Chapter 12
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WebQuizzing – Ch. 12
Book ISBN-10 0538477490
Book ISBN-13 9780538477499
Author: Gerald Keller
Title: Statistics for Management and Economics
Ed: 9e
# Questions Submitted: 20 Multiple Choice
1. The expected value of the difference of two sample means equals the difference of the
corresponding population means when:
A. the populations are normally distributed.
B. the samples are independent.
C. the populations are approximately normal and the sample sizes are large.
D. All of these choices are true.
Analysis:
A. Incorrect. All of these choices are true.
B. Incorrect. All of these choices are true.
C. Incorrect. All of these choices are true.
D. Correct. All of these choices are true.
ANSWER D Ref: Section 12.1-12.2
2. In testing the difference between the means of two normally distributed populations, the
number of degrees of freedom associated with the unequal-variances t-test statistic usually
results in a non-integer number. It is recommended that you:
A. round to the nearest integer.
B. change the sample sizes until the number of degrees of freedom becomes an integer.
C. assume that the population variances are equal, and then use df = n1  n2  2 .
D. None of these choices.
Analysis:
A. Correct. It is recommended that you round to the nearest integer.
B. Incorrect. It is recommended that you round to the nearest integer.
C. Incorrect. It is recommended that you round to the nearest integer.
D. Incorrect. It is recommended that you round to the nearest integer.
ANSWER: A Ref: Section 12.1-12.2
3. The quantity s 2p is called the pooled variance estimate of the common variance of two
unknown but equal population variances. It is the weighted average of the two sample
variances, where the weights represent the:
A. sample variances.
B. sample standard deviations.
C. degrees of freedom for each sample.
D. None of these choices.
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Analysis:
A. Incorrect. The weights represent the degrees of freedom for each sample.
B. Incorrect. The weights represent the degrees of freedom for each sample.
C. Correct. The weights represent the degrees of freedom for each sample.
D. Incorrect. The weights represent the degrees of freedom for each sample.
ANSWER: C Ref: Section 12.1-12.2
4. In testing the difference between two population variances are unknown and not assumed to
be equal, two independent samples are drawn from the populations. Which of the following
tests is appropriate?
A. z-test.
B. pooled variances t-test.
C. unequal variances t-test.
D. None of these choices.
Analysis:
A. Incorrect. The unequal variances t-test is appropriate.
B. Incorrect. The unequal variances t-test is appropriate.
C. Correct. The unequal variances t-test is appropriate.
D. Incorrect. The unequal variances t-test is appropriate.
ANSWER C Ref: Section 12.1-12.2
5. In testing the difference between the means of two normal populations using two
independent samples when the population variances are unequal, the sampling distribution of
the resulting statistic is:
A. normal
B. Student-t
C. approximately normal
D. approximately Student-t
Analysis:
A. Incorrect. The sampling distribution of the resulting statistic is approximately Student-t
B. Incorrect. The sampling distribution of the resulting statistic is approximately Student-t
C. Incorrect. The sampling distribution of the resulting statistic is approximately Student-t
D. Correct. The sampling distribution of the resulting statistic is approximately Student-t
ANSWER: D Ref: Section 12.1-12.2
6. In testing the difference between two population means using two independent samples, we
use the pooled variance in estimating the standard error of the sampling distribution of the
sample mean difference x1  x2 if:
A. the sample sizes are both large.
B. the populations are normal with equal variances.
C. the populations are non-normal with unequal variances.
D. All of these choices are true.
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Analysis:
A. Incorrect. We use the pooled variance if the populations are normal with equal variances.
B. Correct. We use the pooled variance if the populations are normal with equal variances.
C. Incorrect .We use the pooled variance if the populations are normal with equal variances.
D. Incorrect .We use the pooled variance if the populations are normal with equal variances.
ANSWER: B Ref: Section 12.1-12.2
7. In constructing a confidence interval estimate for the difference between the means of two
independent normally distributed populations, we:
A. pool the sample variances when the unknown population variances are equal.
B. pool the sample variances when the population variances are known and equal.
C. pool the sample variances when the population means are equal.
D. never pool the sample variances.
Analysis:
A. Correct. We pool the sample variances when the unknown population variances are equal.
B. Incorrect. We pool the sample variances when the unknown population variances are equal.
C. Incorrect. We pool the sample variances when the unknown population variances are equal.
D. Incorrect. We pool the sample variances when the unknown population variances are equal.
ANSWER: A Ref: Section 12.1-12.2
8. The t-test for the difference between the means of two independent populations assumes that
the respective:
A. sample sizes are equal.
B. means are equal.
C. populations are normal.
D. All of these choices are true.
Analysis:
A. Incorrect. It assumes that the respective populations are normal.
B. Incorrect. It assumes that the respective populations are normal.
C. Correct. It assumes that the respective populations are normal.
D. Incorrect. It assumes that the respective populations are normal.
ANSWER: C Ref: Section 12.1-12.2
9. If some natural relationship exists between each pair of observations that provides a logical
reason to compare the first observation of sample 1 with the first observation of sample 2, the
second observation of sample 1 with the second observation of sample 2, and so on, the
samples are referred to as:
A. matched pairs.
B. independent samples.
C. nonrandom samples.
D. None of these choices.
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Analysis:
A. Correct. The samples are referred to as matched pairs.
B. Incorrect. The samples are referred to as matched pairs.
C. Incorrect. The samples are referred to as matched pairs.
D. Incorrect. The samples are referred to as matched pairs.
ANSWER: A Ref: Section 12.2.3
10. The symbol xD refers to:
A. the difference in the means of two independent populations.
B. one matched pairs difference.
C. the mean difference in the pairs of observations.
D. None of these choices.
Analysis:
A. Incorrect. The symbol xD refers to the mean difference in the pairs of observations.
B. Incorrect. The symbol xD refers to the mean difference in the pairs of observations.
C. Correct. The symbol xD refers to the mean difference in the pairs of observations.
D. Incorrect. The symbol xD refers to the mean difference in the pairs of observations.
ANSWER: C Ref: Section 12.2
11. A test is being conducted to test the difference between two population means using data that
are gathered from a matched pairs experiment. If the paired differences are normal, then the
distribution used for testing is the:
A. normal distribution.
B. binomial distribution.
C. Student t distribution.
D. F distribution.
Analysis:
A. Incorrect. The distribution used for testing is the Student t distribution.
B. Incorrect. The distribution used for testing is the Student t distribution.
C. Correct. The distribution used for testing is the Student t distribution.
D. Incorrect. The distribution used for testing is the Student t distribution.
ANSWER: C Ref: Section 12.2