670 CHAPTER 13 Nonparametric Tests Appendix B Data Sets. In Exercises 9–12, refer to the indicated data set in Appendix B and use the Wilcoxon rank-sum test. 9.Queues Repeat Exercise 8 using all of the waiting times from the two line configuration and the single line configuration. The data are from Data Set 30 “Queues” in Appendix B. 10.Do Men and Women Talk the Same Amount? Refer to Data Set 14 “Word Counts” in Appendix B and use the measured word counts from men in the third column (“M2”) and the measured word counts from women in the fourth column (“F2”). Use a 0.01 significance level to test the claim that contrary to a popular belief, the median of the numbers of words spoken by men in a day is the same as the median of the numbers of words spoken by women in a day. 11.IQ and Lead Exposure Data Set 11 “IQ and Lead” in Appendix B lists full IQ scores for a random sample of subjects with “medium” lead levels in their blood and another random sample of subjects with “high” lead levels in their blood. Use a 0.05 significance level to test the claim that subjects with medium lead levels have a higher median of the full IQ scores than subjects with high lead levels. Does lead level appear to affect full IQ scores? 12.IQ and Lead Exposure Data Set 11 “IQ and Lead” in Appendix B lists performance IQ scores for a random sample of subjects with low lead levels in their blood and another random sample of subjects with high lead levels in their blood. Use a 0.05 significance level to test the claim that subjects with low lead levels have a higher median of the performance IQ score than those with high lead levels. Does lead exposure appear to have an adverse effect? 13.Using the Mann-Whitney U Test The Mann-Whitney U test is equivalent to the Wilcoxon rank-sum test for independent samples in the sense that they both apply to the same situations and always lead to the same conclusions. In the Mann-Whitney U test we calculate z = U - n1n2 2 Bn1n21n1 + n2 + 12 12 where U = n1n2 + n11n1 + 12 2 - R and R is the sum of the ranks for Sample 1. Use the male height values in Table 13-5 on page 666 to find the z test statistic for the Mann-Whitney U test. Compare this value to the z test statistic found using the Wilcoxon rank-sum test. 14.Finding Critical Values Assume that we have two treatments (A and B) that produce quantitative results, and we have only two observations for treatment A and two observations for treatment B. We cannot use the Wilcoxon signed-ranks test given in this section because both sample sizes do not exceed 10. Rank Rank Sum for Treatment A 1 2 3 4 A A B B 3 a. Complete the accompanying table by listing the five rows corresponding to the other five possible outcomes, and enter the corresponding rank sums for treatment A. b. List the possible values of R and their corresponding probabilities. (Assume that the rows of the table from part (a) are equally likely.) c. Is it possible, at the 0.10 significance level, to reject the null hypothesis that there is no difference between treatments A and B? Explain. 13-4 Beyond the Basics
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