9. Hypothesis Testing for One Sample

What Are We Testing? Refer to the sample data in Exercise 1. Assuming that we use the Wilcoxon rank-sum test with those data, identify the null hypothesis and all possible alternative hypotheses.

Requirements Assume that we want to use the data from Exercise 1 with the Kruskal-Wallis test. Are the requirements satisfied? Explain.

Notation For the data given in Exercise 1, identify the values of n1, n2, n3 and N.

HIC Measurements Listed below are head injury criterion (HIC) measurements from crash tests of small, midsize, large, and SUV vehicles. In using the Kruskal-Wallis test, we must rank all of the data combined, and then we must find the sum of the ranks for each sample. Find the sum of the ranks for each of the four samples.

Arsenic in Rice Listed below are amounts of arsenic in samples of brown rice from three different states. The amounts are in micrograms of arsenic and all samples have the same serving size. The data are from the Food and Drug Administration. Use a 0.01 significance level to test the claim that the three samples are from populations with the same median.

Clancy, Rowling, and Tolstoy Ease of Reading Pages were randomly selected from three books: The Bear and the Dragon by Tom Clancy, Harry Potter and the Sorcerer’s Stone by J. K. Rowling, and War and Peace by Leo Tolstoy. Listed below are Flesch Reading Ease Scores for those pages. Higher scores correspond to pages that are easier to read. Use a 0.01 significance level to test the claim that pages from books by those three authors have the same median Flesch Reading Ease score.

Hospital Admissions For the matched pairs listed in Exercise 1, identify the following components used in the Wilcoxon signed-ranks test:

e. The value of the test statistic T

In Exercises 9–12, use the sign test for the claim involving nominal data.

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.

In Exercises 9–12, use the sign test for the claim involving nominal data.

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?

In Exercises 13–16, refer to the indicated data set in Appendix B and use the sign test for the claim about the median of a population.

Cotinine in Smokers Data Set 15 “Passive and Active Smoke” includes cotinine measurements from 902 smokers. Cotinine is a biomarker of nicotine in the body. Use a 0.01 significance level to test the claim that smokers have cotinine levels with a median of 2.84 ng/mL, which is the median for nonsmokers not exposed to tobacco smoke.

Hospital Admissions For the matched pairs listed in Exercise 1, identify the following components used in the Wilcoxon signed-ranks test:

a. Differences d

Hospital Admissions For the matched pairs listed in Exercise 1, identify the following components used in the Wilcoxon signed-ranks test:

b. The ranks corresponding to the nonzero values of |d|

Hospital Admissions For the matched pairs listed in Exercise 1, identify the following components used in the Wilcoxon signed-ranks test:

c. The signed ranks

Hospital Admissions For the matched pairs listed in Exercise 1, identify the following components used in the Wilcoxon signed-ranks test:

d. The sum of the positive ranks and the sum of the absolute values of the negative ranks

Hospital Admissions For the matched pairs listed in Exercise 1, identify the following components used in the Wilcoxon signed-ranks test:

f. The critical value of T (assuming a 0.05 significance level in a test of no difference between hospital admissions of Friday 6th and the following Friday 13th).