656 CHAPTER 13 Nonparametric Tests 3. Contradicting H1 An important step in conducting the sign test is to determine whether the sample data contradict the alternative hypothesis H1. For the sign test described in Exercise 1, identify the null hypothesis and the alternative hypothesis, and explain how the sample data contradict or do not contradict the alternative hypothesis. 4. Efficiency of the Sign Test Refer to Table 13-2 on page 645 and identify the efficiency of the sign test. What does that value tell us about the sign test? Matched Pairs. In Exercises 5–8, use the sign test for the data consisting of matched pairs. 5. Measured and Reported Weights Listed below are measured and reported weights (lb) of random female subjects (from Data Set 4 “Measured and Reported” in Appendix B). Use a 0.05 significance level to test the claim that for females, there is no difference between measured weights and reported weights. Measured 147.3 268.7 213.4 201.3 107.1 172.0 187.4 132.5 122.1 151.9 Reported 142 267 210 204 107 176 187 135 122 150 6. Do Men and Women Talk the Same Amount? Listed below are word counts of males and females in couple relationships (from Data Set 14 “Word Counts” in Appendix B). Use a 0.05 significance level to test the claim that there is no significant difference between the numbers of words spoken by males and females in couple relationships. Men 13,560 18,876 13,825 9274 20,547 17,190 Women 21,261 12,964 33,789 8709 10,508 11,909 7. Do Men and Women Talk the Same Amount? Repeat Exercise 6 using all of the paired word counts of males and females in couple relationships listed in the first two columns from Data Set 14 “Word Counts” in Appendix B. 8. Oscars Refer to Data Set 21 “Oscar Winner Age” in Appendix B and use all of the ages of actresses and actors when they won Academy Awards for their performances. Each pair of ages is from the same year. Use a 0.05 significance level to test the claim that there is no significant difference between ages of Oscar-winning actresses and Oscar-winning actors. Nominal Data. In Exercises 9–12, use the sign test for the claim involving nominal data. 9. Buttered Toast Drop Test The Discovery channel television show MythBusters conducted an experiment to study what happens when buttered toast is dropped on the floor. When 48 buttered slices of toast were dropped, 29 of them landed with the buttered side up and 19 landed with the buttered side down. Use a 0.05 significance level to test the claim that toast will land with the buttered side down 50% of the time. 10. Medical Malpractice In a study of 1228 randomly selected medical malpractice lawsuits, it was found that 856 of them were dropped or dismissed (based on data from the Physicians Insurers Association of America). Use a 0.01 significance level to test the claim that there is a difference between the rate of medical malpractice lawsuits that go to trial and the rate of such lawsuits that are dropped or dismissed. 11. Overtime Rule in Football Before the overtime rule in the National Football League was changed in 2011, among 460 overtime games, 252 were won by the team that won the coin toss at the beginning of overtime. Using a 0.05 significance level, test the claim that the coin toss is fair in the sense that neither team has an advantage by winning it. Does the coin toss appear to be fair? 12. Overtime Rule in Football Repeat the preceding exercise using these results from 111 overtime games (excluding ties) played after the overtime rule in the National Football League was changed in 2011: Among 111 overtime games, 59 were won by the team that won the coin toss at the beginning of overtime, and 52 were lost by the team that won the coin toss at the beginning of overtime. These results are current as of this writing.
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