13-4 Wilcoxon Rank-Sum Test for Two Independent Samples 669 ANSUR I 1988 1620 1693 1558 1783 1609 1649 1628 1597 1640 1660 1597 1569 ANSUR II 2012 1672 1621 1623 1633 1526 1570 1616 1690 1637 1718 1588 1520 1618 1631 1642 2. 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. 3. 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. 4. Efficiency Refer to Table 13-2 on page 645 and identify the efficiency of the Wilcoxon rank-sum test. What does that value tell us about the test? Wilcoxon Rank-Sum Test. In Exercises 5–8, use the Wilcoxon rank-sum test. 5. Heights of Females from ANSUR I and ANSUR II Use the sample data given in Exercise 1 and test the claim that the sample of female heights from ANSUR I and the sample of female heights from ANSUR II are from populations with the same median. Use a 0.05 significance level. 6. Radiation in Baby Teeth Listed below are amounts of strontium-90 (in millibecquerels, or mBq, per gram of calcium) in a simple random sample of baby teeth obtained from Pennsylvania residents and New York residents born after 1979 (based on data from “An Unexpected Rise in Strontium-90 in U.S. Deciduous Teeth in the 1990s,” by Mangano et al., Science of the Total Environment). Use a 0.05 significance level to test the claim that the median amount of strontium-90 from Pennsylvania residents is the same as the median from New York residents. Pennsylvania 155 142 149 130 151 163 151 142 156 133 138 161 New York 133 140 142 131 134 129 128 140 140 140 137 143 7. Clinical Trials of Lipitor The sample data below are changes in LDL cholesterol levels in clinical trials of Lipitor (atorvastatin). It was claimed that Lipitor had an effect on LDL cholesterol. (The data are based on results given in a Parke-Davis memo from David G. Orloff, M.D., the medical team leader for clinical trials of Lipitor. Pfizer declined to provide the author with the original data values.) Negative values represent decreases in LDL cholesterol. Use a 0.05 significance level to test the claim that for those treated with 20 mg of Lipitor and those treated with 80 mg of Lipitor, changes in LDL cholesterol have the same median. What do the results suggest? Group Treated with 20 mg of Lipitor: -28 -32 -29 -39 -31 -35 -25 -36 -35 -26 -29 -34 -30 Group Treated with 80 mg of Lipitor: -42 -41 -38 -42 -41 -41 -40 -44 -32 -37 -41 -37 -34 -31 8. Queues Listed below are observed waiting times (seconds) of cars at a Delaware vehicle inspection station. The data from two waiting lines are real observations and the data from the single waiting line are modeled from those real observations. These data are from Data Set 30 “Queues” in Appendix B. The data were collected by the author. Use a 0.01 significance level to test the claim that cars in two lines have a median waiting time equal to that of cars in a single common line. Two Lines 64216 86340200630333329915553 5978651090663518566268350 95100 163 101 One Line 64 157 142 279 253 476 478 474 402 722 761 692 837 903 734 606 268 310 129 133 122 129 233 461 482 518 509 580
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