None of the above.
        e.  Impossible to obtain an estimate from such data.

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1968-2

    Q:  A "large number" of random samples, of n cases each, is drawn from  a
        certain  population  of scores.  The mean of each sample was computed
        and the "large number" of means thus obtained was  organized  into  a
        frequency  distribution.  The standard deviation of this distribution
        was determined.  The whole process was then repeated  with  the  same
        population  as before, but using samples of size 9n, i.e., 9 times as
        large as before.  How will  the  standard  deviation of  this  second
        distribution of means compare with that of the first distribution?

        a.  It will be one-ninth as large.
        b.  It will be one-third as large.
        c.  Since "large numbers" are involved, it will be the same.
        d.  It will be three times as large.
        e.  It will be nine times as large.

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1969-1

    Q:  The standard error of the mean

        a.  is theoretically determined.
        b.  behaves just like a standard deviation.
        c.  is affected by sample size.
        d.  is characterized by all of the above.

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1969-2

    Q:  Which of the following best describes the standard error of YBAR?

        a.  [SIGMA(Y)**2]/[n]
        b.  [SIGMA(Y)]/[n]
        c.  SQRT([SIGMA(Y)]/[n])
        d.  [SIGMA(Y)]/[SQRT(n)]

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1971-1

    Q:  Investigator X conducted a survey in which he randomly selected and
        weighed 1000 persons in a population of 1 million to estimate mean
        weight.

        Investigator B conducted a similar survey except that he obtained data
        on 500 persons in a population of 10,000.

        Which investigator is apt to obtain a better estimate of the corres-
        ponding population mean?  Why?

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1977-4

    Q:  True or False?  If False, correct it.

        As the sample size increases, the standard error of the mean remains
        unchanged.

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1978-1

    Q:  True or False?  If false, correct it.

        The standard deviation of the random sampling distribution of the mean
        is equal to the population standard deviation.

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1978-3

    Q:  True or False?  If False, correct it.

        If the sample size is greater than one, the sampling distribution of
        the mean will always have a variance which is larger than the variance
        of the associated parent population.

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1979-3

    Q:  True or False?  If False, correct it.

        The standard error of the sample mean increases with the sample
        size.

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1981-1

    Q:  True or False?  If False, correct it.

        The formula SIGMA(XBAR) = SIGMA/SQRT(n) requires the population
        to be normally distributed.

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2074-2

    Q:  The standard error of the median is an index of

        a.  the variability of a sampling distribution of S(y)'s.
        b.  the variability of a sampling distribution of medians.
        c.  the central tendency of a sampling distribution of S(y)'s.
        d.  the central tendency of a sampling distribution of medians.
        e.  none of the above.

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2074-4

    Q:  If the appropriate measure of variability for a distribution is the
        standard error it must be a _________________ distribution.

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2103-1

    Q:  Let MU(X)  and  SIGMA(X)**2  be  the  mean  and  the  variance  of  a
        population.  If MU(XBAR) and SIGMA(XBAR)**2 are the mean and variance
        of the sampling distribution of XBAR, then:

             a.  MU(X) > MU(XBAR) and SIGMA(X)**2 >= SIGMA(XBAR)**2

             b.  MU(X) = MU(XBAR) and SIGMA(X)**2 >= SIGMA(XBAR)**2

             c.  SIGMA(X)**2 >= SIGMA(XBAR)**2; one cannot predict the
                 relationship between MU(X) and MU(XBAR)

             d.  MU(X) < MU(XBAR) and SIGMA(X)**2 <= SIGMA(XBAR)**2

             e.  none of these

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2857-1

    Q:  A sampling distribution:

        a)  is a distribution of all the various sample statistics that can be
            found for one sample.
        b)  of the mean is a distribution of the means taken from all possible
            samples of a given size n that could be taken from the population.
        c)  of any statistic has an approximately normal distribution.
        d)  is a histogram showing the distribution of the sample.
        e)  all of the above are correct.

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2859-1

    Q:  Which is NOT a characteristic of a (random) sampling distribution of
        means?

        a.  Its mean is the same as the mean of the population of scores.
        b.  Its standard deviation is greater than that of the population
            of scores.
        c.  It tends to resemble the normal distribution irrespective of
            the shape of the population of scores with sufficient n.
        d.  Its standard deviation changes with variation in sample size.

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2860-3

    Q:  We __________ have a complete sampling distribution displayed for us.
        a.  always
        b.  frequently
        c.  seldom
        d.  never

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2862-4

    Q:  How does a sampling distribution differ  from  the  distribution  of
        a sample?

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2866-1

    Q:  True or False?  If False, correct it.

        Assuming random sampling, if the sample size is increased nine-
        fold, then the standard deviation of the sample mean is reduced
        by one third.

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2867-3

    Q:  True or false?

             A sampling distribution could be considered a population.

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2889-1

    Q:  True or False?  Explain your answer.

        If a population is very large an especially large sample is usually
        taken or needed.

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Answers:

29-1

    A:  c.  Assuming the population variance is known, then if the sample size
            is doubled, the variance of the distribution of the sample mean of
            a variable would be halved.

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79-1

    A:  (d)  2.947

             df = n - 1
                = 16 - 1
                = 15

             t(ALPHA = .005, df = 15) = 2.947

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79-2

    A:  (3)  -2.49.

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80-1

    A:  (4)  7

             t value from t table at 7 df = 1.90.

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80-2

    A:  (c)  (t distributed with 6 degrees of freedom)

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83-1

    A:  T-distributions are spread out MORE than a normal distribution
        with MU = 0, SIGMA = 1.

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84-2

    A:  d.  normal distribution with mean = 0 and variance = 1.

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86-1

    A:  c.  The greater the df, the more the t-distributions resemble the
            standard normal distribution.

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87-2

    A:  A t-distribution is used in estimating MU when SIGMA is unknown but
        its use assumes that the sample data COMES FROM A NORMAL DISTRIBUTION.

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88-1

    A:  a.  MU
            s/SQRT(n)
        b.  6
        c.  10

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88-2

    A:  t = -1.86 and +1.86

        If available, consult file of graphs and diagrams that could not be
        computerized for appropriate sketch.

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89-1

    A:  Zero
        Zero

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92-1

    A:  1)  Both center at zero and are symmetric.

        2)  The student t has more area in the tails.   The variance of the
            standard normal is 1 while the variance of the student t depends
            on the degrees of freedom and is in general greater than 1.

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96-1

    A:  True

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148-1

    A:  a.  90%

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148-2

    A:  d.  +2.5

            Sample Mean = XBAR
                E(XBAR) = 7 = MU
              VAR(XBAR) = SIGMA**2/n = 4/25
            SIGMA(XBAR) = 2/5
                 Then Z = (XBAR - MU)/SIGMA(XBAR)
                        = (8 - 7)/(2/5) = 2.5

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154-2

    A:  e)  3.92

        Z(ALPHA = .05/2) = 1.96
        2 * 1.96 = 3.92

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155-1

    A:  A. First midterm

        Z = (X - MU)/SIGMA
        Z(1) = (93 - 81)/9       Z(2) = (93 - 78)/12
             = 12/9                   = 15/12
             = 1.33                   = 1.25

        Since Z(1) > Z(2), the student did better on the first midterm
        relative to the class.

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156-1

    A:  c) .7938

           P(70.5 < XBAR < 71.3) = P([(70.5-71)/.3] < Z < [(71.3-71)/.3])
                                 = P((-.5/.3) < Z < (.3/.3))
                                 = P(-1.67 < Z < 1)
                                 = .4525 + .3413
                                 = .7938

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161-1

    A:  a.  .4987

                       stderr = 10/6 = SS below
            P(75 < XBAR < 80) = P[(75-80)/SS < Z < (80-80)/SS]
                              = P(-3  < Z < 0)
                              = .4987

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161-2

    A:  d.  (75.71, 84.29)

            99% C.I. = MU +/- (Z*S(XBAR))
                     = 80 +/- (2.575*(10/6))
                     = from 75.71 to 84.29

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162-1

    A:  d.  P(Z > 2.5)

            Z = (195 - 190)/[SQRT((100)/25)]
              = 2.5

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163-1

    A:  d.  (186.71, 193.29)

                      Z = 1.645

            SIGMA(XBAR) = SQRT(100/25) = 2

            190 +/- (2)(1.645)

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175-1

    A:  d.  .1587

            P[XBAR>2] = P[Z > [[2-0]/[20/SQRT(100)]]]
= P[Z > [[2]/[2]]]
                      = P[Z > 1]
                      = .1587

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193-1

    A:  MU = 18.7
        SIGMA**2 = 1.08
        SIGMA = 1.04

        SIGMA(XBAR) = SIGMA/SQRT(n)
                    = 1.04/SQRT(27)
                    = .200

        P(X >= 19.3) = P(Z >= (19.3 - 18.7)/.200)
         = P(Z >= 3)
                     = .0013

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201-1

    A:  a.  Z = (1.85 - 2.00)/(.10/SQRT(4)) or (2.15 - 2.00)/(.10/SQRT(4))
                = -.15/.05                    or = +.15/.05
               = -3                = +3
        P(Z<-3 or Z>+3) = .0013 + .0013
                        = .0026
        b.  Z = (1.85 - 2.10)/.05    or    (2.15 - 2.10)/.05
              = -2.5/.05                           .05/.05
              = -5                                  1
        P(Z<-5 or Z>1) = .00000 + .1587
                       = .1587
        c.  Using MU = 2.15:
        Z = (1.85 - 2.15)/.05    or    (2.15 - 2.15)/.05
          = -.30/.05                   0/.05
          = -6                         0
        P(-6

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215-2

    A:  Z = (XBAR - MU)/(SIGMA/SQRT(n))
          = (31 - 30)/(3/SQRT(9))
          = 1/(3/3) = 1

        Area beyond Z = .1587.

        Therefore, the probability that the average of a random sample of 9
        setters will exceed 31 inches is 0.1587 or 15.87%.

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732-1

    A:  b.  A conjecture about a population made by measuring some sample of
            that population.

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765-2

    A:  Definition: A measure of variation among values for sample  means for a
                   particular sample size.  The usual method used to calculate
                   an estimate of the standard error of a mean for sample size n
                   is to obtain an estimate of the population variance from the
                   sample elements (S**2), convert it to an estimated variance
                   of a mean for the desired sample size (Divide S**2 by n), and
                   take the square root.  Notice that the same estimated popula-
                   tion variance can be used to calculate standard errors of a
                   mean for several different sample sizes.  If the population
                   variance is known, the process is the same but you are no
                   longer estimating.

        Example:   Suppose that a random sample of size 10 has provided an
                   estimated population variance of 25 with 9 df.  That esti-
                   mated variance provides the basis for calculating
                           A:  Estimated standard error of a mean for a sample
                               size of 4 = 2.5
                           B:  Estimated standard error of a mean for a sample
                               size of 16 = 1.25
                           C:  Estimated standard error of a mean for a sample
                               size of 25 = 1.00

        Symbols:   S(YBAR), S(XBAR), SIGMA(YBAR), SIGMA(XBAR),...

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777-1

    A:  Definition: A Greek letter usually used to indicate the population mean.

        Example:     Suppose that we are concerned with the population of coins
                     carried by each student in this class on a certain day.
                     MU, the population mean = .78, would be the arithmatic
                     average of the amounts carried by all students in the class
                     that day.

        Symbol:      MU

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1342-1

    A:  Using ALPHA = .10, Z = 1.645
        S = SQRT(pq/n) = SQRT((.6)(.4)/200) = .0346

        a.  C.I. = .6 +/- 1.645*.0346
            C.I. = .6 +/- .057
            C.I. = .543 to .657 at 90% confidence

        b.  Since .8 is not included in our confidence interval we must
            reject his claim at the 10% significance level.

