Wilcoxon RankSum Test. In Exercises 58, use the Wilcoxon ranksum test.Clinical Trials of

Arrival Delay Times Example 2 in this section used samples of departure delay times from American Airlines Flights 19 and 21, but the table below lists simple random samples of arrival delay times (min) from those same flights. (The data are from Data Set 15 in Appendix B.) Are the requirements for using the Wilcoxon ranksum test satisfied? Why or why not? Flight 19 5 32 13 9 19 49 30 23 14 21 32 11 Flight 21 23 28 103 19 5 46 13 3 13 106 34 24

Rank Sum After ranking the combined list of 24 arrival delay times, find the sum of the ranks for Flight 19

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

Efficiency Refer to Table 132 in Section 131 and identify the efficiency of the Wilcoxon ranksum test. What does that value tell us about the test?

Wilcoxon RankSum Test. In Exercises 58, use the Wilcoxon ranksum test.Arrival Delay Times Use the sample data given in Exercise 1 and test the claim that arrival delay times for Flight 19 and Flight 21 have the same median. Use a 0.05 significance level.

Wilcoxon RankSum Test. In Exercises 58, use the Wilcoxon ranksum test.TaxiOut Times Listed below are samples of taxiout times (min) for American Airlines Flights 19 and 21 (from Data Set 15 in Appendix B). Use the sample data to test the claim that taxiout times for Flight 19 and Flight 21 have the same median. Use a 0.05 significance level. Flight 19 15 12 19 18 21 20 13 15 43 18 17 19 Flight 21 13 20 12 17 35 19 22 43 49 45 13 23

Wilcoxon RankSum Test. In Exercises 58, use the Wilcoxon ranksum test.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 ParkeDavis 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 atorvastatin and those treated with 80 mg of atorvastatin, changes in LDL cholesterol have the same median. What do the results suggest? Group treated with 20 mg of atorvastatin : 28 32 29 39 31 35 25 36 35 26 29 34 30 Group treated with 80 mg of atorvastatin : 42 41 38 42 41 41 40 44 32 37 41 37 34 31

Wilcoxon RankSum Test. In Exercises 58, use the Wilcoxon ranksum test.Radiation in Baby Teeth Listed below are amounts of strontium90 (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 Strontium90 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 strontium90 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

Appendix B Data Sets. In Exercises 912, refer to the indicated data set in Appendix B and use the Wilcoxon ranksum test.. IQ and Lead Exposure Data Set 5 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 full IQ scores with a higher median than the median full IQ score for subjects with high lead levels. Does lead level appear to affect full IQ scores?

Appendix B Data Sets. In Exercises 912, refer to the indicated data set in Appendix B and use the Wilcoxon ranksum test..IQ and Lead Exposure Data Set 5 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 performance IQ score than those with high lead levels. Does lead exposure appear to have an adverse effect?

Appendix B Data Sets. In Exercises 912, refer to the indicated data set in Appendix B and use the Wilcoxon ranksum test.Weights of Quarters Data Set 21 in Appendix B lists weights (g) of pre1964 quarters and post1964 quarters. Use a 0.05 significance level to test the claim that the samples are from populations with the same median. Does it appear that the design of quarters changed in 1964?

Appendix B Data Sets. In Exercises 912, refer to the indicated data set in Appendix B and use the Wilcoxon ranksum test.. Weights of Coke Data Set 19 in Appendix B lists weights (lb) of the cola in cans of regular Coke and diet Coke. Use a 0.05 significance level to test the claim that the samples are from populations with the same median. If there appears to be a difference, try to explain it.

Using the MannWhitney U Test The MannWhitney U test is equivalent to the Wilcoxon ranksum test for independent samples in the sense that they both apply to the same situations and always lead to the same conclusions. In the MannWhitney U test we calculate z = U n 1 n 2 2 n 1 n 2 ( n 1 + n 2 + 1 ) 12 where U = n 1 n 2 + n 1 ( n 1 + 1 ) 2 R Use the pulse rates listed in Table 135 in this section to find the z test statistic for the MannWhitney U test. Compare this value to the z test statistic found using the Wilcoxon ranksum test

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 test statistic 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 cases, 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.