# Practice Questions for Business Statistics

## Contents:

729-3 A population is:

777-2 FACTOR

1565-1 Target Population.

2726-2 What is a placebo?

2752-1 FACTOR

2766-1 CONTROLLED INVESTIGATION

## Questions:

28-1

```    Q:  Any characteristic of a population distribution may properly be
referred to as a

a.  standard deviation.
b.  raw score.
c.  standard score.
d.  standard error.
e.  parameter.
```

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36-2

```    Q:  A researcher studying consumer buying habits questions every twentieth
person entering Publix Supermarket.  He asks, "How many times per week
do you go grocery shopping?"  He then records the answer as T.

i)  Then [T = 3] is

a) a sample space    b) a random variable    c) an event of interest
d) b and c           e) none of these

Suppose the researcher questions 427 shoppers during the survey.

ii)  Give an example relating to this survey of the kind of question
which the tools of descriptive statistics can be used to answer.

iii)  Give an example relating to this survey of the kind of question
which the tools of inferential statistics can be used to answer.
```

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721-3

```    Q:  A factor that is varied by an experimenter in order to
assess its effect is known as a(n):

a.  dependent variable
b.  independent variable
c.  control variable
d.  none of the above
```

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729-1

```    Q:  Characteristics of a population are called ________, while those of a
sample are termed _________.

a.  statistics;  measures           d.  statistics;  parameters
b.  parameters;  statistics         e.  none of these
c.  statistics;  variables
```

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729-3

```    Q:  A population is:

a.  a number or measurement collected as a result of observation
b.  a subset of a population
c.  a characteristic of a population which is measurable
d.  a complete set of individuals, objects, or measurements having
some common observable characteristics
e.  none of these
```

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733-1

```    Q:  Suppose  we  are  interested  in the average reading achievement test
score of the currently enrolled students in Edison Elementary School.

i.  The set of test scores for Miss Grady's class comprise

a. an element.
b. a sample.
c. a statistic.
d. a population.

ii.  The average score of all students in Edison School is a

a. sample.
b. statistic.
c. parameter.
d. variable.
```

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743-2

```    Q:  True or False?

Populations are always infinite.
```

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744-1

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

Statistical interpretation depends not only upon statistical ideas
but also upon "ordinary" clear thinking regarding ideas of cause and
effect.
```

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746-2

```    Q:  True or False?

The smallest unit used in the selection process of the sample is
called a sampling unit.
```

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777-2

```    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.

FACTOR
```

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1131-2

```    Q:  An experiment is conducted to determine if the use of certain specified
amounts of a drug will increase the IQ scores differentially for high
and low anxious students in the fifth grade.

In this experiment, IQ serves as:

a)  a primary independent variable
b)  a moderator variable
c)  a dependent variable
d)  a control variable
e)  an intervening variable.
```

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1132-1

```    Q:  An experiment is conducted to determine if the use of certain specified
amounts of  a  drug will increase the IQ scores differentially for high
and low anxious students in the fifth grade.

In this experiment, anxiety serves as:

a)  a primary independent variable
b)  a moderator variable
c)  a dependent variable
d)  a control variable
e)  an intervening variable.
```

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1132-2

```    Q:  An experiment is conducted to determine if the use of certain specified
amounts of a drug will increase the IQ scores differentially for high
and low anxious students in the fifth grade.

In this experiment, the drug serves as:

a)  a primary independent variable
b)  a moderator variable
c)  a dependent variable
d)  a control variable
e)  an intervening variable.
```

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1134-2

```    Q:  Male students are assigned randomly to either a rote learning (memori-
zation) treatment or to a discovery learning treatment.  At the end of
the experiment, students are tested for their ability to answer ques-
tions on an achievement test.  The results indicate that fast learners
in the discovery treatment do better than the slow learners in this
treatment, but there is no difference in performance between the two
types of learners in the rote treatment.

In this experiment, the achievement test serves as:

a.  a primary independent variable
b.  a moderator variable
c.  a dependent variable
d.  a control variable
e.  an intervening variable
```

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1136-2

```    Q:  Male students are assigned randomly to either a rote learning (memori-
zation) treatment or to a discovery learning treatment.  At the end of
the experiment, students are tested for their ability to answer ques-
tions on an achievement test.  The results indicate that fast learners
in the discovery treatment do better than the slow learners in this
treatment, but there is no difference in performance between the two
types of learners in the rote treatment.

Which of the following names a variable and not a level of a variable?

a.  Male sophomores
b.  High anxious students
d.  Treatment A
e.  All of the above
```

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1141-2

```    Q:  In a study on the effect of reinforcement on learning from pro-
grammed text, two experimental treatments are planned:  reinforce-
ment given after every frame of programmed text or reinforcement
given after every three frames.  Which one of the following control
groups would serve best in this study?

a.  A group which does not read the programmed text material.
b.  A group which reads the programmed material in prose format.
c.  A group which reads the programmed material but does not re-
ceive reinforcement.
d.  A group which reads the programmed text material and rein-
forcement is given at random.
```

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1142-1

```    Q:  The control group in an experiment should be designed to receive:

a.  the opposite of the experiences afforded the experimental group.
b.  the experiences afforded the experimental group except for the
treatment under examination.
c.  the experiences afforded the experimental group except for
receiving the treatment at random.
d.  the experiences which constitute an absence of the experiences
```

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1144-1

```    Q:  A coach in a large high school thinks that ballet training will im-
prove the batting performance of his baseball team.  He decides to
have a randomly selected half of the team take six weeks of ballet
training before the baseball season begins while the other half does
not take such training.  He will then compare the season batting aver-
ages of group A (those with ballet training) and group B (those with-
out ballet training) by comparing the mean of group A with the mean
of group B.

This study would be classified as:

a.  a survey study
b.  an ex post facto study
c.  a correlational study
d.  a trend study
e.  an experimental study
```

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1148-1

```    Q:  A coach in a large high school thinks that ballet training will  improve
the batting performance of his baseball team.  He decides to have a ran-
domly selected half of the team take six weeks of ballet training before
the baseball season begins,  while  the  other  half does not take  such
training.  He will then compare the season batting  averages  of group A
(those with ballet training) and group B (those without ballet training)
by comparing the mean of group A with the mean of group B.

