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 rank-sum 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
Table 13-1 from the Chapter Problem lists departure delay times (min) for samples from American Airlines Flights 19 and 21. In the Chapter Problem we noted that the parametric t test (Section 9-4) should not be used because the sample data violate this requirement: “The two sample sizes are both large (with n1 > 30 and n2 > 30) or both samples come from populations having normal distributions.” Instead of using the t test, we can use the Wilcoxon rank-sum test. The accompanying STATDISK display results from the data in Table 13-1. We can see that the test statistic is z = −1.44 (rounded). The test statistic does not fall in the critical region bounded by the critical values of −1.96 and 1.96, so we fail to reject the null hypothesis of equal medians. Using the samples in Table 13-1, we do not have enough evidence to conclude that departure delay times for Flight 19 have a median different from the median of departure delay times for Flight 21.
Its given that the given data are the arrival delay times of the American Airlines flights 19 and 21 taken randomly , so the first requirement of the Wilcoxon Rank-Sum test is satisfied. Also each...