Chapter 15 Distribution-free procedures - Devore Test Bank

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