An independent variable is:

a.  ballet training
b.  batting average
c.  runs batted in
d.  the size of the school
e.  the grades the players make in the ballet school
```

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1422-1

```    Q:  A 95% confidnece interval for a population mean will be ______ a
99% confidence interval for the same population mean.  (Both cal-
culations based on the same set of data.)

a.  longer than
b.  shorter than
c.  the same length as
d.  it depends on the particular set of data
e.  none of these
```

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1425-2

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

A confidence interval estimate for a parameter is used to eliminate
the element of chance from estimation.
```

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1426-2

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

Confidence intervals can be shortened by increasing the sample size.
```

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1460-1

```    Q:  If the size of the sample being used is increased, then the width of
a 0.95 confidence interval estimate for a population mean will:

a)  Become narrower.
b)  Become wider.
c)  Not be changed.
d)  The effect on the width cannot be determined from the given
information.
```

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1461-1

```    Q:  Which set of circumstances is most  likely  to  result  in  a  narrow
confidence interval?

a.  large n and a confidence coefficient of .95.
b.  large n and a confidence coefficient of .99.
c.  small n and a confidence coefficient of .95.
d.  small n and a confidence coefficient of .99.
```

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1511-1

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

For a given situation, the longer your confidence interval
is, the lower your confidence in it is.
```

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1513-1

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

Generally, a larger sample size implies a shorter confidence interval.
```

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1513-2

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

Generally a larger sample size implies a larger level of confidence
in estimating a parameter.
```

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1548-1

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

The larger the sample size the wider the confidence interval.
```

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1563-1

```    Q:  A sample is chosen by numbering all the red books in the
library and then choosing the ones that correspond to random
digits in a table.

Is the sample independent?
Is it a simple random sample?
Of what population?

```

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1564-2

```    Q:  True or False?

An important objective of statistics is to draw conclusions about
the population from information obtained from a sample.
```

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1565-1

```    Q:  Define the following term and give an example of its use:

Target Population.
```

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1573-1

```    Q:  All possible samples of size 10 were taken from a particular population.
The mean of all the sample means was found to be 12.7 and the variance
of the sample means was 0.32.

a.  What are the mean and variance of the population?
b.  What would the mean and variance of sample means have been if
the samples had been of size 100?
```

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1727-2

```    Q:  Of a sample of 63 deaths of people aged 12 to 21 in a large metro-
politan area, 52 or 83% were caused by accidents.  The stated con-
clusion is that "teenagers" are accident prone in the sense that
they are more likely to die of accidents than older people or in-
fants.  Do you agree or disagree with the stated conclusion?
```

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1789-1

```    Q:  Around 1970 a research organization sent questionnaires to all of the
15,000 or  so  high  school  systems  in  the  United  States.  These
many as 3,600 schools systems returned answers.  Of these 3,600,  27%
indicated that some of their students used computers.

In  a  recent  speech,  an  authority on the use of computers in high
school education cited this study as evidence that "students  in  27%
of  the high school systems in the United States use computers during
their high school careers."

Do you regard 27% as a trustworthy  estimate  of  the  proportion  of
school  systems  providing  computer  access  in  1970?  Explain your
```

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1832-1

```    Q:  Given:  Population 1:  3, 4, 5
Population 2:  0, 3

Draw all possible samples of size 2 from population 1 with replacement,
and all possible samples of size 3 from population 2 with replacement.

```

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1870-1

```    Q:  Suppose that you have been assigned to study the impact of a new
appliance on the energy demands in a region.  You find that there are
very many brands of this appliance and that there are no obvious
characteristics that suggest differences in energy requirements.  Your
resources will permit an experiment with adequate replication of six
treatments.

a.  How will you select brands?
b.  What parameter(s) associated with treatments will you estimate?
```

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1893-3

```    Q:  Create a simple data set and explain how it would be used
to verify whether a computer program or calculator computes a
population standard deviation or an estimate of the population
standard deviation.
```

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1908-4

```    Q:  A population consists of the numbers [2003, 1999, 2001, 1997, 2000,
2005, 1995].  The variance of the population is:

1)  11.6
2)  the mean deviation
3)  10
4)  2010
5)  none of the above
```

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1911-2

```    Q:  Consider the following data:

-4, 3, 8, -2, 7, 7, 6, 11, 4, 10

The variance (SIGMA**2) for this population of data is:

A. 10.3   D. 21.4
B. 16     E. none of these.
C. 18.3
```

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1952-1

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

If a random sample is sufficiently large its variance will be
very close to SIGMA**2/n.
```

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1961-1

```    Q:  For random samples of size 100 from a normal distribution with mean 92
and standard deviation 25,  the range  of  the middle fifty percent of
sample means is approximately:

(1)  80 to 100
(2)  88 to 96
(3)  90 to 94
(4)  91.7 to 92.3
(5)  90.3 to 93.7
```

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2629-1

```    Q:  What is the importance of randomization in experimental investigation?
```

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2726-2

```    Q:  What is a placebo?
a.  an experimental treatment
b.  a control treatment
c.  a parameter
d.  a statistic
```

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2748-1

```    Q:  True or False?

A treatment effect is the increase or decrease in the size of the
response over what would have been observed had the treatment not
been applied.
```

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2749-1

```    Q:  True or False?

Random assignment of experimental units to treatments is necessary for
the application of most tests involving comparisons among a set of
treatments.
```

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2752-1

```    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.

FACTOR
```

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2752-2

```    Q:  Give an example that could be described by the following phrase.
Your example should not be one given in class or in a handout.

ILLUSTRATION OF FACTORS HELD CONSTANT IN AN INVESTIGATION
```

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2753-1

```    Q:  Give an example that could be described by the following phrase.
Your example should not be one given in class or in a handout.

ILLUSTRATION OF FACTORS NOT HELD CONSTANT BUT REGARDED AS NEGLIGIBLE
```

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2760-1

```    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.

CONTROL OR CHECK TREATMENT
```

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2766-1

```    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.

CONTROLLED INVESTIGATION
```

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2813-1

```    Q:  What are the reasons for sampling?
```

