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

In Exercises 1–4, use the following listed measured amounts of chest compression (mm) from car crash tests (from Data Set 35 “Car Data” in Appendix B). Also shown are the SPSS results from analysis of variance. Assume that we plan to use a 0.05 significance level to test the claim that the different car sizes have the same mean amount of chest compression.

Why Not Test Two at a Time? Refer to the sample data given in Exercise 1. If we want to test for equality of the four means, why don’t we use the methods of Section 9-2 “Two Means: Independent Samples” for the following six separate hypothesis tests?

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.

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.

Using the Kruskal-Wallis Test

In Exercises 5–8, use the Kruskal-Wallis test.

HIC Measurements Use the sample data from Exercise 1 with a 0.05 significance level to test the claim that small, midsize, large, and SUV vehicles have the same median HIC measurement in car crash tests.

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.