Chapter 15 Distribution-free procedures
COMPLETION
1. Because the t and F procedures require the distributional assumption of normality, they are not
procedures.
ANS: distribution free
PTS: 1
2. Because the t and F procedures are based on a particular parametric family of distributions (normal), they are not
procedures.
ANS: nonparametric
PTS: 1
3. The observed value of the Wilcoxon Signed-Rank Test statistic is the sum of the ranks associated with the
observations.
ANS: positive
PTS: 1
4. Let be a random sample from a continuous and symmetric probability distribution with mean (and
median) In testing using the Wilcoxon signed-rank test, the rejection region for
level .01 test is
ANS: 50
PTS: 1
5. Let be a random sample from a continuous and symmetric probability distribution with mean (and
median) In testing using the Wilcoxon signed-rank test, the rejection region for
level .01 test is
ANS: 5
PTS: 1
6. For n = 8 observations, there are _ possible signed-rank sequences, and to list these sequences would be
very tedious.
ANS: 256
PTS: 1
7. The table of critical values for the Wilcoxon signed-rank test, as shown in your text, provides critical values for level
tests only when n is less than or equal to .
, ANS: 20
PTS: 1
8. When the underlying distribution being sampled is normal, the t test or the Wilcoxon signed-rank test can be used to
test a hypothesis about the population mean However, the is the best test in such a situation because
among all level tests it is the one having minimum (i.e., minimum probability of Type II error)
ANS: t test
PTS: 1
9. The asymptotic relative efficiency (ARE) of one test with respect to another is essentially the limiting ratio of the
necessary to obtain identical error probabilities for the two tests.
ANS: sample sizes
PTS: 1
10. When the underlying distribution is normal, the asymptotic relative efficiency (ARE) of the Wilcoxon signed-rank
test with respect to the t test is approximately .
ANS: .95
PTS: 1
11. For any distribution, the asymptotic relative efficiency (ARE) will be at least , and for many distributions
will be much greater than 1.
ANS: .86
PTS: 1
12. An alternative name for the Wilcoxon rank-sum test is the test.
ANS: Mann-Whitney
PTS: 1
13. The Wilcoxon rank-sum test is applied to three values of x and four values of y. Then, the smallest possible value of
the test statistic W is w = and the largest possible value is w = .
ANS: 6, 18
PTS: 1
14. The Wilcoxon rank-sum test statistic W is the sum of the ranks in the combined X and Y sample observations associated
with observations.
ANS: X
, PTS: 1
15. Suppose Then, the computed value of the Wilcoxon
rank-sum test statistic W is w = .
ANS: 9
PTS: 1
16. For values of m (number of observed x values) and n (number of observed y values) that exceed , a normal
approximation for the distribution of the Wilcoxon rank-sum statistic W can be used.
ANS: 8
PTS: 1
17. Suppose that a random sample of size 30 from a normal population is used to test
The t test at level .10 specifies that should be rejected if the test statistic value t is either
ANS: 1.699, -1.699
PTS: 1
18. A 95% distribution-free confidence interval for a parameter can be obtained from a level test for
ANS: .05
PTS: 1
19. For large samples when the underlying population is normal, the Wilcoxon signed-rank interval will tend to be slightly
than the t interval.
ANS: longer
PTS: 1
20. For large samples when the underlying population is quite nonnormal (symmetric but with heavy tails), the Wilcoxon
signed-rank interval will tend to be much than the t interval.
ANS: shorter
PTS: 1
21. The Wilcoxon signed-rank interval uses pairwise averages from a single sample, whereas the Wilcoxon rank-sum
interval uses pairwise differences from samples.
ANS: two
COMPLETION
1. Because the t and F procedures require the distributional assumption of normality, they are not
procedures.
ANS: distribution free
PTS: 1
2. Because the t and F procedures are based on a particular parametric family of distributions (normal), they are not
procedures.
ANS: nonparametric
PTS: 1
3. The observed value of the Wilcoxon Signed-Rank Test statistic is the sum of the ranks associated with the
observations.
ANS: positive
PTS: 1
4. Let be a random sample from a continuous and symmetric probability distribution with mean (and
median) In testing using the Wilcoxon signed-rank test, the rejection region for
level .01 test is
ANS: 50
PTS: 1
5. Let be a random sample from a continuous and symmetric probability distribution with mean (and
median) In testing using the Wilcoxon signed-rank test, the rejection region for
level .01 test is
ANS: 5
PTS: 1
6. For n = 8 observations, there are _ possible signed-rank sequences, and to list these sequences would be
very tedious.
ANS: 256
PTS: 1
7. The table of critical values for the Wilcoxon signed-rank test, as shown in your text, provides critical values for level
tests only when n is less than or equal to .
, ANS: 20
PTS: 1
8. When the underlying distribution being sampled is normal, the t test or the Wilcoxon signed-rank test can be used to
test a hypothesis about the population mean However, the is the best test in such a situation because
among all level tests it is the one having minimum (i.e., minimum probability of Type II error)
ANS: t test
PTS: 1
9. The asymptotic relative efficiency (ARE) of one test with respect to another is essentially the limiting ratio of the
necessary to obtain identical error probabilities for the two tests.
ANS: sample sizes
PTS: 1
10. When the underlying distribution is normal, the asymptotic relative efficiency (ARE) of the Wilcoxon signed-rank
test with respect to the t test is approximately .
ANS: .95
PTS: 1
11. For any distribution, the asymptotic relative efficiency (ARE) will be at least , and for many distributions
will be much greater than 1.
ANS: .86
PTS: 1
12. An alternative name for the Wilcoxon rank-sum test is the test.
ANS: Mann-Whitney
PTS: 1
13. The Wilcoxon rank-sum test is applied to three values of x and four values of y. Then, the smallest possible value of
the test statistic W is w = and the largest possible value is w = .
ANS: 6, 18
PTS: 1
14. The Wilcoxon rank-sum test statistic W is the sum of the ranks in the combined X and Y sample observations associated
with observations.
ANS: X
, PTS: 1
15. Suppose Then, the computed value of the Wilcoxon
rank-sum test statistic W is w = .
ANS: 9
PTS: 1
16. For values of m (number of observed x values) and n (number of observed y values) that exceed , a normal
approximation for the distribution of the Wilcoxon rank-sum statistic W can be used.
ANS: 8
PTS: 1
17. Suppose that a random sample of size 30 from a normal population is used to test
The t test at level .10 specifies that should be rejected if the test statistic value t is either
ANS: 1.699, -1.699
PTS: 1
18. A 95% distribution-free confidence interval for a parameter can be obtained from a level test for
ANS: .05
PTS: 1
19. For large samples when the underlying population is normal, the Wilcoxon signed-rank interval will tend to be slightly
than the t interval.
ANS: longer
PTS: 1
20. For large samples when the underlying population is quite nonnormal (symmetric but with heavy tails), the Wilcoxon
signed-rank interval will tend to be much than the t interval.
ANS: shorter
PTS: 1
21. The Wilcoxon signed-rank interval uses pairwise averages from a single sample, whereas the Wilcoxon rank-sum
interval uses pairwise differences from samples.
ANS: two
