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Nonparametric Hypothesis Testing

Need help for the following:

(1) Airline Fares. Listed below are the costs of flights from New York to San Francisco for US Air, Continental, Delta, United, American, Alaska, and Northwest. Use a 0.05 significance level to test the claim that there is no difference in cost between flights scheduled one day in advance and those scheduled 30 days in advance. What appears to be a prudent scheduling strategy?

Flight scheduled one day in advance 456 614 628 1088 943 567 536
Flight scheduled 30 days in advance 244 260 264 264 278 318 280

(2) Cheating gas pumps. When testing gas pumps in Michigan for accuracy, fuel quality enforcement specialists tested pumps and found that 1299 were not accurate (within 3.3 oz when 5 gal is pumped) and 5686 were accurate. Use a 0.01 significance level to test the claim of an industry representative that less than half of Michigan gas pumps are inaccurate.
(Use the sign test for the claim involving nominal data)

(3) Weather forecasts. Listed below are actual high temperatures and the high temperatures forecast one day in advance . Use a 0.05 significance level to test the claim that the population of differences has a median of zero. What do the results suggest about the accuracy of the predictions?

Actual high temperature 80 77 81 85 73 73 80 72

High temperature forecast one day before 78 75 81 85 76 75 79 74

(4) Presidents and Popes. Refer to the longevity data for US presidents and popes below. Use a 0.05 significance level to test the claim that the two samples are from populations with the same median.

Presidents 10 29 26 28 15 23 17 25 0 20 4 1 24 16 12 4 10 17 16 0 7 24 12 4
18 21 11 2 9 36 12 28 3 16 9 25 23 32

Popes 2 9 21 3 6 10 18 11 6 25 23 6 2 15 32 25 11 8 17 19 5 15 0 26

(5) Cigarettes. Refer to attached data set for the amounts of tar in the sample of king size cigarettes, which are nonfiltered, nonmenthol, and non-light. Use a 0.01 signifance level to test the claim that the median amount of tar in nonfiltered king size cigarettes is greater than the median amount of tar in 100 mm filtered cigarettes.

(6) Tar in Cigarettes. Refer to the attached data set 4 and use the amounts of tar (mg per cigarette) in the three categories of cigarettes. Use a 0.05 signifance level to test the claim that the three categories of cigarettes yield the same median amount of tar. Given that only the king size cigarettes are not filtered, do the filters appear to make a difference?

(Use the Kruskal-Wallis test with the data from Appendix B)

King size are non-filtered, non-menthol , and non-light

100 mm are filtered and non-light

100 mm nonmenthol are filtered and nonlight

Attachments

Solution Summary

The solution provides step by step method for the calculation of non-parametric testing of hypothesis. Formula for the calculation and Interpretations of the results are also included.

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