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1394-1

    A:  a.  60.0 miles per hour

        b.  C.I. = XBAR +/- [Z * SIGMA(XBAR)]
                 = 60.0 +/- [1.645 * (15/SQRT(64))]
                 = 60.0 +/- [3.08]
                 = from 56.92 to 63.08

            This means that the method used for arriving at this interval will
            produce intervals containing the mean 90% of the time.  This parti-
            cular interval could be one of those, or it could be one of the 5%
            that fail to include the mean.

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1398-1

    A:  b.  1/6.

            Standard Error of Mean = Standard Deviation/SQRT(n)
                                   = 10/SQRT(3600) = 1/6

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1399-2

    A:  False - change "less" to "more".

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1399-3

    A:  False - in general, the sampling distribution of the mean and the
                distribution of the parent population have different shapes.

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1400-2

    A:  True, the central limit theorem implies that the sampling distribution
        of the mean will approach normality for large samples, even if the
        original population distribution is not normal.

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1401-1

    A:  False.

        The Central Limit Theorem states that the sampling distribution
        of the mean will be normal in shape for large samples, even
        if the original population distribution is not.

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1418-1

    A:  (e)  30 +/- .99

            Since SIGMA = 3, SQRT(n) = 5, and Z(critical) for 5% in each
            tail = 1.645:

            SIGMA/SQRT(n) = .6 and
             (.6)*(1.645) = .987

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1418-2

    A:  (1)  0.6

             Lower confidence limit = XBAR - [t * (S/SQRT(n))]
                                    = 3.2 - [2.6 * (4/4)]
                                    = 0.6

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1419-1

    A:  (3)  The variance of the population is usually not known.

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1420-2

    A:  (c)  (70.7%, 89.3%)

             Confidence interval is:
                 80.0 +/- (100*1.645*SQRT(.80*(1 - .80)/50))

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1421-1

    A:  b.  the interval brackets the unknown MU approximately 95 times out
            of a 100.

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1421-2

    A:  c.  68 to 72 inches

        C.I. = XBAR +/- Z * Standard Error
             = 70 +/- 1.96 * SIGMA/SQRT(n)
             = 70 +/- 1.96 * 3/SQRT(9)
             = 68.04 to 71.96 inches or approximately 68 to 72 inches.

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1425-3

    A:  False, the confidence interval increases as the confidence coefficient
        increases, other things being equal.

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1426-1

    A:  False, it means that in about  95  percent of all samples drawn by the
        same method, the true mean will be included in the confidence interval.

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1428-1

    A:  c.  .866

        Z = (X - MU)/(SIGMA/SQRT(n))
        Z = (2.95-28)/(4/SQRT(16)) = 1.50

        Area between 26.5 and 29.5 is .866.

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1429-1

    A:  e.  -0.15 to 10.15

        SIGMA(XBAR) = 20/10 = 2
        C.I. = XBAR +/- Z(.005)SIGMA(XBAR)
             = 5 +/- 2.576(2)
             = 5 +/- 5.15

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1429-2

    A:  b.  1.04 - 4.96

            Noting n = 5, we find:  XBAR = 3, S**2 = 2.5, S = SQRT(2.5) = 1.581
            Using t(ALPHA = .05, df = 4) = 2.776:

            C.I. = XBAR +/- (t)*(S/SQRT(n))
                 = 3 +/- (2.776)*(1.581/SQRT(5))
                 = 3 +/- 1.96
                 = 1.04 to 4.96

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1430-2

    A:  d.  student's t--this assumes depression scores are normally
        distributed and student's t is the most common way of making
        statements about 1 or 2 means.

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1431-2

    A:  (d)  20 +/- .8

             SIGMA(XBAR) = SIGMA/SQRT(n)
                         = 2/5
                         = .40

             (SIGMA(XBAR))*Z(crit) = (.40)( 1.96)
                                   =  .784
                                  == .8

                              C.I. = 20 +/- .8

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1433-1

    A:  b.  2.060

            Since all statistics involved are sample statistics, use the
            t distribution with df = 25, and it is found that 2.5% of the
            area lies in each tail in a two-tailed test when t = 2.060.

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1433-2

    A:  d.  11.2 +/- 2.306(3)

        C.I. = XBAR +/- t(C)(S/SQRT(n))
             = 11.2 +/- 2.306(9/SQRT(9))
             = 11.2 +/- 2.306(3)

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1434-1

    A:  (c)  .56 +/- 1.96SQRT((.44)(.56)/400)

                             SIGMA = SQRT((P)(Q)/n) = SQRT((.56)(.49)/400).

             Population Proportion = P +/- Z(C)(S) = .56 +/- 1.96((.44)(.56)/
                                                     400)

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1434-2

    A:  (3)  B's interval will always be larger than A's interval.

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1435-1

    A:  c.  Increasing sample size decreases the length, given a fixed
            coefficient.

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1435-2

    A:  d.  .8 + 2.576*SQRT(.16/625)

            C.I. = p +/- Z(ALPHA/2)*SQRT(pq/n)
                    p = 500/625 = .8,  q = 125/625 = .2
            C.I. = .8 +/- Z(.005)*SQRT(.8*.2/625)

            Upper limit = .8 + 2.576*SQRT(.16/625)

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1438-1

    A:  e.  a, b, and c

            Confidence Interval = XBAR +/- (Z)*(Standard Deviation/SQRT(n))

            Z value is dependent on the confidence coefficient, and the
            standard error is SQRT(Variance).

            Therefore, a, b, and c affect the size of the confidence in-
            terval.

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1439-1

    A:  (d)  31 +/- 1.81

        Since the df are so high, we can use the normal table even though SIGMA
        is unknown.

   93% confidence interval = XBAR +/- Z*S/SQRT(n)
        Area beyond Z = .035
        Therefore,  Z = 1.81

        C.I.  = 31 +/- (1.81)(SQRT(89)/SQRT(89))
              = 31 +/- 1.81

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1440-1

    A:  1.  A.  1.28

        2.  B.  (2/5) +/- (1.28)(SQRT((6/25)(1/50)))

                PI(1) = 20/50 = 2/5
                 S.D. = SQRT(pq/n) = SQRT((2/5)(3/5)/50)

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1441-2

    A:  (c)  .5 +/- .129

                S = SQRT((.5)(.5)/100)
                  = .05

             C.I. = .5 +/- (2.576)(.05)
                  = .5 +/- (.1288)

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1443-1

    A:  (e)  .0456

             Half confidence interval = (SIGMA/SQRT(n))*Z
                                      = (3/6)*2

                                    Z = 2
                        Area beyond Z = .0228

             Total Probability = 2(.0228) = .0456, because it is the proba-
             bility of getting the difference of -1 as well as +1.

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1443-2

    A:  (a)  XBAR +/- 1.96(1/2)

             C.I. = XBAR +/- Z*SIGMA/SQRT(n)
                  = XBAR +/- 1.96*(3/6)

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1445-1

    A:  b)  58 +/- (2.13*2)

            C.I. = MU +/- (t*S/SQRT(N))
                 = 58 +/- (2.13 * 8/4)
                 = 58 +/- 4.26

            Note: t(df=15, ALPHA=.05, two-tailed) = 2.13

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1446-1

    A:  (b)  [30.80, 31.19]

             C.I. = XBAR +/- Z*S/SQRT(n)
                  = 31 +/- 1.96*2/SQRT(400)
                  = 30.80, 31.19

             note:

             VARIANCE = 1596/(n - 1) = 1596/399 = 4

             Therefore, S will be = SQRT(4) = 2

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1447-1

    A:  (a)  [15.8, 24.3]

             C.I. = XBAR +/- t*S/SQRT(n)
                  = 20 +/- 2.13*8/4
                  = [15.8, 24.3]

                           Variance = 960/15 = 64
                 Standard Deviation = SQRT(64) = 8
             Standard Error Of Mean = 8/SQRT(16) = 2

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1448-2

    A:  B. [.761, .839]

        C.I. = PHAT +/- Z(ALPHA/2) * SQRT((PHAT*(1-PHAT))/n)
       = .8 +/- 1.96 * SQRT((.8*.2)/400)
             = .8 +/- .0392

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1449-1

    A:  a.  12 +/- 3.92

               XBAR = (8 + 11 + 9 + 17 + 12 + 15)/6
                    = 12

        SIGMA(XBAR) = SQRT(24/6)
                    = 2

               C.I. = XBAR +/- Z(ALPHA/2) * (SIGMA(XBAR))
                    = 12 +/- (1.96)(2)
                    = 12 +/- (3.92)

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1454-1

    A:  a.  (14116, 15884)

            C.I. = 15,000 +/- (2.947*1200)/SQRT(16)
                 = 15,000 +/- 884.1
                 = from 14116 to 15884

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1455-1

    A:        d.  1.96   (Using normal table)

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1455-2

    A:  a.  (73.79, 76.41)

            75.1 +/- (1.75)[SQRT(9)/SQRT(16)]
            75.1 +/- 1.31

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1456-1

    A:  a.  43 and 57.

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1457-1

    A:  a.  98.9 - 107.1

            S(XBAR) = S/SQRT(n) = 12/5 = 2.4
            t(critical, df=24, two-tailed, ALPHA=.1) = 1.711

            C.I. = XBAR +/- [t * S(XBAR)]
                 = 103 +/- [1.711 * (12/5)]
                 = 103 +/- [4.1064]
                 = from 98.89 to 107.1064

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1459-1

    A:  d.  (9.02, 10.98)

            Since SIGMA is unknown, use the t distribution. However because
            n=400, t is approximated by the Z distribution.

            95% C.I. = MU +/- Z(.025)*[S/SQRT(n)]
                     = 10 +/- (1.96)(10/SQRT(400))
                     = 10 +/- (1.96)(.5)
                     = 10 +/- 0.98
                     = from 9.02 to 10.98

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1460-2

    A:  2)  49.66 to 65.34

            CI = XBAR +/- [Z*SIGMA(XBAR)]
               = 57.5 +/- [1.96*(20/SQRT(25))]
               = 57.5 +/- [7.84]
               = from 49.66 to 65.34

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1461-2

    A:  c.  variable from sample to sample.

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1463-1

    A:  c.  100

            .10 * 1000 = 100

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1463-2

    A:  b.  74.1 - 75.9

            C.I. = 75 +/- (1.96) * (7/SQRT(225))
                 = 75 +/- .91467
                 = (74.1, 75.9)

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1464-1

    A:  d.  if many samples are drawn, the computed confidence intervals will
            contain MU 95% of the time.

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1469-2

    A:     XBAR = 110.67
        S(X)**2 = 7.1
           S(X) = 2.667
             df = 8

        (a)  110.67 +/- 2.306 * 2.667/SQRT(9)
             108.61 <= MU <= 112.72 at 95% confidence

        (b)  No, it is outside the interval in part a.

        (c)  110.67 +/- 3.355 (2.667/3)
             107.69 <= MU <= 113.65 at 99% confidence

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1470-1

    A:  CI = XBAR +/- ((Z(.025))*SIGMA)/SQRT(n)
           = 800  +/- ((1.96)(120))/SQRT(100)
           = 800  +/- 23.52
           = from 776.48 to 823.52

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1471-1

    A:  S = SQRT((.21)(.79)/100)
          = .0407

        Z(ALPHA/2 = .025) = 1.96

        C.I. = .21 +/- (1.96)(.0407)
             = .21 +/- (.0798)
             = from .13 to .29

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1471-2

    A:  S(YBAR) = SQRT([n/(n-1)][.01660/n])
                = .0263

        YBAR - t(crit)*S(YBAR) < MU < YBAR + t(crit)*S(YBAR)
          7.25 - 1.711 * .0263 < MU < 7.25 + 1.711 * .0263
                         7.205 < MU < 7.295

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1472-1

    A:  C.I. = XBAR +/- [t(df=15,ALPHA=.01)*S/SQRT(n)]
        C.I. = 100 +/- [2.602*(3/SQRT(16))]
        C.I. = 100 +/- 1.95
             = from 98.05 to 101.95

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1472-2

    A:  Using t with ALPHA = .01 and df = 499,

             C.I. = XBAR +/- (t) (S/SQRT(n))
                  = 242.30 +/- (2.576) (3.20/SQRT(500))
                  = 241.93 to 242.67.

