LESSON 10: Nonparametric Statistics

Exercise Problems

For problems 1, 2 and 3, use the following sample of 10 measurements:

8.4 15.8 10.3 12.9 23.7 16.9 12.5 4.9 9.8 7.3

1. Conduct the following sign tests using the binomial tables and a = .05.

1. Ho: \(\eta =9\)
2. H0: \(\eta >9\)
   2. Repeat the tests from the previous problem using the normal approximation to the binomial probabilities. How do the results compare?
3. What assumptions are necessary to ensure the validity of the preceding tests?
4. Approximately what sample sizes are needed for the Chi-Squared distribution to provide an appropriate characterization of the sampling distribution of the Kruskal-Wallis H statistic?
5. Answer problem 14.4 on page 828 of the textbook.

14.4 Consider the following sample of 10 measurements:

8.4 16.9 15.8 12.5 10.3 4.9 12.9 9.8 23.7 7.3

se these data to conduct each of the following sign tests using the binomial tables (Table II, Appendix A) and a = .05.

1. Ho: \(\eta \) = 9 versus Ha: \(\eta \) > 9
2. Ho: \(\eta \) = 9 versus Ha: \(\eta \) \(\ne \) 9
3. Ho: \(\eta \) = 20 versus Ha: \(\eta \) < 20
4. Ho: \(\eta \) = 20 versus Ha: \(\eta \) \(\ne \) 20
5. Repeat each of the preceding tests using the normal approximation to the binomial probabilities. Compare the results
6. What assumptions are necessary to ensure the validity of each of the preceding tests?

6. Answer problem 14.26 on page 837 of the textbook.

14.26 Rain in Colorado. The data in the table, extracted from Technometrics (Feb. 1986), represent daily accumulated stream flow and precipitation (in inches) for two U.S. Geological Survey stations in Colorado. Conduct a test to determine whether the distributions of daily accumulated stream flow and precipitation for the two stations differ in location. Use a = .10. Why is a nonparametric test appropriate for these data?

7. Answer problem 14.32a, b on page 844 of the textbook.

14.32 Specify the test statistic and the rejection region for the Wilcoxon signed rank test for the paired difference design in each of the following situations:

(a) H0: Two probability distributions, A and B, are identical

Ha: Probability distribution for population A is shifted to the right or left of the probability distribution for population B, n = 20, a = 0.10

(b) Ho: Two probability distributions, A and B, are identical

Ha: Probability distribution for population A is shifted to the right of the probability distribution for population B, n = 39, a = .05.

9. Answer problem 14.66 on page 859 of the textbook.

Refer to Exercise 10.68 (p. 559) and Ihe Nov li•chnology, Work. and Employment (July 2001) study of daily worker absentee rates at a jeans plant. Nine weeks were randomly selected and the absentee rate (percentage of workers absent) determined lor each day (Monday through Friday) of the work week. The data are reproduced in the table. Conduct a nonparametric analysis of the data to compare the distributions of absentee rates for the live days of the work

10. Answer problem 14.72 on page 865 of the textbook.

Compute Spearman's rank correlation coefficient for each of the following pairs of sample observations:

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