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2814-2

```    Q:  The smallest unit used in the selection process in a sample survey
design is known as the ____________________________ unit.
```

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2814-3

```    Q:  The smallest unit on which a measurement or record in a sample survey
is obtained is known as ___________________________________ unit.
```

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2814-4

```    Q:  The method of choosing individuals from one or more populations is
called the ____________________.
```

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2820-1

```    Q:  The major advantage of a probability sample compared with a non-
probability sample is that

a.  it saves time          c.  it prevents destructive sampling
b.  it costs less          d.  sampling error can be estimated
```

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2822-1

```    Q:  In statistics we speak often of a random sample.  What is a
random sample, and why is randomization so important in
statistics?
```

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2822-3

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

Consider an experiment to test the effectiveness of the Salk Vaccine.
If we intend to use probability theory to guide us in our judgement
about the results, we should be doubtful about the accuracy of our
conclusions since we have used randomization at some level in the
experimental design.
```

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2823-3

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

A random sample is a representative sample.
```

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2824-3

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

Generally, in most applied situations sampling with replacement is
used.
```

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2825-1

```    Q:  True or False?  Explain your answer.

Randomness is less important in a large sample than in a small
sample.
```

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2825-3

```    Q:  A simple random sample is one where

a)  you decide on a sample size and sample proportionately from
the population.
b)  you choose each item with no regard to previous choices.
c)  each item in the population has an equal chance of being chosen.
d)  all of the above are true.
e)  none of the above are true.
```

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2826-1

```    Q:  Which of the following is a necessary condition for a sample to be
random?

a.  Every person in the population has the same likelihood of being
included in the sample.
b.  The choice of the method of selecting individuals from the popu-
lation is governed entirely by chance.
c.  Proportions of various grooups selected are equal to correspond-
ing proportions in the population.
d.  The characteristics of the sample are the same as the characteris-
tics of the population.
e.  None of the above is necessary.
```

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2826-2

```    Q:  A (simple) random sample is defined by

a.  the method of selection.
b.  outcome of selection.
c.  both of the above.
d.  its degree of resemblance to the population.
```

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2827-1

```    Q:  Which of the following is NOT true of simple random sampling?

a.  Whether or not a sample is random cannot be told from inspection
of the sample.
b.  Characteristics of a random sample may differ widely from
characteristics of its population.
c.  A sample must be reasonably large to be considered a random sample.
d.  Every element in the population must be given an equal chance for
inclusion in the sample.
```

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2829-1

```    Q:  Samuel Student wanted a random sample of 50 students.  He decided
to choose the first fifty students entering one of the dining halls
at a randomly selected time during the dinner hour.

a.  Is his sample random?  Why or why not?

b.  Is his sample representative?  Why or why not?
```

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2830-2

```    Q:  Suppose that you have been assigned to estimate the height of a
group of corn plants arranged in 4 rows with 50 plants in each row.
You may take measurements of 10 plants.

a.  Outline a method for obtaining a random sample in such a situation.
```

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2831-1

```    Q:     Street                                                    Street
|  |                                                      |  |
|  |                                                      |  |
|  |  +---+    +---+    +---+    +---+    +---+    +---+  |  |
|  |  | 1 |    | 2 |    | 3 |    | 4 |    | 5 |    | 6 |  |  |
|  |  +---+    +---+    +---+    +---+    +---+    +---+  |  |
----+  +------------------------------------------------------+  +----
Street
----------------------------------------------------------------------

You have been instructed to obtain interviews from 2 randomly selected
households in the above set of 6 houses.  Each house contains one
household.
a)  Which houses would you visit to obtain the interviews?  Indicate how
you would choose these houses.
b)  Suppose that you plan to visit this neighborhood between 1:00 pm and
4:00 pm on a particular day.  How will you provide for the possi-
bility that no one will be available to interview in one or both of
the houses that you have chosen?
c)  Would you expect any differences among these 6 units on the basis
of the above sketch?
```

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2833-2

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

If  you  are  to take a random sample of n = 10 people from a certain
area, you must be careful to replace individuals chosen before drawing
another.
```

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2891-2

```    Q:  Your statistics class

a. is a representative sample of your college student body
b. is not a representative sample of your college student body
c. is not a sample of your college student body
d. none of the above
```

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2902-1

```    Q:  A list or a description of every sampling unit in the universe is
known as the _______________________________.
```

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2904-1

```    Q:  Sampling error occurs because

a.  most interviewers are not accurate in their reports
b.  a sample is used instead of a population
c.  the statistician uses judgement in choosing the sample
d.  all of the above
```

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2904-3

```    Q:  Sampling error, which can be attributed to the fact that only a sample
of values is observed, is

a.  the expected value of a sample statistic.
b.  the difference between a population value and an estimate of that
value.
c.  the variance of a random sample.
d.  the standard error of the mean of random samples.
```

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2921-1

```    Q:  For a daytime house-to-house survey to study women's attitudes about
their role in society, which one of the following errors would be most
likely to occur:

a.)  reporting and processing errors
b.)  interviewer contamination
c.)  non-response
d.)  false information by the respondents
```

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2922-1

```    Q:  In the 1936 Presidential Election Franklin D. Roosevelt defeated Alfred
E. Landon in a landslide vote.  A Landon victory had been predicted by
the Literary Digest, a magazine which ran the oldest, largest, and most
widely publicized of the polls at the time.  The Digest's final predic-
tion was based on ten million sample ballots mailed to prospective vo-
ters and 2.3 million were returned.  The sample of voters was drawn from
lists of automobile and telephone owners.  Despite the massive size
of this sample, it failed to predict a Roosevelt victory, being off the
mark by 19 percentage points.  Explain why the Digest was so wrong.
```

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28-1

```    A:  e.  parameter.

The parameter can be the mean of a population or the standard devi-
ation of a population.  Both mean and standard deviation are charac-
teristics of a population distribution.
```

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36-2

```    A:  i)  c) an event of interest

(T = 3) is one event in a sample space. T is a random variable.

ii)  What is the average number of times people in this sample go
grocery shopping per week?

iii)  What is the average number of times per week people who shop at
Publix Supermarket go grocery shopping?
```