        99% of the time that this procedure is used to calculate an interval,
        the resulting interval will contain MU.  This interval may or may not
        include MU.

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1473-1

    A:  PHAT = .33
        n = 2600
        Z(ALPHA=.025) = 1.96

        Stand. error of proportion = SQRT((PHAT(1-PHAT))/n)
                                   = SQRT((.33*.67)/2600)
                                   = .009

        C.I. = .33 +/- (1.96 * .009)
             = from .312 to .348

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1473-3

    A:  C.I. = XBAR +/- (Z)*(SIGMA(XBAR))
             = 24 +/- (1.645) (2)
             = 24 +/- 3.29

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1474-2

    A:  PHAT = 225/360 = .625 or 62.5%

        Standard error of proportion =  SQRT((PHAT(1-PHAT))/n)
        S(PHAT) = SQRT(.625*.375/360)
             = .026

        C.I. = PHAT +/- Z(ALPHA = .01) * S(PHAT)
             = 62.5% +/- (2.58)*(02.6)%
             = 62.5% +/- 6.7%
             = from 55.8 to 69.2%

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1478-1

    A:  S(XBAR) = S/SQRT(n)
                = 30.9/3
                = 10.3

        C.I. = XBAR +/- ([t(ALPHA = .005, df = 8)]*S(XBAR))
             = 210 +/- (3.355*10.3)
             = from 175.4 to 244.6

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1478-2

    A:  .475 +/- 2.58 SQRT((.475*.525)/200) = .475 +/- .091

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1480-1

    A:  SIGMA = SQRT(pq/n) and t with ALPHA = .05 and df = 29 equals 2.042
        C.I. = .6 +/- 2.042 * SQRT ((.6*(1-.6))/30)
        C.I. = .6 +/- 2.042 * SQRT (.008)
        C.I. = .6 +/- .1826
        C.I. = .417 - .783 at 95% confidence

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1481-1

    A:  C.I. = XBAR +/- (Z) (SIGMA/SQRT(n))
             = 35 +/- (1.96) (SQRT(4/9))
             = 35 +/- 1.31
             = 33.69 to 36.31

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1481-2

    A:  90% confidence interval is from .1342 to .2658.

        C.I. = PHAT +/- [Z(ALPHA(2))*SQRT((PHAT*QHAT)/n)]
             = .2 +/- [1.645 * (.2*.8/100)]
             = .1342 to .2658

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1482-1

    A:  a.  Confidence interval = XBAR +/- [Z * S(XBAR)]
                                = 72 +/- (2.576 * [15/SQRT(25)])
                                = 72 +/- (2.576 * 3)
                                = from 64.272 to 79.728

        b.  Based  on  the  sample  statistic, we are 99% confident that the in-
            terval from 64.27 to 79.73 covers the mean. This implies that if all
            possible samples of size n (= 25) were taken from the population,
            and a 99% confidence interval were calculated from each sample,  99%
            of all these intervals would contain the true population mean.

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1483-1

    A:  a)  C.I. = XBAR +/- (t(ALPHA=.05,df=8) * [s/SQRT(n)])
                 = 12 +/- (2.306 * [1/SQRT(9)])
                 = 12 +/- .769
                 = from 11.231 to 12.769

            This procedure for producing confidence limits will yield a confi-
            dence interval that contains MU 95% of the time.  A probability
            statement cannot be made about the calculated interval (11.231,
            12.769) since it either contains MU or does not contain MU.

        b)  Yes, because a Z value would then be used.
            Z(.025) = 1.96 < 2.306

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1484-1

    A:  a.  C.I. = XBAR +/- [t*S(XBAR)]; t(ALPHA=.01, one-tail, df=15) = 2.602
                 = 16.35 +/- [2.602*(4.56/SQRT(16))]
                 = from 13.384 to 19.316

        b.  According  to  the confidence  interval  found  in part a, Mr.
            Blackwater's  estimate  of  $19.01  is a possible estimate for
            the population mean.  It should be pointed out that we are 98%
            confident  that  such  a confidence interval would contain the
            population mean.

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1485-1

    A:  n = 3
        SUM(X(i)) = 37.53

        XBAR = [37.53]/[3]
             = 12.51

        S**2 = [[(12.50-12.51)**2]+[(10.75-12.51)**2]+[(14.28-12.51)**2]]/[2]
             = [[0.0001] +[3.0976] + [3.1329]]/[2]
             = 3.1153

        S = 1.7650

        S(XBAR) = [1.7650]/[SQRT(3)]
                = 1.0190

        90% C.I. = XBAR +/- [t(ALPHA=0.05, df=2) * S(XBAR)]
                 = 12.51 +/- [2.92 * 1.019]
                 = 12.51 +/- 2.98
                 = from $9.53 to $15.49

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1486-1

    A:  n = 7
        SUM(X(i)) = 421

        XBAR = 421/7
             = 60.143

        S(XBAR) = [9.856]/[SQRT(7)]
                = 3.725

        90% C.I. = XBAR +/- [t(ALPHA=.05, df=6) * S(XBAR)]
                 = 60.143 +/- [(1.943) * (3.725)]
                 = 60.143 +/- [7.238]
                 = from 52.905 to 67.381

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1487-1

    A:  n = 10

        90% C.I. = 5.9 +/- [t(df=9,ALPHA=.05,one-tail)*(2.18/SQRT(10)]
                 = 5.9 +/- [1.833 * 0.69]
                 = 5.9 +/- [1.266]
                 = from 4.63 to 7.166

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1488-1

    A:  n = 6
        XBAR = 3.83
        90% C.I. = 3.83 +/- [t(df=5,ALPHA=.05,one-tail)*(0.983/SQRT(6)]
                 = 3.83 +/- [2.015 * 0.401]
                 = 3.83 +/- [0.809]
                 = from 3.02 to 4.64

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1491-2

    A:  (a)  MU(HAT) = 22

        (b)  With t(ALPHA = .01, df = 99) = 2.63
             22 +/- 2.63 * 5/SQRT(100)
             22 +/- 1.315
             20.685 to 23.315

        (c)  There are several reasons why this confidence interval is approxi-
             mate, among them is that the term average is not clearly defined
             and that S approximates SIGMA.  Also, the population distribution
             may not be normal.

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1495-1

    A:  P = 3/10

        C.I. for this proportion = 3/10 +/- 10%
                                 = 3/10 +/- 1/10
                                 = 2/10 to 4/10

        Therefore, between 20% and 40% of the Democrats favored Senator Kennedy.

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1499-3

    A:  Confidence Interval for the difference:
            = .20 +/- .14
            = .06 <= the true difference <= .34 at 95% confidence.

        Since this interval does not include zero, I would forecast
        a win for candidate A.

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1500-1

    A:  The most favorable confidence limit for my candidate would be
        c., 4% +/- 10%, 1-ALPHA=.80.  This limit indicates a larger
        standard deviation than the other two, since t(ALPHA=.20) is
        smaller than t(ALPHA=.05).  Since my candidate is behind
        the most favorable situation is that which indicates the greatest
        uncertainty that the difference is anything more than random
        sampling variation.

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1501-1

    A:  1.  a.  To set 90% confidence limits including MU, we need XBAR, the
                sample standard deviation, s, the sample size, n, and a t
                value for ALPHA = .1.

                Use the formula:
                    XBAR +/- (t, ALPHA/2)(s/SQRT(n)) with t(ALPHA/2) = 2.015.

            b.  Use the same procedure as in 1a,  but use t(ALPHA/2) = 4.032.

        2.  XBAR = 11
            Standard deviation = 2.28
            n = 6

            a.  11 +/- (2.015)(2.28/SQRT(6))
                    = 11 +/- (2.015)(.93)
                    = 11 +/- 1.876
                    = 9.124 to 12.876

                This is inconsistent with the specification of hoppiness = 8.0.

            b.  11 +/- (4.032)(2.28/SQRT(6))
                    = 11 +/- (4.032)(.93)
                    = 11 +/- 3.753
                    = 7.247 to 14.753

            This is consistent with the specification of hoppiness = 8.0.

        3.  Ths basic weakness seems to be in using a procedure that produces a
            confidence interval consistent with a wide range  of values,  which
            makes it difficult to detect departures from MU = 8.  This situation
            is exaggerated when the 99% level is used.  In addition, the sample
            size used seems small relative to the variability measured.

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1509-1

    A:  False.

        If (5,8) is a 95% confidence interval for MU then we are 95%
        "confident" that the interval contains the value of MU.  However,
        since MU is a constant it either does (P=1.00) or does not (P=0.00)
        lie in the interval, so it does not make sense to say that P=.95.

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1509-2

    A:  True - the more confidence one needs to place in the interval containing
        the true mean, the more leeway one must provide.

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1510-1

    A:  True
        CONFIDENCE INTERVAL = Mean +/- Z*Standard Error

        As you increase (1 - ALPHA) the Z value increases, so the width of the
        confidence interval will also increase.

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1510-2

    A:  True

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1511-2

    A:  False.  If confidence intervals are based on the same sample
                observations, and are for the same unknown parameter,
                then, for example, under normality assumption, a 90%
                CI for MU is = XBAR +/- 1.645 S(XBAR)

                A 95% CI for MU is:   XBAR +/- 1.96 S(XBAR)
                Hence the statement is not true.

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1513-3

    A:  True.

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1522-2

    A:  e.  Sufficient information but correct result is not given.

            midpoint of interval = PHAT = .65

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1523-1

    A:  d.  all of the above.

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1547-1

    A:  False - the confidence coefficient is the probability that an unknown
        parameter will be within the given interval.

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1547-3

    A:  True.

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1548-2

    A:  Definition:  The product of a probability dependent multiplier
                     times the standard error of a random variable.  If
                     the standard error is known the multiplier usually comes
                     from the standard normal table.  If the standard error
                     is estimated the multiplier usually comes from the
                     student's t.

        Example:     Suppose that the significance level is .05 and the
                     population variance is known to be 16.  Suppose further
                     that a sample of size 4 has been drawn.  Then the 95%
                     margin of error for the population mean is 1.96 times 2
                     or 3.92.  (The population standard error of a mean is the
                     square root of the variance divided by the sample size,
                     here:  SQRT(16/4).

        Symbol:      Such as MOE = Z(.05) * S(XBAR)

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1551-2

    A:  c.  estimate the mean of the population

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1566-1

    A:  a.  the n is large enough

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1566-3

    A:  d.  MU(X) and ((SIGMA(X))**2)/n

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1568-1

    A:  e)  none of the above are true.

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1568-2

    A:  a)  zero

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1569-1

    A:  d.  refers to a matter other than those stated above.

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1570-1

    A:  c.  if n is large regardless of the shape of the parent population
            distribution.

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1572-3

    A:  Confidence Interval = XBAR +/- Z*SIGMA(XBAR)
                            = XBAR +/- 10

                         10 = Z * SIGMA(XBAR)
                            = Z * (25/6)
                          Z = 2.4

                Probability = 2 * (.4918) = .9836

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1576-1

    A:  The variance of the sampling distribution of means decreases as sample
        size increases.  Therefore,  one's  estimate becomes more accurate as
        sample size increases.

