1. What is a nonparametric hypothesis test? Explain why the term “distribution-free” may be more accurate.

2. Explain why the sign test may be less efficient than the Wilcoxon signed rank test when both are compared to the test for dependent sample data.

3. Why is there no efficiency rating in Table 1 (page 14-4) for the runs test?

4. Explain the meaning of the notation in the hypotheses for the sign test for a single population median.

5. Explain the meaning of the notation in the hypotheses for the sign test for matched-pair data.

1. Use Appendix Table I to find the value of .
2. State the rejection rule.
3. Calculate .
4. Provide the conclusion and the interpretation of the hypothesis test.

6. vs. , , level of significance . There are 10 pluses and 6 minuses. One data value equals 50.

7. vs. , , level of significance . There are 9 pluses, 0 minuses, and 3 ties.

8. NHI Goals Scored. Between 2003 and 2014, the National Hockey League endured two lockout seasons and underwent a number of rules changes. Did this affect the number of goals scored? The following table shows the mean goals scored per game for a random sample of five NHL teams for the 2003-2004 and the 2013-2014 seasons. Test whether the population median of the difference in mean number of goals scored per game is greater than zero, using level of significance .

9. Eighth-Grade Alcohol Use. The National Institute on Alcohol Abuse and Alcoholism (NIAAA) reports on the proportion of eighth-graders who have used alcohol (Source: http://www.niaaa.nih.gov/publications). A random sample of 100 eighth-graders this year showed that 41 of them had used alcohol. Test whether the population proportion of eighth-graders who have used alcohol is less than 0.5, using level of significance .

10. For the Wilcoxon signed rank test, what do the notations and mean?

11. vs. , with and .

12. vs. , with , , and .

13. vs. , with and .

14. vs. , with , , and .

15. Precipitation in Florida. The following table shows the annual precipitation (in inches) for a random sample of cities in Florida. Use the Wilcoxon signed rank test to test whether the population median annual precipitation in Florida differs from 50 inches, using level of significance .

16. Hot and Cold in Texas. Is the weather in Texas on the hot side or the cold side? The following table shows the annual number of heating degree-days and cooling degree-days for a random sample of cities in Texas.¹⁷ Test, using the Wilcoxon signed rank test, whether the population median of the differences (heating degree-days minus cooling degree-days) is less than zero, using level of significance .

17.

18.

19. Unemployment Rates. The following table contains the unemployment rates for independent random samples of cities in Ohio and Virginia. Test whether the population median unemployment rate differs between cities in Ohio and cities in Virginia, using level of significance .

20.

21.

22. Manufacturing Workers. The following tables contain the number of workers employed in manufacturing for independent random samples of cities in Connecticut, Georgia, and Illinois. Test whether the population median number of manufacturing workers differs among the three states. Use level of significance .

23.

24.

25. Hot and Cold in California. The following table contains a random sample of 13 cities in California, along with the average number of heating degree-days and cooling degree-days for each city. Test whether a rank correlation exists between heating degree-days and cooling degree-days, using level of significance .

26. Y Y Y Y Y N N N N N N N Y Y Y Y Y Y Y N N N N N

27. M F F M M M F F M F F M F M M M F F F M F M

28. Presidential Election Winners. Since 1852, every U.S. presidential election has been won by either the Democratic Party or the Republican Party. The following sequence represents the presidential election winners since 1852, with D representing Democrat and R representing Republican.¹⁸ Test whether the sequence is random, using level of significance .