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721-3

```    A:  b.  independent variable
```

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729-1

```    A:  b.  parameters;  statistics
```

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729-3

```    A:  d.  a complete set of individuals, objects, or measurements having
some common observable characteristics
```

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733-1

```    A:   i.  b. a sample.
ii.  c. a parameter.
```

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743-2

```    A:  False.
```

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744-1

```    A:  True.
```

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746-2

```    A:  True
```

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777-2

```    A:  Definition:  The name of a condition, characteristic, quality or
property suspected of being able to affect a response.

Example:     If we write a list of factors suspected of affecting the
productivity of say, tomato plants, we can compile quite
a long list including such things as amount of sunlight,
moisture supply, supply of various nutrient (Nitrogen,
Phosphorus, Potassium, etc.), variety, night temperature,
etc.
```

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1131-2

```    A:  c)  a dependent variable.  (IQ is the response measure in the study.)
```

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1132-1

```    A:  b)  a moderator variable.  (Anxiety may moderate the effect of the drug
on children's IQ.)
```

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1132-2

```    A:  a)  a primary independent variable.  (The drug is being manipulated to
exert an effect on IQ.)
```

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1134-2

```    A:  c.  a dependent variable

The achievement test serves as a dependent variable because
achievement is the response measure.
```

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1136-2

```    A:  c.  Grade point average

All other alternatives are levels or values of variables.
```

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1141-2

```    A:  c.  A group which reads the programmed material but does not

Control group is identical to experimental groups except that
reinforcement, the independent variable, is withheld.
```

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1142-1

```    A:  b.  the experiences afforded the experimental group except for the
treatment under examination.
```

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1144-1

```    A:  e.  an experimental study

This is an experimental study because an independent variable was
manipulated.
```

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1148-1

```    A:  a.  ballet training
```

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1422-1

```    A:  b.  shorter than

When the data set is the same, the length of the confidence
interval depends on the Z or t value used.  This value is
smaller for 95% confidence than for 99% confidence, so it
will result in a smaller interval.
```

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1425-2

```    A:  False, the confidence interval is used to acknowledge the element of
chance in estimation.
```

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1426-2

```    A:  True, other things being equal, the confidence interval will decrease as
sample size increases.
```

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1460-1

```    A:  a)  Become narrower.
```

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1461-1

```    A:  a.  large n and a confidence coefficient of .95.
```

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1511-1

```    A:  False.  For a given situation, the longer your confidence
interval is, the higher your confidence in it is.
```

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1513-1

```    A:  True
```

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1513-2

```    A:  False, the level of confidence (1  -  ALPHA)  is  not  influenced  by
sample size.  However, the interval estimate will be made more precise
(narrower) by the larger sample size for the same level of confidence.
```

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1548-1

```    A:  False - The larger the sample size the narrower the
confidence interval.
```

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1563-1

```    A:  Population: Red books in the library.

Sample: Simple random, because every one of the distinct
samples has an equal chance of being drawn,
where M = sample size, N = number of red books.

Every sample of size M is independent of any other sample
of size M.
```

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1564-2

```    A:  True
```

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1565-1

```    A:  Target  Population  is the totality of elementary units relevant to a
given study.  The working population (frame) and the  gap  constitute
the target population

Example:

In a study to find out average daily consumption of beer per person in
a given restaurant,  the target population will be all the people vis-
iting the restaurant on the day of the survey.
```

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1573-1

```    A:  a.  MU = MU(XBAR) = 12.7
SIGMA(XBAR)**2 = (SIGMA**2)/n
SIGMA**2 = 10 * .32 = 3.2

b.               n = 10
MU(XBAR) = 12.7
SIGMA(XBAR)**2 = .32

If n = 100:
MU(XBAR) = 12.7
SIGMA(XBAR)**2 = 10 * .32/100 = .032
```

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1727-2

```    A:  Teenagers may, in fact, be accident prone, but the data don't support
this conclusion.  If a teenager dies he is likely to die of an acci-
dent, because he is less susceptible to disease and "natural" causes
to which older people and infants are more susceptible.

The sample is not of sufficient size to conclude that teenagers as a
group are accident prone.  The sample may be biased because it is
a large metropolitan area, thus excluding suburban and rural teen-
agers.  It may be that there are more accidents in a metropolitan
area to everyone, not just teenagers, simply because it is a metro-
politan area.

The 83% figure seems high, but no corresponding accident rates are
given for infants and older people.
```

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1789-1

```    A:  No.   Only  about one-quarter of the high school systems responded to
the  questionnaire.   Since  having  a  computer  then  was  probably
regarded  as  a  good  thing,  I  would  expect  that  schools having
computers would be more likely to respond to the  questionnaire  than
those  that didn't. I don't think that a check on non-respondents would
reveal a percentage mean of 27% that used a computer.  (If  the overall
percentage is 27% and that  is the  percentage among  the  respondents,
then it must also be the percentage using computers among the  three-
quarters that didn't respond.  The  above  reasoning indicates  this is
not the case.)
```

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1832-1

```    A:  All possible samples of size 2 from population 1 with replacement:

(3, 3)     (3, 4)     (3, 5)
(4, 3)     (4, 4)     (4, 5)
(5, 3)     (5, 4)     (5, 5)

All possible samples of size 3 from population 2 with replacement:

(0, 0, 0)     (0, 0, 3)     (0, 3, 0)     (0, 3, 3)
(3, 0, 0)     (3, 0, 3)     (3, 3, 0)     (3, 3, 3)

```

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1870-1

```    A:  a.  Randomly select six brands from those available.
b.  Since treatments have been randomly selected, the treatment effects
calculated in this trial can be used to estimate the variance component
due to brands.  This variance indicates the spread of a population of
brand effects having a mean of zero.
```

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1893-3

```    A:  Data set:  1, 1, 3, 5, 5
MU = 3
SIGMA = SQRT (((1-3)**2 + (1-3)**2 + (3-3)**2 + (5=3)**2 + (5-3)**2)/5)
=  SQRT ((4+4+0+4+4)/5)
=  SQRT (16/5)
=  SQRT (3.2)
= 1.79
S = SQRT(16/4)
= 2
Using the above data set, if the standard deviation is given
as two, then it has been calculated as an estimate of the
population standard deviation, if it is given as 1.79, then it has
been calculated as a population standard deviation, and if
neither of these two values result, something is going wrong.
```

