9. Hypothesis Testing for One Sample

Robust What does it mean when we say that the F test described in this section is not robust against departures from normality?

Exercises 1–5 refer to the sample data in the following table, which summarizes the frequencies of 500 digits randomly generated by Statdisk. Assume that we want to use a 0.05 significance level to test the claim that Statdisk generates the digits in a way that they are equally likely.

What are the null and alternative hypotheses corresponding to the stated claim?

Transformations of Data Example 1 illustrated the use of two-way ANOVA to analyze the sample data in Table 12-3. How are the results affected in each of the following cases?

c. The format of the table is transposed so that the row and column factors are interchanged.

Sitting Heights The sitting height of a person is the vertical distance between the sitting surface and the top of the head. The following table lists sitting heights (mm) of randomly selected U.S. Army personnel collected as part of the ANSUR II study. Using the data with a 0.05 significance level, what do you conclude? Are the results as you would expect?

Heights of Females from ANSUR I and ANSUR II Example 1 in this section used samples of heights of males from Data Set 1 “ANSUR I 1988” and Data Set 2 “ANSUR II 2012.” Listed below are samples of heights (mm) of females from those same data sets. Are the requirements for using the Wilcoxon rank-sum test satisfied? Why or why not?

Rank Sum After ranking the combined list of female heights given in Exercise 1, find the sum of the ranks for the ANSUR I 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?