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1577-1

    A:  A.  The sampling distribution of XBAR for a sample size of 25 is the
            frequency distribution of XBARs that results from finding the mean
            of every distinct sample of 25 from the population.  The Central
            Limit Theorem states, among other things, that the shape of this
            sampling distribution of the means will approach that of a normal
            distribution as larger samples are used, regardless of the shape
            of the population distribution.  The figure below is an example
            of a sampling distribution of XBAR where MU is the population
            mean and SIGMA is the population standard deviation.

            (If available, consult file of graphs and diagrams that could not
            be computerized for appropriate figure.)

        B.  They will be the same.

        C.  SIGMA(XBAR) = SIGMA/SQRT(n)

        D.  1)  Confidence interval size will decrease.
            2)  Confidence interval size will increase.

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1578-1

    A:  a.)  Z is approximately normally distributed with MEAN = 0
             and SIGMA = 1.

        b.)  MU(Z) = 0

        c.)  VAR(Z) = 1

        d.)  It is of fundamental importance because it specifies that
             the sampling distribution of the mean will be normal in
             shape for large samples, even if the original population
             distribution is not.

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1580-2

    A:  False.

        The Central Limit Theorem holds equally whether we sample from a
        normal distribution or not.

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1581-1

    A:  True, the Central Limit Theorem justifies approximating the distribution
        of XBAR with a normal distribution when n is sufficiently large.

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1581-2

    A:  True, the Central Limit Theorem applies to sampling from any
        distribution.

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1582-2

    A:  True, the mean of the sampling distribution of means is exactly
        equal to the population mean regardless of sample size and type
        of distribution.

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1583-2

    A:  True, the normal approximation to the probability distribution of XBAR
        is reasonably good in most cases for sample sizes of 30 or more,  pro-
        vided we have a random sample from X(i).

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1584-2

    A:  False.

        The central limit theorem says that, under the given condition, the
        sample means, obtained upon repeated sampling from a population,
        will be normally distributed.

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1585-2

    A:  False.  The sampling distribution of XBAR will be normal in shape
        for large samples, (n>30), even if the original population distri-
        bution is not.

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1691-1

    A:  False.
        Other things being equal, a HIGH level of confidence is desirable.

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1730-1

    A:  STATISTICAL INFERENCE is the process of drawing conclusions about popula-
        tion characteristics from the facts given by a sample.  It is generali-
        from the specific to the general.

        Other possible answers might be:  INFERENCE, INDUCTIVE INFERENCE,
                                          INFERENTIAL STATISTICS

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1791-3

    A:  True. Let X = 1 if it has the desired attribute and X = 0
        if it does not. Then the proportion, p, is:  p = (SUM(X))/n.

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1815-1

    A:  b.  18 and 4 respectively

            Sampling distribution for the sample mean has a mean equal to
            the population mean and variance equal to SIGMA**2/n.

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1820-2

    A:  b.  normally for any given sample size if the sample is randomly
            selected.

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1857-4

    A:  True

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1858-3

    A:  False, size of mean is independent of size of standard deviation.
        Standard deviation depends on the variability among individual ob-
        servations.

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1859-1

    A:  True.

        Mean of sampling distribution = population mean.
        Standard deviation of sampling distribution = SIGMA/SQRT(n)
                                                    = 1/SQRT(4)
                                                    = .5

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1865-1

    A:  (b)  .9

             Since SIGMA(XBAR)**2 = SIGMA(X)**2/n.

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1869-1

    A:  This question cannot be answered accurately without knowing the
        standard deviation for IQ scores.  Then these differences from
        the mean or average can be evaluated relative to the standard
        deviation as to whether there is a significant difference between
        them.

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1869-2

    A:  The difference in mean income between two towns of 10,000 people,
        when based on samples of 5 people, will be much more variable from
        sampling situation to situation than a difference based on samples of
        100 people.  The standard error allows us to take this into account.

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1891-2

    A:  SIGMA is the standard deviation of the population, while  SIGMA(XBAR)
        is the standard error of the mean, which is the standard deviation of
        the sampling  distribution  of  means.  The relationship between the
        two is:

             SIGMA(XBAR) = SIGMA/SQRT(n);

        where n is the size of the sample.

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1898-1

    A:  False.  For large n, S(XBAR) should be smaller than the standard
        deviation because we know S(XBAR) = S/SQRT(n).

        Therefore, S(XBAR) will always be smaller than S, since n is larger
        than 1.

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1898-2

    A:  True.  The standard deviation of all possible sample means should equal
        SIGMA/SQRT(n), where SIGMA is the standard  deviation  of  the original
        observations, and n is the sample size.

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1901-1

    A:  True.

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1905-2

    A:  b.  13.00

            XBAR = (5 + 10 + 3)/3 = 6
            S(X)**2 = [(5 - 6)**2 + (10 - 6)**2 + (3 - 6)**2]/(3 - 1)
                    = (1 + 16 + 9)/2
                    = 26/2 = 13

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1927-1

    A:  MU = E(X) = (0*.4) + (1*.3) + (2*.2) + (3*.1) = 1.0
        E(X**2) = (0*.4) + (1*.3) + (4*.2) + (9*.1) = 2.0
        VAR(X) = E(X**2) - (E(X))**2 = 2.0 - 1.0 = 1.0
        VAR(XBAR) = (VAR(X))/n = 1.0/5 = 0.2

        SUM(X) = 6
        SUM(X**2) = 14

        S(X)**2 = [SUM(X**2) - ((SUM(X))**2)/n]/(n - 1)
                = [14 - (36/5)]/4
                = 1.7

        S(XBAR)**2 = (S(X)**2)/n = 1.7/5
                   = 0.34

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1928-1

    A:  A.  3
        B.  25

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1951-3

    A:  False.

        The distribution of XBAR will have a variance equal to the
        population variance divided by n.

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1959-1

    A:  (3)  As the sample size decreases, the variability of the distribution
             of XBAR about MU increases.

             Variability = (XBAR - MU)/(SIGMA/SQRT(n))

             Therefore, variability increases as n decreases because n is in
             the denominator.

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1960-2

    A:  c.  2

            SIGMA(XBAR) = SIGMA/SQRT(n)
                        = 8/4
                        = 2

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1962-1

    A:  (1)  .1056

      Z = (XBAR - MU)/(SIGMA/SQRT(n))
                Z = (0 - 5)/(20/5) = -1.25
             AREA = .5 - .3944 = .1056

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1963-2

    A:  (e.)  b and d
              According to the Central Limit Theorem:
              MU(XBAR) = MU = 138
              SIGMA(XBAR)**2 = SIGMA**2/n = 126/6 = 21

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1964-1

    A:  (d.)  the sampling distribution of the mean.

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1964-3

    A:  c.  it decreases

            SIGMA(XBAR) = SIGMA/SQRT(n)

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1966-1

    A:  c.  an estimate of the standard error of the mean

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1966-3

    A:  d)  standard error of the mean.

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1967-1

    A:  c)  3.0

            SIGMA(XBAR) = SIGMA/SQRT(n)
                        = 18/SQRT(36)
                        = 3

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1968-1

    A:  c.  Use [s(Y)]/[SQRT(n)]

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1968-2

    A:  b.  It will be one-third as large.

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1969-1

    A:  d.  is characterized by all of the above.

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1969-2

    A:  d.  [SIGMA(Y)]/[SQRT(n)]

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1971-1

    A:  Investigator X.  It is the size of the sample rather than the population
        that matters, when dealing with such large populations and samples.

                SIGMA(sample) = SIGMA(population)/SQRT(n)

        If we regard SIGMA(population) as a known constant, then

                1/SQRT(500) = .044    and    1/SQRT(1000) = .031

        These "multiplication factors" will be introduced, leading to a larger
        standard error with a smaller sample.  I.E., the bigger the sample,
        the larger our denominator when we take the square root, and the
        larger the denominator, the smaller the value of the standard error
        of the mean.

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1977-4

    A:  False, as the sample size increases, the standard error of the mean
        decreases.  [SIGMA(XBAR) = SIGMA/SQRT(n)]

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1978-1

    A:  False - the standard deviation of the random sampling distribution of
        the mean is equal to the population standard deviation divided
        by SQRT(n).

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1978-3

    A:  False, the sampling distribution of the mean will always have a variance
        which is less than the variance of the associated parent population.

        Variance of sampling distribution of mean = S**2/n

                    Variance of parent population = S**2

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1979-3

    A:  False, the standard error of the sample mean decreases as the
        sample size increases.

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1981-1

    A:  False.

        The only requirement for this formula is that sample members are
        independently and identically distributed.

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2074-2

    A:  b.  the variability of a sampling distribution of medians.

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2074-4

    A:  If the appropriate measure of variability for a distribution is the
        standard error it must be a sampling distribution.

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2103-1

    A:  b.  MU(X) = MU(XBAR) and SIGMA(X)**2 >= SIGMA(XBAR)**2

        Mean  of  a  sampling  distribution is always equal to mean of parent
        distribution and  variance  of  sampling  distribution  is  equal  to
        variance of parent distrbution divided by n.

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2857-1

    A:  b)  of the mean is a distribution of the means taken from all possible
            samples of a given size n that could be taken from the population.

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2859-1

    A:  b.  Its standard deviation is greater than that of the population
            of scores.

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2860-3

    A:  c.  We SELDOM have a complete sampling distribution displayed for us.

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2862-4

    A:  The sampling distribution is the distribution of estimates  for  some
        particular  statistic found from taking many samples.  The process is
        to take a  sample,  calculate  the  estimate,  draw  another  sample,
        calculate its estimate, and repeat this a large number of times.  The
        sampling distribution is formed by getting  a  frequency  diagram  of
        these  estimates.  In contrast,  the  distribution of the sample is a
        frequency diagram of the observations occurring within one sample.

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2866-1

    A:  True.

        Standard deviation of the sample mean = (SIGMA)/SQRT(n)
        and:
        (SIGMA)/SQRT(9*n) = (1/3)*[(SIGMA)/SQRT(n)]

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2867-3

    A:  True.

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2889-1

    A:  False, sample size depends on economic considerations and the varia-
        bility in the population.  A more variable population needs a bigger
        sample, while a less variable population requires a smaller sample.