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1908-4

```    A:  (3)  10

Coding (X - 2000):  3, -1, 1, -3, 0, 5, -5

Mean = 0
X**2 = 9, 1, 1, 9, 0, 25, 25

SIGMA**2 = (SUM(X**2))/n = 70/7 = 10
```

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1911-2

```    A:  D. 21.4
```

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1952-1

```    A:  False.
If a random sample is sufficiently large its variance will be
very close to SIGMA**2.
```

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1961-1

```    A:  (5)  90.3 to 93.7

XBAR +/- Z*SIGMA/SQRT(n)
92 +/- .675*(25/10)
92 +/- 1.69
(90.3, 93.7)
```

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2629-1

```    A:  Randomization makes the assumption of independent errors appropriate,
and helps to eliminate systematic bias.
```

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2726-2

```    A:  b.  a control treatment
```

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2748-1

```    A:  True
```

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2749-1

```    A:  True
```

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2752-1

```    A:  Definition:  A condition or state that is thought to influence
response.

Example:     Suppose that the response measured is miles per gallon
for a car.  Factors that may influence that response
include:  brand and model of car, driving speed, type
of transmission, driving conditions (city vs. open
highway), driver, etc.  Any condition that can vary and
has some potential of affecting miles per gallon when
it varies may be regarded as a factor with respect to
that response.
```

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2752-2

```    A:  Example:     Suppose we were investigating the relationship between
kind of pot used for boiling water and time required to
bring one quart of water to a boil.  Factors held con-
stant for each experimental unit might include size of
pot, initial temperature of water and pot, amount of
water, source of heat and rate of delivery, person making
a judgement about when boiling begins, atmospheric pres-
sure, and device used to measure elapsed time.  These
factors would be held constant or nearly constant so that
differences in time needed to bring water to a boil would
in fact reflect differences among pots rather than dif-
ferences in other factors.
```

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2753-1

```    A:  Example:     Suppose we were investigating the relationship between
kind of pot used for boiling water and time required to
bring one quart of water to a boil.  If one person con-
ducts the trial, each occasion of starting with cold
water and ending with boiling water will occur at a
different time and the observer will almost certainly
vary in attentiveness or fatigue.  Usually this varia-
tion in the person conducting the trial would be
regarded as negligible.
```

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2760-1

```    A:  Definition:  A condition or state that is included in a treatment
set because it is regarded as standard or a reasonable
reference state.  Often a control or check treatment
corresponds to what is regarded as current practice.

Example:     Suppose that a chemical company wishes to test 5
compounds that are thought to provide protection against
diseases that interfere with seed germination or early
seedling development.  In such a case at least two dif-
ferent kinds of check or control treatments might be
considered for inclusion in the treatment set.  One
check might be a treatment in which seed was not treated
with any chemical so that comparisons could be made be-
tween untreated seed and seed treated with one of the 5
test chemicals.  Another check might be a treatment in
which seed was treated with a compound currently in wide-
spread use.  In either case, the reason for using the
check treatments is to provide for comparison of the test
compounds with what are regarded as common practice (or
common practices) where the test compounds and the check
treatments are subjected to the same experimental condi-
tions.  (There are few groans louder than those that come
from someone who momentarily believes that a test material
has completely prevented disease only to find that the un-
treated check or standard also is disease free.)
```

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2766-1

```    A:  Definition:  An inquiry in which it is possible to assign treatments to
test units and to arrange matters so that mean differences
in response to treatment provide an indication of the in-
fluence of treatments only.

Example:     Suppose that the treatments to be assessed were 4 asking
prices for a type of house, that the response was time to
sell, and that we could control the assignment of asking
prices to a large number of houses.  Then we should be able
to conduct a controlled investigation that will allow us
to estimate differences in selling time due to asking price
in a manner where other complicating factors are constant
or balanced out.  This would be in contrast to the usual
situation where asking price and time to sell can be ob-
served only in circumstances where other complicating
factors are not balanced out but often are closely linked
to asking price.  (Then it's often not possible to say
whether a difference in selling time is due to price,
location, style, salesman, etc.).
```

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2813-1

```    A:  Sampling is used when:

1.  it will yield more accurate results than a census
2.  the population is infinite
3.  there is a limited amount of time available
4.  the nature of the test is destructive
5.  the cost of gathering the data is a factor.
```

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2814-2

```    A:  The smallest unit used in the selection process in a sample survey
design is known as the sampling unit.
```

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2814-3

```    A:  The smallest unit on which a measurement or record in a sample survey
is obtained is known as the observational or experimental unit.
```

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2814-4

```    A:  The method of choosing individuals from one or more populations is
called the sampling procedure.
```

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2820-1

```    A:  d.  sampling error can be estimated
```

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2822-1

```    A:  A random sample occurs when every observation in the population
has a known (usually equal) chance of becoming part of the sample.
Randomization is important because the probability associated with
the statistics computed from the sample are measurable, thus enabling
one to make valid inferences about the population from which the sample
was drawn.
```

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2822-3

```    A:  False, you would be doubtful only if you had "not used randomization".
```

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2823-3

```    A:  False - A random sample does not guarantee a representative sample.
```

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2824-3

```    A:  False, in most applied situations the population is large enough
that sampling is performed without replacement.
```

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2825-1

```    A:  False.  No matter what the size of the sample, in order for the
theory of probability to apply it is necessary that a probability
sampling technique be used.
```

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2825-3

```    A:  c)  each item in the population has an equal chance of being chosen.
```

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2826-1

```    A:  a.  Every person in the population has the same likelihood of being
included in the sample.
```

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2826-2

```    A:  a.  the method of selection.
```

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2827-1

```    A:  c.  A sample must be reasonably large to be considered a random sample.
```

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2829-1

```    A:  a.  His sample is not random.  Those who eat elsewhere, i.e. those
who live off campus, have no chance of being selected.  Thus, not
every student has the same chance of being selected as every other
and this makes the sample non-random.

b.  There is no way of knowing whether the sample accurately represents
or mirrors the population of students.  For some purposes it may,
for others, maybe not.
```

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2830-2

```    A:  a.  Assign numbers to plants (1 - 200).  Draw a random sample of size 10
using a random numbers table.  Simplest procedure is to use
sampling with replacement.

b.  Advantage is that common formulas for mean and variance apply,
but it's a nuisance to have to number plants and use random
selection.
```

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2831-1

```    A:  a)  I would roll a die or use a random numbers table or some other means
of selecting 2 numbers between 1 and 6 so that each possible pair of
values were equally likely.
b)  Ordinarily the possibility of no one being present in the selected
units should be covered by allowing time for repeat visits at other
times of day.  If a procedure is adopted that allows substitution
of other houses because the selected houses were empty between 1:00
pm and 4:00 pm, the frame sampled is apt to be quite different - a
frame consisting of households in which at least one member remains
at home between 1 and 4.  Among others this would exclude households
in which all members worked.
c)  Sometimes income levels are higher for households living in corner
houses.  If that were the case and samples were drawn over many sets
of households like the above, it would be especially important to
use random selection so that the complete collection of samples
included a proper representation of corner households.
```

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2833-2

```    A:  False, depending upon the situation, a random sample can be taken with
or without replacement.
```

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2891-2

```    A:  b. is not a representative sample of your college student body
```

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2902-1

```    A:  A list or a description of every sampling unit in the universe is
known as the sampling frame.
```

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2904-1

```    A:  b.  a sample is used instead of a population
```

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2904-3

```    A:  b.  the difference between a population value and an estimate of that
value.
```

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2921-1

```    A:  c.)  non-response, because responses would be collected during the
daytime, women who work outside their homes during the daytime would
not be represented in the sample.
```

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2922-1

```    A:  The problem developed because the Digest relied on voluntary response
and such samples are practically always biased.  The respondents repre-
sented a subset of the population owning cars and telephones.  In 1936
this was a limited group and represented a biased sample.  In addition
those returning ballots represent a group with special interest and so
would be more biased.  This was in no way a random or representative
sample.
```

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## Identification:

28-1

```Based upon item submitted by R. Pruzek - SUNY at Albany
Multiple Choice
BASICTERMS/STATS  BASICTERMS/PROB
STATISTICS        PROBABILITY

T= 2    Comprehension
D= 2    General
```

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36-2

```Item is still being reviewed
SCOPEOFINFERENCE  BASICTERMS/STATS  BASICTERMS/PROB
RANDOMVARIABLES   EVENTS            CONCEPT
STATISTICS        PROBABILITY

T= 5    Comprehension
D= 4    General
***Multiple Parts***
```

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721-3

```Based upon item submitted by R. L. Stout & R. M. Paolino - Brown
Multiple Choice
BASICTERMS/STATS
STATISTICS

T= 2    Comprehension
D= 2    General
```

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729-1

```Item is still being reviewed
Multiple Choice
BASICTERMS/STATS  PARAMETRIC
STATISTICS

T= 2    Comprehension
D= 2    General
```

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729-3

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

T= 2    Comprehension
D= 2    General
```

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733-1

```Item is still being reviewed
Multiple Choice
BASICTERMS/STATS  SAMPLE
STATISTICS        SAMPLING

T= 2    Comprehension
D= 2    General             Education           Psychology
***Multiple Parts***
```

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743-2

```Based upon item submitted by W. Federer - Cornell
True/False
POPULATION        BASICTERMS/STATS
CONCEPT           STATISTICS

T= 2    Comprehension
D= 2    General
```

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744-1

```Based upon item submitted by W. J. Hall - Univ. of Rochester
True/False
BASICTERMS/STATS
STATISTICS

T= 2    Comprehension
D= 2    General
```

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746-2

```Based upon item submitted by W. Federer - Cornell
True/False
SAMPLE            BASICTERMS/STATS
SAMPLING          STATISTICS

T= 2    Comprehension
D= 1    General
```

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777-2

```Based upon item submitted by J. Warren - UNH
Definition
BASICTERMS/REG    BASICTERMS/STATS
I650A             REGRESSION        PARAMETRIC
STATISTICS

T= 5    Comprehension
D= 3    General
```

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1131-2

```Item is still being reviewed
Multiple Choice
DESIGN            CONCEPT
STATISTICS

T= 2    Comprehension
D= 1    General             Education           Psychology
```

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1132-1

```Item is still being reviewed
Multiple Choice
DESIGN            CONCEPT
STATISTICS

T= 2    Comprehension
D= 1    General             Education           Psychology
```

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1132-2

```Based upon item submitted by R. Shavelson - UCLA
Multiple Choice
DESIGN            CONCEPT
STATISTICS

T= 2    Comprehension
D= 1    General             Education           Psychology
```

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1134-2

```Based upon item submitted by R. Shavelson - UCLA
Multiple Choice
DESIGN            CONCEPT
STATISTICS

T= 2    Comprehension
D= 1    General             Education           Psychology
```

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1136-2

```Item is still being reviewed
Multiple Choice
DESIGN            CONCEPT
STATISTICS

T= 2    Comprehension
D= 1    General
```

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1141-2

```Item is still being reviewed
Multiple Choice
DESIGN            CONCEPT
STATISTICS

T= 2    Comprehension
D= 1    General             Education           Psychology
```

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1142-1

```Item is still being reviewed
Multiple Choice
EXPERDESIGN/TERM  DESIGN            CONCEPT
ANOVA             PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 1    General
```

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1144-1

```Based upon item submitted by R. Shavelson - UCLA
Multiple Choice
EXPERDESIGN/TERM  CONCEPT           DESIGN
ANOVA             PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 1    General
```

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1148-1

```Based upon item submitted by R. Shavelson - UCLA
Multiple Choice
EXPERDESIGN/TERM  DESIGN            CONCEPT
ANOVA             PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 1    General
```

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1422-1

```Based upon item submitted by J. Inglis
Multiple Choice
CONFIDENCEINTERV  TYPE1ERROR
ESTIMATION        CONCEPT           STATISTICS