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Return to the list of chapters

Return to Brian Schott @ GSU

Identification:

29-1

Item is still being reviewed
        Multiple Choice
BASICTERMS/PROB   SIMPLE/CI
        SAMPLESIZE        PROBABILITY       CONFIDENCEINTERV
        ESTIMATION        CONCEPT           STATISTICS
        SAMPLING

T= 5    Comprehension
D= 4    General

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79-1

Based upon item submitted by H. B. Christensen - BYU
        Multiple Choice
TDISTRIBUTION     SIMPLE/CI
        PROBDISTRIBUTION  PROBABILITY       CONFIDENCEINTERV
        ESTIMATION        CONCEPT           STATISTICS

T= 2    Computation
D= 1    General

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79-2

Item is still being reviewed
        Multiple Choice
TDISTRIBUTION
        PROBDISTRIBUTION  PROBABILITY

T= 2    Application
D= 1    General
                ***Statistical Table Necessary***

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80-1

Based upon item submitted by B. Weir - N. C. State & Massey Univ.
        Multiple Choice
TDISTRIBUTION
        PROBDISTRIBUTION  PROBABILITY

T= 2    Comprehension   Application
D= 2    General
                ***Statistical Table Necessary***

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80-2

Based upon item submitted by F. J. Samaniego - UC Davis
        Multiple Choice
TDISTRIBUTION
        PROBDISTRIBUTION  PROBABILITY

T= 5    Comprehension
D= 2    General

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83-1

Based upon item submitted by J. L. Mickey -UCLA
        Multiple Choice
TDISTRIBUTION
        OTHER/N           PROBDISTRIBUTION  PROBABILITY
        NORMAL

T= 2    Comprehension
D= 2    General

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84-2

Item is still being reviewed
        Multiple Choice
STANDUNITS/NORMA  TDISTRIBUTION
        PROBDISTRIBUTION  PROBABILITY

T= 2    Comprehension
D= 2    General

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86-1

Item is still being reviewed
        Multiple Choice
TDISTRIBUTION
        OTHER/N           PROBDISTRIBUTION  PROBABILITY
        NORMAL

T= 2    Comprehension
D= 4    General             Education

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87-2

Based upon item submitted by J. L. Mickey -UCLA
        Fill-in
TDISTRIBUTION     ESTIMATION/OTHER
        PROBDISTRIBUTION  PROBABILITY       ESTIMATION
        CONCEPT           STATISTICS

T= 2    Comprehension
D= 4    General
                ***Multiple Parts***

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88-1

Based upon item submitted by J. Warren - UNH
        Fill-in
TDISTRIBUTION     STANDUNITS/NORMA
        I650I             PROBDISTRIBUTION  PROBABILITY

T= 5    Comprehension
D= 3    General
                ***Multiple Parts***
                ***Statistical Table Necessary***

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88-2

Based upon item submitted by J. Warren - UNH
        Numerical Answer
TDISTRIBUTION
        I650I             PROBDISTRIBUTION  PROBABILITY

T= 5    Comprehension   Computation
D= 2    General
                ***Statistical Table Necessary***

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89-1

Based upon item submitted by J. Warren - UNH
        Numerical Answer
TDISTRIBUTION     STANDUNITS/NORMA
        I650I             PROBDISTRIBUTION  PROBABILITY

T= 2    Comprehension
D= 1    General

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92-1

Item is still being reviewed
        Short Answer
NORMAL            TDISTRIBUTION
        PROBDISTRIBUTION  PROBABILITY

T= 5    Comprehension
D= 2    General
                ***Multiple Parts***

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96-1

Item is still being reviewed
        True/False
TDISTRIBUTION     OTHER/T
        PROBDISTRIBUTION  PROBABILITY       TTEST
        PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 3    General

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148-1

Based upon item submitted by W. J. Hall - Univ. of Rochester
        Multiple Choice
ZSCORE            SIMPLE/CI         TWOTAIL/Z
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS        ZTEST             PARAMETRIC

T= 2    Computation     Comprehension
D= 1    General
                ***Statistical Table Necessary***

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148-2

Based upon item submitted by W. J. Hall - Univ. of Rochester
        Multiple Choice
ZSCORE
        STANDERROROFMEAN  OTHER/CI          STANDUNITS/NORMA
        PROBDISTRIBUTION  PROBABILITY       DESCRSTAT/P
        PARAMETRIC        STATISTICS        CONFIDENCEINTERV
        ESTIMATION        CONCEPT

T= 2    Computation
D= 2    General

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154-2

Item is still being reviewed
        Multiple Choice
SIMPLE/CI         ZSCORE
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS        STANDUNITS/NORMA  PROBDISTRIBUTION
        PROBABILITY

T= 2    Computation
D= 2    General
                ***Statistical Table Necessary***

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155-1

Based upon item submitted by F. J. Samaniego - UC Davis
        Multiple Choice
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 5    Computation
D= 2    Education           General

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156-1

Based upon item submitted by F. J. Samaniego - UC Davis
        Multiple Choice
ZSCORE
        MEAN              STANDERROROFMEAN  STANDUNITS/NORMA
        PROBDISTRIBUTION  PROBABILITY       DESCRSTAT/P
        PARAMETRIC        STATISTICS

T=10    Computation
D= 4    General

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161-1

Item is still being reviewed
        Multiple Choice
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 5    Application
D= 4    Biological Sciences Education
                ***Statistical Table Necessary***

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161-2

Item is still being reviewed
        Multiple Choice
ZSCORE            SIMPLE/CI
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 5    Application     Comprehension
D= 3    Biological Sciences Education
                ***Statistical Table Necessary***

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162-1

Item is still being reviewed
        Multiple Choice
ZSCORE
        STANDERROROFMEAN  STANDUNITS/NORMA  PROBDISTRIBUTION
        PROBABILITY       DESCRSTAT/P       PARAMETRIC
        STATISTICS

T= 2    Comprehension
D= 2    Biological Sciences General

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163-1

Based upon item submitted by D. Kleinbaum - Univ of North Carolina
        Multiple Choice
SIMPLE/CI         ZSCORE
        MEAN              CONFIDENCEINTERV  ESTIMATION
        CONCEPT           STATISTICS        STANDUNITS/NORMA
        PROBDISTRIBUTION  PROBABILITY       DESCRSTAT/P
        PARAMETRIC

T= 5    Application     Comprehension
D= 6    Biological Sciences General
                ***Statistical Table Necessary***

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175-1

Item is still being reviewed
        Multiple Choice
ZSCORE
        STANDERROROFMEAN  STANDUNITS/NORMA  PROBDISTRIBUTION
        PROBABILITY       DESCRSTAT/P       PARAMETRIC
        STATISTICS

T= 2    Computation
D= 2    General
                ***Statistical Table Necessary***

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193-1

Item is still being reviewed
        Numerical Answer
ZSCORE
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T=10    Computation
D= 2    General             Education
                ***Calculator Necessary***
                ***Statistical Table Necessary***

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201-1

Based upon item submitted by G. Miaoulis - Wright State Univ.
        Numerical Answer
ZSCORE
        STANDERROROFMEAN  TESTING           I650I
        DESCRSTAT/P       PARAMETRIC        STATISTICS
        CONCEPT           STANDUNITS/NORMA  PROBDISTRIBUTION
        PROBABILITY

T=10    Application
D= 6    General             Natural Sciences
                ***Multiple Parts***
                ***Statistical Table Necessary***

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215-2

Based upon item submitted by J. Warren - UNH
        Numerical Answer
STANDERROROFMEAN  ZSCORE            SAMPLINGDISTRIB
        I650I             DESCRSTAT/P       PARAMETRIC
        STATISTICS        STANDUNITS/NORMA  PROBDISTRIBUTION
        PROBABILITY       SAMPLING

T= 5    Comprehension
D= 3    General
                ***Statistical Table Necessary***

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732-1

Item is still being reviewed
        Multiple Choice
SCOPEOFINFERENCE  BASICTERMS/STATS
        CONCEPT           STATISTICS

T= 2    Comprehension
D= 1    General             Education

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765-2

Based upon item submitted by J. Warren - UNH
        Definition
STANDERROROFMEAN  BASICTERMS/STATS
        I650I             DESCRSTAT/P       PARAMETRIC
        STATISTICS

T= 5    Comprehension
D= 3    General

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777-1

Based upon item submitted by J. Warren - UNH
        Definition
MEAN              BASICTERMS/STATS
        I650I             DESCRSTAT/P       PARAMETRIC
        STATISTICS

T= 5    Comprehension
D= 3    General

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1342-1

Item is still being reviewed
        Short Answer
PROPORTION        SIMPLE/CI         TESTING
        STANDERROR/OTHER  I650I             DESCRSTAT/P
        PARAMETRIC        STATISTICS        CONFIDENCEINTERV
        ESTIMATION        CONCEPT

T= 5    Application
D= 6    General
                ***Calculator Necessary***
                ***Multiple Parts***
                ***Statistical Table Necessary***

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1394-1

Item is still being reviewed
        Numerical Answer
ESTIMATION        CONFIDENCEINTERV
        CONCEPT           STATISTICS

T= 5    Computation     Comprehension
D= 3    General
                ***Statistical Table Necessary***

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1398-1

Based upon item submitted by R. Pruzek - SUNY at Albany
        Multiple Choice
STANDERROROFMEAN  SAMPDIST/C
        DESCRSTAT/P       PARAMETRIC        STATISTICS
        ESTIMATION        CONCEPT

T= 5    Computation
D= 2    General
***Calculator Necessary***

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1399-2

Based upon item submitted by R. Pruzek - SUNY at Albany
        True/False
SAMPDIST/C        SAMPLESIZE
        ESTIMATION        CONCEPT           STATISTICS
        SAMPLING

T= 5    Comprehension
D= 3    General

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1399-3

Based upon item submitted by R. Pruzek - SUNY at Albany
        True/False
SAMPDIST/C        MEAN
        ESTIMATION        CONCEPT           STATISTICS
        DESCRSTAT/P       PARAMETRIC

T= 5    Comprehension
D= 3    General

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1400-2

Based upon item submitted by R. Pruzek - SUNY at Albany
        True/False
SAMPDIST/C        CENTRALLIMITTHM
        ASSUMPTCUSTOMARY  ESTIMATION        CONCEPT
        STATISTICS        MISCELLANEOUS

T= 5    Comprehension
D= 4    General

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1401-1

Based upon item submitted by R. Pruzek - SUNY at Albany
        True/False
CENTRALLIMITTHM   SAMPDIST/C
        CONCEPT           STATISTICS        ESTIMATION

T= 5    Comprehension
D= 3    General

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1418-1

Item is still being reviewed
        Multiple Choice
SIMPLE/CI         CONFIDENCEINTERV
        MEAN              ESTIMATION        CONCEPT
        STATISTICS        DESCRSTAT/P       PARAMETRIC

T= 2    Computation     Comprehension
D= 5    General
                ***Calculator Necessary***
                ***Statistical Table Necessary***

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1418-2

Based upon item submitted by B. Weir - N. C. State & Massey Univ.
        Multiple Choice
CONFIDENCEINTERV
        ESTIMATION        CONCEPT           STATISTICS

T= 2    Computation     Comprehension   Application
D= 2    General
                ***Calculator Necessary***

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1419-1

Item is still being reviewed
        Multiple Choice
CONFIDENCEINTERV
        ESTIMATION        CONCEPT           STATISTICS

T= 2    Comprehension
D= 1    General

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1420-2

Item is still being reviewed
        Multiple Choice
CONFIDENCEINTERV  PROPORTION
        ZSCORE            ESTIMATION        CONCEPT
        STATISTICS        DESCRSTAT/P       PARAMETRIC
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T= 5    Computation
D= 4    General             Biological Sciences
                ***Calculator Necessary***
                ***Statistical Table Necessary***

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1421-1

Based upon item submitted by J. Inglis
        Multiple Choice
CONFIDENCEINTERV
        TYPE1ERROR        ESTIMATION        CONCEPT
        STATISTICS

T= 5    Comprehension
D= 4    General

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1421-2

Based upon item submitted by J. Inglis
        Multiple Choice
CONFIDENCEINTERV
        STANDERROROFMEAN  TYPE1ERROR        ESTIMATION
        CONCEPT           STATISTICS        DESCRSTAT/P
        PARAMETRIC

T= 5    Computation
D= 4    General
                ***Statistical Table Necessary***

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1425-3

Based upon item submitted by D. Kleinbaum - Univ of North Carolina
        True/False
CONFIDENCEINTERV
        SIMPLE/CI         ESTIMATION        CONCEPT
        STATISTICS

T= 2    Comprehension
D= 5    General

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1426-1

Based upon item submitted by D. Kleinbaum - Univ of North Carolina
        True/False
CONFIDENCEINTERV
        SIMPLE/CI         ESTIMATION        CONCEPT
        STATISTICS

T= 2    Comprehension
D= 5    General

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1428-1

Based upon item submitted by F. J. Samaniego - UC Davis
        Multiple Choice                ***Calculus Necessary***
SIMPLE/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 5    Computation
D= 3    General
                ***Statistical Table Necessary***