T= 2    Comprehension
D= 2    General
```

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1425-2

```Item is still being reviewed
True/False
CONFIDENCEINTERV  SCOPEOFINFERENCE
ESTIMATION        CONCEPT           STATISTICS

T= 2    Comprehension
D= 4    General
```

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1426-2

```Item is still being reviewed
True/False
CONFIDENCEINTERV
SIMPLE/CI         ESTIMATION        CONCEPT
STATISTICS

T= 2    Comprehension
D= 4    General
```

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1460-1

```Item is still being reviewed
Multiple Choice
SIMPLE/CI         SAMPLESIZE        STANDERROROFMEAN
CONFIDENCEINTERV  ESTIMATION        CONCEPT
STATISTICS        SAMPLING          DESCRSTAT/P
PARAMETRIC

T= 2    Comprehension
D= 3    General
```

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1461-1

```Item is still being reviewed
Multiple Choice
SIMPLE/CI
CONFIDENCEINTERV  ESTIMATION        CONCEPT
STATISTICS

T= 2    Comprehension
D= 3    General             Education
```

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1511-1

```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= 4    General
```

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1513-1

```Item is still being reviewed
True/False
SAMPLESIZE        SIMPLE/CI
SAMPLING          STATISTICS        CONFIDENCEINTERV
ESTIMATION        CONCEPT

T= 2    Comprehension
D= 2    General
```

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1513-2

```Based upon item submitted by J. L. Mickey -UCLA
True/False
SIMPLE/CI         TYPE1ERROR        SAMPLESIZE
CONFIDENCEINTERV  ESTIMATION        CONCEPT
STATISTICS        SAMPLING

T= 2    Comprehension
D= 3    General
```

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1548-1

```Based upon item submitted by W. J. Hall - Univ. of Rochester
True/False
SAMPLESIZE        OTHER/CI
SAMPLING          STATISTICS        CONFIDENCEINTERV
ESTIMATION        CONCEPT

T= 5    Comprehension
D= 3    General
```

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1563-1

```Based upon item submitted by W. J. Hall - Univ. of Rochester
SIMPLERANDOM      SAMPLE            POPULATION
PROBABILITYSAMPL  SAMPLING          STATISTICS
CONCEPT

T=10    Comprehension
D= 4    General
***Multiple Parts***
```

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1564-2

```Based upon item submitted by W. Federer - Cornell
True/False
SAMPLE            POPULATION
SAMPLING          STATISTICS        CONCEPT

T= 2    Comprehension
D= 1    General
```

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1565-1

```Based upon item submitted by D. Michener - UNH
Definition
POPULATION
I650E             CONCEPT           STATISTICS
I650/TEMPORARY    MISCELLANEOUS

T= 5    Comprehension
D= 3    General
```

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1573-1

```Item is still being reviewed
CENTRALLIMITTHM
CONCEPT           STATISTICS

T= 5    Computation
D= 4    General
***Multiple Parts***
```

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1727-2

```Based upon item submitted by J. Mowbray - Shippensburg State
Essay
OPERATIONALFAULT  SCOPEOFINFERENCE
COMMONPITFALLS    TYPICALSUMMARY    APPLICATIONEX
NONSAMPLINGERROR  SAMPLING          STATISTICS
CONCEPT           MISCELLANEOUS

T=10    Comprehension   Application
D= 2    Sociology           General             Social Sciences
```

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1789-1

```Based upon item submitted by J. Warren - UNH
NONRESPONSE       PROPORTION
COMMONPITFALLS    NONSAMPLINGERROR  SAMPLING
STATISTICS        DESCRSTAT/P       PARAMETRIC
MISCELLANEOUS

T= 5    Application
D= 4    General             Social Sciences     Education
```

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1832-1

```Based upon item submitted by W. Beyer - Univ. of Akron
VARIANCE/OTHER    MEAN
DESCRSTAT/P       PARAMETRIC        STATISTICS

T=20    Computation
D= 3    General
```

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1870-1

```Item is still being reviewed
SIMPLERANDOM      VARIABILITY/P
EXPERDESIGN/TERM  I650C             PROBABILITYSAMPL
SAMPLING          STATISTICS        DESCRSTAT/P
PARAMETRIC        CONCEPT           ANOVA
SCOPEOFINFERENCE

T= 5    Comprehension   Application
D= 5    General
***Multiple Parts***
```

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1893-3

```Based upon item submitted by D. Halley - Virginia Polytechnic Univ.
STANDARDDEVIATIO
I650I             DESCRSTAT/P       PARAMETRIC
STATISTICS

T=10    Comprehension
D= 4    General
***Calculator Necessary***
```

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1908-4

```Based upon item submitted by W. J. Hall - Univ. of Rochester
Multiple Choice
VARIANCE
DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 5    Computation
D= 3    General
```

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1911-2

```Item is still being reviewed
Multiple Choice
VARIANCE
SAMPLE            DESCRSTAT/P       PARAMETRIC
STATISTICS        SAMPLING

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

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1952-1

```Item is still being reviewed
True/False
VARIANCE          SAMPLESIZE
DESCRSTAT/P       PARAMETRIC        STATISTICS
SAMPLING

T= 2    Comprehension
D= 3    General
```

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1961-1

```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
***Calculator Necessary***
***Statistical Table Necessary***
```

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2629-1

```Item is still being reviewed
TREATMENTASSIGN   SIMPLERANDOM      EXPERDESIGN/TERM
ANOVA             PARAMETRIC        STATISTICS
PROBABILITYSAMPL  SAMPLING

T= 5    Comprehension
D= 1    General
```

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2726-2

```Item is still being reviewed
Multiple Choice
EXPERDESIGN/TERM
ANOVA             PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 1    General
```

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2748-1

```Item is still being reviewed
True/False
EXPERDESIGN/TERM
ANOVA             PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General
```

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2749-1

```Based upon item submitted by W. Federer - Cornell
True/False
EXPERDESIGN/TERM
ANOVA             PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 3    General
```

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2752-1

```Based upon item submitted by J. Warren - UNH
Definition
EXPERDESIGN/TERM
I650C             ANOVA             PARAMETRIC
STATISTICS

T= 5    Comprehension
D= 3    General
```

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2752-2

```Based upon item submitted by J. Warren - UNH
Definition
EXPERDESIGN/TERM
I650C             ANOVA             PARAMETRIC
STATISTICS

T= 5    Comprehension
D= 3    General
```

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2753-1

```Based upon item submitted by J. Warren - UNH
Definition
EXPERDESIGN/TERM
I650C             ANOVA             PARAMETRIC
STATISTICS

T= 5    Comprehension
D= 3    General
```

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2760-1

```Based upon item submitted by J. Warren - UNH
Definition
EXPERDESIGN/TERM
I650C             ANOVA             PARAMETRIC
STATISTICS

T= 5    Comprehension
D= 3    General
```

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2766-1

```Based upon item submitted by J. Warren - UNH
Definition
EXPERDESIGN/TERM
ANOVA             PARAMETRIC        STATISTICS
I650C

T= 5    Comprehension
D= 3    General
```

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2813-1

```Item is still being reviewed
Essay
PROBSAMPCONCEPT   SAMPLING          SAMPLE
PROBABILITYSAMPL  STATISTICS

T= 5    Comprehension
D= 3    General
```

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2814-2

```Item is still being reviewed
Fill-in
SAMPLE            SAMPLING
STATISTICS

T= 2    Comprehension
D= 1    General
```

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2814-3

```Item is still being reviewed
Fill-in
SAMPLE            SAMPLING
STATISTICS

T= 2    Comprehension
D= 2    General
```

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2814-4

```Item is still being reviewed
Fill-in
SAMPLE            SAMPLING
STATISTICS

T= 2    Comprehension
D= 1    General
```

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2820-1

```Item is still being reviewed
Multiple Choice
PROBABILITYSAMPL  SAMPLINGERROR
SAMPLING          STATISTICS

T= 2    Comprehension
D= 3    General
```

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2822-1

```Based upon item submitted by A. Bugbee - UNH
SIMPLERANDOM      PROBSAMPCONCEPT
PROBABILITYSAMPL  SAMPLING          STATISTICS

T= 5    Comprehension
D= 3    General
```

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2822-3

```Based upon item submitted by W. J. Hall - Univ. of Rochester
True/False
ACCURACY          PROBSAMPCONCEPT
NONSAMPLINGERROR  SAMPLING          STATISTICS
PROBABILITYSAMPL

T= 2    Comprehension
D= 2    General
```

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2823-3

```Based upon item submitted by W. J. Hall - Univ. of Rochester
True/False
PROBSAMPCONCEPT
PROBABILITYSAMPL  SAMPLING          STATISTICS

T= 5    Comprehension
D= 3    General
```

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2824-3

```Item is still being reviewed
True/False
PROBSAMPCONCEPT   SAMPLE
PROBABILITYSAMPL  SAMPLING          STATISTICS

T= 2    Comprehension
D= 2    General
1                                                                        Page 2825
```

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2825-1

```Item is still being reviewed
True/False
PROBSAMPCONCEPT
PROBABILITYSAMPL  SAMPLING          STATISTICS

T= 2    Comprehension
D= 2    General
```

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2825-3

```Item is still being reviewed
Multiple Choice
SIMPLERANDOM
PROBABILITYSAMPL  SAMPLING          STATISTICS

T= 2    Comprehension
D= 1    General
```

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2826-1

```Item is still being reviewed
Multiple Choice
SIMPLERANDOM
PROBABILITYSAMPL  SAMPLING          STATISTICS

T= 2    Comprehension
D= 1    General
```

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2826-2

```Item is still being reviewed
Multiple Choice
SIMPLERANDOM
PROBABILITYSAMPL  SAMPLING          STATISTICS

T= 2    Comprehension
D= 2    General             Education
```

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2827-1

```Item is still being reviewed
Multiple Choice
SIMPLERANDOM
PROBABILITYSAMPL  SAMPLING          STATISTICS

T= 2    Comprehension
D= 2    General             Education
```

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2829-1

```Based upon item submitted by J. Mowbray - Shippensburg State
SIMPLERANDOM      MISCELLANEOUS
PROBABILITYSAMPL  SAMPLING          STATISTICS

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

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2830-2

```Item is still being reviewed
RANDOMNUMBERS/S   SIMPLERANDOM
I650I             SAMPLING          STATISTICS
PROBABILITYSAMPL

T= 5    Comprehension
D= 3    General             Biological Sciences Natural Sciences
***Multiple Parts***
```

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2831-1

```Item is still being reviewed
SIMPLERANDOM      NONRESPONSE
PROBABILITYSAMPL  SAMPLING          STATISTICS
NONSAMPLINGERROR

T=10    Application     Comprehension   Computation
D= 4    Social Sciences     General
***Multiple Parts***
```

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2833-2

```Based upon item submitted by J. L. Mickey -UCLA
True/False
SIMPLERANDOM
PROBABILITYSAMPL  SAMPLING          STATISTICS

T= 2    Comprehension
D= 3    General
```

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2891-2

```Item is still being reviewed
Multiple Choice
SAMPLE            CONVENIENCE/CHUN
SAMPLING          STATISTICS

T= 2    Comprehension
D= 2    General
```

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2902-1

```Item is still being reviewed
Fill-in
FRAME
SAMPLING          STATISTICS

T= 2    Comprehension
D= 2    General
```

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2904-1

```Item is still being reviewed
Multiple Choice
SAMPLINGERROR
SAMPLING          STATISTICS

T= 2    Comprehension
D= 3    General
```

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2904-3

```Item is still being reviewed
Multiple Choice
PRECISION         SAMPLINGERROR
SAMPLING          STATISTICS

T= 2    Comprehension
D= 4    General             Education
```

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2921-1

```Item is still being reviewed
Multiple Choice
NONRESPONSE
NONSAMPLINGERROR  SAMPLING          STATISTICS

T= 2    Comprehension
D= 2    General             Social Sciences
```

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2922-1

```Based upon item submitted by W. J. Hall - Univ. of Rochester
NONRESPONSE
I650I             NONSAMPLINGERROR  SAMPLING
STATISTICS

T= 5    Comprehension
D= 4    General
```

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