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1429-1

Item is still being reviewed
        Multiple Choice
SIMPLE/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 5    Application     Computation
D= 3    General
                ***Statistical Table Necessary***

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1429-2

Item is still being reviewed
        Multiple Choice
SIMPLE/CI
        STANDARDDEVIATIO  SIMPLEDATASET     I650I
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS        DESCRSTAT/P       PARAMETRIC

T= 5    Application
D= 5    General
                ***Statistical Table Necessary***

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1430-2

Based upon item submitted by R. L. Stout & R. M. Paolino - Brown
        Multiple Choice
SIMPLE/CI         OTHER/T
        TDISTRIBUTION     CONFIDENCEINTERV  ESTIMATION
        CONCEPT           STATISTICS        TTEST
        PARAMETRIC        PROBDISTRIBUTION  PROBABILITY

T= 5    Comprehension
D= 5    Psychology

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1431-2

Item is still being reviewed
        Multiple Choice
SIMPLE/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 5    Computation
D= 1    General
                ***Statistical Table Necessary***

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1433-1

Item is still being reviewed
        Multiple Choice
SIMPLE/CI         MEAN
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS        DESCRSTAT/P       PARAMETRIC

T= 2    Analysis
D= 2    General
                ***Statistical Table Necessary***

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1433-2

Based upon item submitted by F. J. Samaniego - UC Davis
        Multiple Choice
SIMPLE/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 5    Comprehension
D= 3    General
                ***Statistical Table Necessary***

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Back to this chapter's Contents


1434-1

Item is still being reviewed
        Multiple Choice
SIMPLE/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 5    Comprehension
D= 3    General
                ***Statistical Table Necessary***

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Back to this chapter's Contents


1434-2

Based upon item submitted by B. Weir - N. C. State & Massey Univ.
        Multiple Choice
SIMPLE/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 2    Comprehension
D= 2    General

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Back to this chapter's Contents


1435-1

Based upon item submitted by A. Bugbee - UNH
        Multiple Choice
SAMPLESIZE        SIMPLE/CI         STANDERROROFMEAN
        SAMPLING          STATISTICS        CONFIDENCEINTERV
        ESTIMATION        CONCEPT           DESCRSTAT/P
        PARAMETRIC

T= 2    Comprehension
D= 2    General

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1435-2

Item is still being reviewed
        Multiple Choice
PROPORTION        SIMPLE/CI
        DESCRSTAT/P       PARAMETRIC        STATISTICS
        CONFIDENCEINTERV  ESTIMATION        CONCEPT

T= 5    Computation
D= 4    Business            General
                ***Statistical Table Necessary***

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1438-1

Item is still being reviewed
    Multiple Choice
VARIANCE          SIMPLE/CI         TYPE1ERROR
        SAMPLESIZE        DESCRSTAT/P       PARAMETRIC
        STATISTICS        CONFIDENCEINTERV  ESTIMATION
        CONCEPT           SAMPLING

T= 2    Comprehension
D= 3    General

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1439-1

Based upon item submitted by F. J. Samaniego - UC Davis
        Multiple Choice
SIMPLE/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 5    Computation
D= 3    General
                ***Statistical Table Necessary***

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Back to this chapter's Contents


1440-1

Item is still being reviewed
        Multiple Choice
SIMPLE/CI         PROPORTION
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS        DESCRSTAT/P       PARAMETRIC

T= 5    Comprehension
D= 3    General
                ***Multiple Parts***
                ***Statistical Table Necessary***

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1441-2

Based upon item submitted by F. J. Samaniego - UC Davis
        Multiple Choice
PROPORTION        SIMPLE/CI
        DESCRSTAT/P       PARAMETRIC        STATISTICS
        CONFIDENCEINTERV  ESTIMATION        CONCEPT

T= 5    Computation
D= 3    General
                ***Statistical Table Necessary***

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Back to this chapter's Contents


1443-1

Based upon item submitted by F. J. Samaniego - UC Davis
        Multiple Choice
SIMPLE/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T=10    Application
D= 4    General
                ***Statistical Table Necessary***

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1443-2

Based upon item submitted by F. J. Samaniego - UC Davis
        Multiple Choice
SIMPLE/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 5    Computation
D= 2    General
                ***Statistical Table Necessary***

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Back to this chapter's Contents


1445-1

Based upon item submitted by F. J. Samaniego - UC Davis
        Multiple Choice
SIMPLE/CI
        TDISTRIBUTION     CONFIDENCEINTERV  ESTIMATION
        CONCEPT           STATISTICS        PROBDISTRIBUTION
        PROBABILITY

T= 5    Computation
D= 3    General
                ***Statistical Table Necessary***

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1446-1

Based upon item submitted by F. J. Samaniego - UC Davis
        Multiple Choice
SIMPLE/CI
        VARIANCE          STANDERROROFMEAN  ZSCORE
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS        DESCRSTAT/P       PARAMETRIC
        STANDUNITS/NORMA  PROBDISTRIBUTION  PROBABILITY

T=10    Computation
D= 3    General
                ***Calculator Necessary***
                ***Statistical Table Necessary***

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1447-1

Based upon item submitted by F. J. Samaniego - UC Davis
        Multiple Choice
SIMPLE/CI
        TSCORE            VARIANCE          STANDERROROFMEAN
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS        STANDUNITS/NORMA  PROBDISTRIBUTION
        PROBABILITY       DESCRSTAT/P       PARAMETRIC

T=10    Computation
D= 3    General
                ***Calculator Necessary***
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1448-2

Based upon item submitted by F. J. Samaniego - UC Davis
        Multiple Choice
SIMPLE/CI         PROPORTION
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS        DESCRSTAT/P       PARAMETRIC

T= 5    Computation
D= 3    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1449-1

Based upon item submitted by F. J. Samaniego - UC Davis
        Multiple Choice
SIMPLE/CI         STANDERROROFMEAN
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS        DESCRSTAT/P       PARAMETRIC

T= 5    Computation
D= 3    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1454-1

Item is still being reviewed
        Multiple Choice
SIMPLE/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 5    Application
D= 5    Biological Sciences Economics
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1455-1

Based upon item submitted by D. Kleinbaum - Univ of North Carolina
        Multiple Choice
SIMPLE/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 2    Comprehension
D= 3    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1455-2

Based upon item submitted by D. Kleinbaum - Univ of North Carolina
        Multiple Choice
SIMPLE/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 5    Application
D= 5    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1456-1

Item is still being reviewed
        Multiple Choice
SIMPLE/CI         MEAN
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS        DESCRSTAT/P       PARAMETRIC

T= 2    Comprehension
D= 3    General

Back to review this question

Back to this chapter's Contents


1457-1

Item is still being reviewed
        Multiple Choice
SIMPLE/CI         STANDERROROFMEAN  MEAN
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS        DESCRSTAT/P       PARAMETRIC

T=10    Computation
D= 3    General             Psychology
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1459-1

Item is still being reviewed
        Multiple Choice
SIMPLE/CI
        MEAN              STANDERROROFMEAN  CONFIDENCEINTERV
        ESTIMATION        CONCEPT           STATISTICS
        DESCRSTAT/P       PARAMETRIC

T= 2    Computation
D= 2    General
              ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1460-2

Item is still being reviewed
        Multiple Choice
SIMPLE/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 2    Computation
D= 3    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1461-2

Item is still being reviewed
        Multiple Choice
SIMPLE/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 2    Comprehension
D= 3    General             Education

Back to review this question

Back to this chapter's Contents


1463-1

Item is still being reviewed
        Multiple Choice
SIMPLE/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 2    Comprehension
D= 3    General             Education

Back to review this question

Back to this chapter's Contents


1463-2

Item is still being reviewed
        Multiple Choice
SIMPLE/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 5    Application
D= 4    General             Education
                ***Calculator Necessary***

Back to review this question

Back to this chapter's Contents


1464-1

Item is still being reviewed
        Multiple Choice
SIMPLE/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 2    Comprehension
D= 3    General

Back to review this question

Back to this chapter's Contents


1469-2

Based upon item submitted by CIID - UNH
        Numerical Answer
SIMPLE/CI
        MEAN              CONFIDENCEINTERV  ESTIMATION
        CONCEPT           STATISTICS        DESCRSTAT/P
        PARAMETRIC

T= 5    Application     Comprehension
D= 3    General
                ***Calculator Necessary***
                ***Multiple Parts***
                ***Statistical Table Necessary***
1                                                                        Page 1470

Back to review this question

Back to this chapter's Contents


1470-1

Item is still being reviewed
        Numerical Answer
SIMPLE/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 5    Application
D= 4    Economics           General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1471-1

Item is still being reviewed
        Numerical Answer
PROPORTION        SIMPLE/CI
        DESCRSTAT/P       PARAMETRIC        STATISTICS
        CONFIDENCEINTERV  ESTIMATION        CONCEPT

T= 5    Computation
D= 2    General
                ***Calculator Necessary***
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1471-2

Item is still being reviewed
        Numerical Answer
SIMPLE/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 5    Computation
D= 1    General
                ***Calculator Necessary***
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1472-1

Based upon item submitted by C. R. Buncher - Cincinnati
        Numerical Answer
SIMPLE/CI
        TDISTRIBUTION     CONFIDENCEINTERV  ESTIMATION
        CONCEPT           STATISTICS        PROBDISTRIBUTION
        PROBABILITY

T= 5    Comprehension   Computation
D= 3    General             Biological Sciences Natural Sciences
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1472-2

Based upon item submitted by G. Miaoulis - Wright State Univ.
        Numerical Answer
SIMPLE/CI         STANDERROROFMEAN
        MEAN              I650I             CONFIDENCEINTERV
        ESTIMATION        CONCEPT           STATISTICS
        DESCRSTAT/P       PARAMETRIC

T= 5    Application     Comprehension
D= 4    General             Business
                ***Calculator Necessary***
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1473-1

Item is still being reviewed
        Numerical Answer
PROPORTION        SIMPLE/CI
        STANDERROR/OTHER  DESCRSTAT/P       PARAMETRIC
        STATISTICS        CONFIDENCEINTERV  ESTIMATION
        CONCEPT

T= 5    Computation
D= 3    Business            General
                ***Calculator Necessary***
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1473-3

Based upon item submitted by W. J. Hall - Univ. of Rochester
        Numerical Answer
SIMPLE/CI
        STANDERROROFMEAN  I650I             CONFIDENCEINTERV
        ESTIMATION        CONCEPT           STATISTICS
        DESCRSTAT/P       PARAMETRIC

T= 5    Computation     Comprehension
D= 4    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1474-2

Based upon item submitted by W. J. Hall - Univ. of Rochester
        Numerical Answer
PROPORTION        SIMPLE/CI
        DESCRSTAT/P       PARAMETRIC        STATISTICS
        CONFIDENCEINTERV  ESTIMATION        CONCEPT

T=10    Comprehension   Computation
D= 4    General
                ***Calculator Necessary***
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1478-1

Based upon item submitted by S. Selvin - UC Berkeley
        Numerical Answer
SIMPLE/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 5    Computation
D= 3    Biological Sciences General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1478-2

Based upon item submitted by K. Gorowara - Wright State U.
        Numerical Answer
SIMPLE/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 5    Application
D= 6    General             Business
                ***Calculator Necessary***

Back to review this question

Back to this chapter's Contents


1480-1

Based upon item submitted by J. Warren - UNH
        Numerical Answer
SIMPLE/CI         PROPORTION
        I650I             CONFIDENCEINTERV  ESTIMATION
        CONCEPT           STATISTICS        DESCRSTAT/P
        PARAMETRIC

T= 5    Comprehension
D= 4    General
                ***Calculator Necessary***
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1481-1

Based upon item submitted by J. Warren - UNH
        Numerical Answer
SIMPLE/CI         STANDERROROFMEAN
        MEAN              I650I             CONFIDENCEINTERV
        ESTIMATION        CONCEPT           STATISTICS
        DESCRSTAT/P       PARAMETRIC

T= 5    Computation
D= 4    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1481-2

Item is still being reviewed
        Numerical Answer
PROPORTION        SIMPLE/CI
        DESCRSTAT/P       PARAMETRIC        STATISTICS
        CONFIDENCEINTERV  ESTIMATION        CONCEPT

T= 5    Computation
D= 4    General
                ***Calculator Necessary***
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1482-1

Item is still being reviewed
        Numerical Answer
SIMPLE/CI         MEAN
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS        DESCRSTAT/P       PARAMETRIC

T=10    Computation     Comprehension
D= 4    General
                ***Multiple Parts***
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1483-1

Item is still being reviewed
        Numerical Answer
SIMPLE/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 5    Comprehension   Computation
D= 2    General
                ***Multiple Parts***
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1484-1

Item is still being reviewed
        Numerical Answer
SIMPLE/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 5    Computation     Comprehension
D= 4    General             Business            Economics
                ***Calculator Necessary***
                ***Multiple Parts***
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1485-1

Item is still being reviewed
        Numerical Answer
SIMPLE/CI         MEAN
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS        DESCRSTAT/P       PARAMETRIC

T= 5    Computation
D= 3    General             Social Sciences     Sociology
                ***Calculator Necessary***
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1486-1

Item is still being reviewed
        Numerical Answer
SIMPLE/CI         MEAN
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS        DESCRSTAT/P       PARAMETRIC

T= 5    Computation
D= 3    General             Psychology          Social Sciences
                ***Calculator Necessary***
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1487-1

Item is still being reviewed
        Numerical Answer
SIMPLE/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 5    Computation
D= 2    Sociology           General
                ***Calculator Necessary***
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1488-1

Item is still being reviewed
        Numerical Answer
SIMPLE/CI
        MEAN              CONFIDENCEINTERV  ESTIMATION
        CONCEPT           STATISTICS        DESCRSTAT/P
        PARAMETRIC

T= 5    Computation
D= 3    General             Sociology           Social Sciences
                ***Calculator Necessary***
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1491-2

Based upon item submitted by R. F. Tate - U. of Oregon
        Short Answer
SIMPLE/CI
        STANDERROROFMEAN  MEAN              I650I
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS        DESCRSTAT/P       PARAMETRIC

T= 5    Comprehension   Computation
D= 5    General
                ***Multiple Parts***
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1495-1

Based upon item submitted by L. J. Tashman - U. of Vermont
        Short Answer
SIMPLE/CI         PROPORTION
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS        DESCRSTAT/P       PARAMETRIC

T=10    Computation
D= 4    General

Back to review this question

Back to this chapter's Contents


1499-3

Based upon item submitted by J. Warren - UNH
        Short Answer
PROPORTION        SIMPLE/CI
        I650I             DESCRSTAT/P       PARAMETRIC
        STATISTICS        CONFIDENCEINTERV  ESTIMATION
      CONCEPT

T= 5    Comprehension   Computation
D= 4    General             Social Sciences

Back to review this question

Back to this chapter's Contents


1500-1

Based upon item submitted by J. Warren - UNH
        Short Answer
SIMPLE/CI         PROPORTION
        TYPE1ERROR        I650I             CONFIDENCEINTERV
        ESTIMATION        CONCEPT           STATISTICS
        DESCRSTAT/P       PARAMETRIC

T= 5    Comprehension
D= 4    General             Social Sciences

Back to review this question

Back to this chapter's Contents


1501-1

Based upon item submitted by J. Warren - UNH
        Short Answer
SIMPLE/CI         STANDERROROFMEAN
        TDISTRIBUTION     MEAN              SIMPLEDATASET
        I650I             CONFIDENCEINTERV  ESTIMATION
        CONCEPT           STATISTICS        DESCRSTAT/P
        PARAMETRIC        PROBDISTRIBUTION  PROBABILITY
        MISCELLANEOUS     I650/TEMPORARY

T=10    Application
D= 6    General             Business
                ***Calculator Necessary***
                ***Multiple Parts***
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1509-1

Item is still being reviewed
        True/False
SIMPLE/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 2    Computation
D= 6    General

Back to review this question

Back to this chapter's Contents


1509-2

Based upon item submitted by R. Pruzek - SUNY at Albany
        True/False
SIMPLE/CI
        TYPE1ERROR        I650I             CONFIDENCEINTERV
        ESTIMATION        CONCEPT           STATISTICS

T= 2    Comprehension
D= 2    General

Back to review this question

Back to this chapter's Contents


1510-1

Based upon item submitted by R. Pruzek - SUNY at Albany
        True/False
SIMPLE/CI         TYPE1ERROR
        TYPE2ERROR        CONFIDENCEINTERV  ESTIMATION
        CONCEPT           STATISTICS

T= 5    Comprehension
D= 3    General

Back to review this question

Back to this chapter's Contents


1510-2

Based upon item submitted by R. Pruzek - SUNY at Albany
        True/False
SIMPLE/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 2    Comprehension
D= 2    General

Back to review this question

Back to this chapter's Contents


1511-2

Based upon item submitted by W. J. Hall - Univ. of Rochester
        True/False
SIMPLE/CI         ESTIMATION/OTHER
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 2    Comprehension
D= 2    General

Back to review this question

Back to this chapter's Contents


1513-3

Item is still being reviewed
        True/False
SIMPLE/CI         SAMPLESIZE
        TYPE1ERROR        CONFIDENCEINTERV  ESTIMATION
        CONCEPT           STATISTICS        SAMPLING

T= 2    Comprehension
D= 2    General

Back to review this question

Back to this chapter's Contents


1522-2

Item is still being reviewed
        Multiple Choice
PROPORTION        OTHER/CI          ESTIMATION/OTHER
        OTHER/Z           DESCRSTAT/P       PARAMETRIC
        STATISTICS        CONFIDENCEINTERV  ESTIMATION
        CONCEPT           ZTEST

T= 5    Computation
D= 5    General             Education           Social Sciences
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1523-1

Item is still being reviewed
        Multiple Choice
OTHER/CI
        MEAN              CONFIDENCEINTERV  ESTIMATION
        CONCEPT           STATISTICS        DESCRSTAT/P
        PARAMETRIC

T= 2    Comprehension
D= 4    General             Education

Back to review this question

Back to this chapter's Contents


1547-1

Based upon item submitted by R. Pruzek - SUNY at Albany
        True/False
OTHER/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 5    Comprehension
D= 3    General

Back to review this question

Back to this chapter's Contents


1547-3

Based upon item submitted by W. J. Hall - Univ. of Rochester
        True/False
OTHER/CI
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        STATISTICS

T= 2    Comprehension
D= 4    General

Back to review this question

Back to this chapter's Contents


1548-2

Based upon item submitted by J. Warren - UNH
        Definition
OTHER/CI
        I650I             CONFIDENCEINTERV  ESTIMATION
        CONCEPT           STATISTICS

T= 5    Comprehension
D= 3    General

Back to review this question

Back to this chapter's Contents


1551-2

Item is still being reviewed
        Multiple Choice
ESTIMATION/OTHER  SAMPLE
        ESTIMATION        CONCEPT           STATISTICS
        SAMPLING

T= 2    Comprehension
D= 2    General

Back to review this question

Back to this chapter's Contents


1566-1

Item is still being reviewed
        Multiple Choice
CENTRALLIMITTHM
        SAMPLESIZE        SAMPLINGDISTRIB   CONCEPT
        STATISTICS        SAMPLING

T= 2    Comprehension
D= 3    General

Back to review this question

Back to this chapter's Contents


1566-3

Based upon item submitted by W. J. Hall - Univ. of Rochester
        Multiple Choice
CENTRALLIMITTHM   VARIANCE/OTHER
        CONCEPT           STATISTICS        DESCRSTAT/P
        PARAMETRIC

T= 2    Comprehension
D= 2    General

Back to review this question

Back to this chapter's Contents


1568-1

Item is still being reviewed
        Multiple Choice
CENTRALLIMITTHM
        CONCEPT           STATISTICS

T= 2    Comprehension
D= 3    General

Back to review this question

Back to this chapter's Contents


1568-2

Item is still being reviewed
        Multiple Choice
CENTRALLIMITTHM   STANDERROROFMEAN
        CONCEPT           STATISTICS        DESCRSTAT/P
        PARAMETRIC

T= 2    Comprehension
D= 3    General

Back to review this question

Back to this chapter's Contents


1569-1

Item is still being reviewed
        Multiple Choice
CENTRALLIMITTHM
        CONCEPT           STATISTICS

T= 2    Comprehension
D= 6    General             Education

Back to review this question

Back to this chapter's Contents


1570-1

Item is still being reviewed
        Multiple Choice
CENTRALLIMITTHM   SAMPLINGDISTRIB
        MEAN              CONCEPT           STATISTICS
        SAMPLING          DESCRSTAT/P       PARAMETRIC

T= 2    Comprehension
D= 3    General

Back to review this question

Back to this chapter's Contents


1572-3

Item is still being reviewed
        Numerical Answer
CENTRALLIMITTHM
        CONCEPT           STATISTICS

T= 5    Application
D= 7    General
                ***Statistical Table Necessary***

Back to review this question

Back to this chapter's Contents


1576-1

Item is still being reviewed
        Short Answer
SAMPLINGDISTRIB   SAMPLESIZE        CENTRALLIMITTHM
        SAMPLING          STATISTICS        CONCEPT

T= 5    Comprehension
D= 4    General
                ***Multiple Parts***

Back to review this question

Back to this chapter's Contents


1577-1

Based upon item submitted by L. J. Tashman - U. of Vermont
        Short Answer
CENTRALLIMITTHM   SAMPLINGDISTRIB   STANDERROROFMEAN
        I650I             CONCEPT           STATISTICS
        SAMPLING          DESCRSTAT/P       PARAMETRIC

T=10    Comprehension
D= 4    General
                ***Multiple Parts***

Back to review this question

Back to this chapter's Contents


1578-1

Based upon item submitted by S. Selvin - UC Berkeley
  Short Answer
CENTRALLIMITTHM
        CONCEPT           STATISTICS

T= 5    Comprehension
D= 3    General
                ***Multiple Parts***

Back to review this question

Back to this chapter's Contents


1580-2

Based upon item submitted by H. B. Christensen - BYU
        True/False
CENTRALLIMITTHM
        CONCEPT           STATISTICS

T= 2    Computation
D= 1    General

Back to review this question

Back to this chapter's Contents


1581-1

Based upon item submitted by H. B. Christensen - BYU
        True/False
CENTRALLIMITTHM
        CONCEPT           STATISTICS

T= 2    Comprehension
D= 2    General

Back to review this question

Back to this chapter's Contents


1581-2

Item is still being reviewed
        True/False
CENTRALLIMITTHM
        CONCEPT           STATISTICS

T= 2    Comprehension
D= 3    General

Back to review this question

Back to this chapter's Contents


1582-2

Based upon item submitted by R. Pruzek - SUNY at Albany
        True/False
MEAN              CENTRALLIMITTHM   STANDERROROFMEAN
        SAMPDIST/C        SAMPLESIZE        DESCRSTAT/P
        PARAMETRIC        STATISTICS        CONCEPT
        ESTIMATION        SAMPLING

T= 5    Comprehension
D= 4    General

Back to review this question

Back to this chapter's Contents


1583-2

Item is still being reviewed
        True/False
CENTRALLIMITTHM
        CONCEPT           STATISTICS

T= 5    Comprehension
D= 3    General

Back to review this question

Back to this chapter's Contents


1584-2

Item is still being reviewed
   True/False
CENTRALLIMITTHM
        CONCEPT           STATISTICS

T= 2    Computation
D= 1    General

Back to review this question

Back to this chapter's Contents


1585-2

Item is still being reviewed
        True/False
SAMPLINGDISTRIB   CENTRALLIMITTHM
        SAMPLING          STATISTICS        CONCEPT

T= 2    Comprehension
D= 3    General

Back to review this question

Back to this chapter's Contents


1691-1

Item is still being reviewed
        True/False
TYPE1ERROR
        CONCEPT           STATISTICS

T= 2    Comprehension
D= 2    General

Back to review this question

Back to this chapter's Contents


1730-1

Based upon item submitted by W. Federer - Cornell
        Fill-in
SCOPEOFINFERENCE  SAMPLE
        CONCEPT           STATISTICS        SAMPLING

T= 2    Comprehension
D= 3    General

Back to review this question

Back to this chapter's Contents


1791-3

Item is still being reviewed
        True/False
PROPORTION        MEAN
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 4    General

Back to review this question

Back to this chapter's Contents


1815-1

Item is still being reviewed
        Multiple Choice
SAMPLINGDISTRIB   MEAN              VARIANCE
        SAMPLING          STATISTICS        DESCRSTAT/P
        PARAMETRIC

T= 2    Computation     Comprehension
D= 2    General

Back to review this question

Back to this chapter's Contents


1820-2

Item is still being reviewed
        Multiple Choice
SAMPLINGDISTRIB   MEAN
        SAMPLING          STATISTICS        DESCRSTAT/P
        PARAMETRIC

T= 2    Comprehension
D= 3    General             Education

Back to review this question

Back to this chapter's Contents


1857-4

Based upon item submitted by R. Pruzek - SUNY at Albany
        True/False
MEAN              SAMPLINGDISTRIB
        DESCRSTAT/P       PARAMETRIC        STATISTICS
        SAMPLING

T= 2    Comprehension
D= 2    General

Back to review this question

Back to this chapter's Contents


1858-3

Item is still being reviewed
        True/False
MEAN              STANDARDDEVIATIO
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 3    General

Back to review this question

Back to this chapter's Contents


1859-1

Item is still being reviewed
        True/False
SAMPLINGDISTRIB   STANDERROROFMEAN  MEAN
        SAMPLING          STATISTICS        DESCRSTAT/P
        PARAMETRIC

T= 2    Comprehension   Application
D= 3    General

Back to review this question

Back to this chapter's Contents


1865-1

Item is still being reviewed
        Multiple Choice
VARIABILITY/P     VARIANCE/OTHER
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Computation     Comprehension
D= 4    General

Back to review this question

Back to this chapter's Contents


1869-1

Based upon item submitted by A. Bugbee - UNH
        Short Answer
VARIABILITY/P     STANDARDDEVIATIO
        I650I             DESCRSTAT/P       PARAMETRIC
        STATISTICS

T= 5    Comprehension
D= 2    General

Back to review this question

Back to this chapter's Contents


1869-2

Based upon item submitted by J. Warren - UNH
        Short Answer
VARIABILITY/P     STANDERROR/OTHER
        I650I             DESCRSTAT/P       PARAMETRIC
        STATISTICS

T= 5    Comprehension
D= 3    General

Back to review this question

Back to this chapter's Contents


1891-2

Item is still being reviewed
        Short Answer
STANDARDDEVIATIO  STANDERROROFMEAN
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 3    General

Back to review this question

Back to this chapter's Contents


1898-1

Based upon item submitted by R. Pruzek - SUNY at Albany
        True/False
STANDERROROFMEAN  STANDARDDEVIATIO
        SAMPLESIZE        SAMPLINGDISTRIB   DESCRSTAT/P
        PARAMETRIC        STATISTICS        SAMPLING

T= 5    Comprehension
D= 4    General

Back to review this question

Back to this chapter's Contents


1898-2

Based upon item submitted by W. J. Hall - Univ. of Rochester
        True/False
STANDARDERROR     STANDARDDEVIATIO  SAMPLINGDISTRIB
        PARAMETRIC        STATISTICS        DESCRSTAT/P       
        SAMPLING

T= 2    Comprehension
D= 3    General

Back to review this question

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1901-1

Item is still being reviewed
        True/False
STANDARDDEVIATIO  STANDERROR/OTHER
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

Back to review this question

Back to this chapter's Contents


1905-2

Item is still being reviewed
        Multiple Choice
VARIANCE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 5    Computation
D= 2    General

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1927-1

Based upon item submitted by S. Selvin - UC Berkeley
        Numerical Answer
VARIANCE          STANDERROR/OTHER
        OTHER/RV          DESCRSTAT/P       PARAMETRIC
        STATISTICS        RANDOMVARIABLES   PROBABILITY

T=10    Computation     Comprehension
D= 6    General
                ***Calculator Necessary***
                ***Multiple Parts***

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1928-1

Based upon item submitted by J. Warren - UNH
        Numerical Answer
VARIANCE          VARIANCE/OTHER
        STANDERROROFMEAN  I650I             DESCRSTAT/P
        PARAMETRIC        STATISTICS

T= 5    Comprehension
D= 3    General
                ***Multiple Parts***

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1951-3

Based upon item submitted by R. Pruzek - SUNY at Albany
        True/False
VARIANCE          SAMPLINGDISTRIB
        DESCRSTAT/P       PARAMETRIC        STATISTICS
        SAMPLING

T= 2    Comprehension
D= 3    General

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1959-1

Item is still being reviewed
        Multiple Choice
STANDERROROFMEAN
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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1960-2

Based upon item submitted by B. Weir - N. C. State & Massey Univ.
        Multiple Choice
STANDERROROFMEAN
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Computation     Comprehension
D= 2    General

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1962-1

Item is still being reviewed
        Multiple Choice
STANDERROROFMEAN
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Computation     Comprehension
D= 2    General
                ***Calculator Necessary***
                ***Statistical Table Necessary***

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1963-2

Based upon item submitted by R. F. Tate - U. of Oregon
        Multiple Choice
STANDERROROFMEAN  SAMPLINGDISTRIB
        CENTRALLIMITTHM   I650I             DESCRSTAT/P
        PARAMETRIC        STATISTICS        SAMPLING
        CONCEPT

T= 2    Computation     Comprehension
D= 3    General

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1964-1

Based upon item submitted by R. Pruzek - SUNY at Albany
        Multiple Choice
STANDERROROFMEAN
        SAMPLINGDISTRIB   I650I             DESCRSTAT/P
        PARAMETRIC        STATISTICS        SAMPLING

T= 2    Comprehension
D= 2    General

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1964-3

Based upon item submitted by W. J. Hall - Univ. of Rochester
        Multiple Choice
STANDERROROFMEAN  SAMPLESIZE
        DESCRSTAT/P       PARAMETRIC        STATISTICS
        SAMPLING

T= 2    Comprehension
D= 1    General

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1966-1

Item is still being reviewed
        Multiple Choice
STANDERROROFMEAN
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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1966-3

Item is still being reviewed
        Multiple Choice
STANDERROROFMEAN
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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1967-1

Item is still being reviewed
        Multiple Choice
STANDERROROFMEAN
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Computation
D= 2    General
                ***Calculator Necessary***

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1968-1

Item is still being reviewed
        Multiple Choice
STANDERROROFMEAN
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 6    General             Education

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1968-2

Item is still being reviewed
        Multiple Choice
SAMPLINGDISTRIB   STANDERROROFMEAN
        SAMPLING          STATISTICS        DESCRSTAT/P
        PARAMETRIC

T= 2    Comprehension
D= 3    General

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1969-1

Item is still being reviewed
        Multiple Choice
STANDERROROFMEAN
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 4    General             Education

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1969-2

Item is still being reviewed
        Multiple Choice
STANDERROROFMEAN
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 5    General             Education

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1971-1

Based upon item submitted by J. Warren - UNH
        Essay                          ***Calculus Necessary***
STANDERROROFMEAN
        I650I             DESCRSTAT/P       PARAMETRIC
        STATISTICS

T= 5    Comprehension
D= 5    General             General

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1977-4

Item is still being reviewed
        True/False
STANDERROROFMEAN
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 3    General

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1978-1

Based upon item submitted by R. Pruzek - SUNY at Albany
        True/False
STANDERROROFMEAN
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 5    Comprehension
D= 3    General

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1978-3

Based upon item submitted by R. Pruzek - SUNY at Albany
        True/False
STANDERROROFMEAN  VARIANCE/OTHER
        SAMPDIST/C        CENTRALLIMITTHM   DESCRSTAT/P
        PARAMETRIC        STATISTICS        ESTIMATION
        CONCEPT

T= 5    Comprehension
D= 3    General

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1979-3

Based upon item submitted by W. J. Hall - Univ. of Rochester
        True/False
SAMPLESIZE        STANDERROROFMEAN
        SAMPLINGERROR     SAMPLING          STATISTICS
        DESCRSTAT/P       PARAMETRIC

T= 2    Comprehension
D= 2    General

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1981-1

Based upon item submitted by J. L. Mickey -UCLA
        True/False
STANDERROROFMEAN
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 3    General

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2074-2

Item is still being reviewed
        Multiple Choice
STANDERROR/OTHER
        MEDIAN            DESCRSTAT/P       PARAMETRIC
        STATISTICS        DESCRSTAT/NP      NONPARAMETRIC

T= 2    Comprehension
D= 4    General             Education

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2074-4

Item is still being reviewed
        Fill-in
SAMPLINGDISTRIB   STANDERROR/OTHER
        SAMPLING          STATISTICS        DESCRSTAT/P
        PARAMETRIC

T= 2    Comprehension
D= 3    General

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2103-1

Item is still being reviewed
        Multiple Choice
SAMPLINGDISTRIB   VARIANCE/OTHER
        SAMPLING          STATISTICS        DESCRSTAT/P
        PARAMETRIC

T= 2    Comprehension
D= 2    General

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2857-1

Item is still being reviewed
        Multiple Choice
SAMPLINGDISTRIB
        SAMPLING          STATISTICS

T= 2    Comprehension
D= 2    General

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2859-1

Item is still being reviewed
        Multiple Choice
SAMPLINGDISTRIB
        SAMPLING          STATISTICS

T= 2    Comprehension
D= 3    General             Education

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2860-3

Item is still being reviewed
        Multiple Choice
SAMPLINGDISTRIB
        SAMPLING          STATISTICS

T= 2    Comprehension
D= 2    General

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2862-4

Item is still being reviewed
        Short Answer
SAMPLE            SAMPLINGDISTRIB
        SAMPLING          STATISTICS

T= 5    Comprehension
D= 3    General

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2866-1

Based upon item submitted by D. Kleinbaum - Univ of North Carolina
        True/False
SAMPLESIZE        SAMPLINGDISTRIB
        STANDERROROFMEAN  SAMPLING          STATISTICS
        DESCRSTAT/P       PARAMETRIC

T= 2    Computation     Comprehension
D= 2    General

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2867-3

Item is still being reviewed
        True/False
SAMPLINGDISTRIB
        SAMPLING          STATISTICS

T= 2    Comprehension
D= 4    General

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2889-1

Item is still being reviewed
        True/False
SAMPLESIZE
        VARIABILITY/P     SAMPLING          STATISTICS
        DESCRSTAT/P       PARAMETRIC

T= 2    Comprehension
D= 4    General

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