Listed below are numbers of hospital admissions in one region due to traffic accidents on different Fridays falling on the 6th day of a month and the following 13th day of the month (based on data from “Is Friday the 13th Bad for Your Health,” by Scanlon et al., British Medical Journal, Vol. 307). Assume that we want to use the Wilcoxon signed-ranks test to test the claim of no difference between traffic accidents that occur on Friday the 6th and those that occur on the following Friday the 13th. Identify the null hypothesis and alternative hypothesis.

a. What requirements must be satisfied for this test? 

b. Is there any requirement that the samples must be from populations having a normal distribution or any other specific distribution? 

c. In what sense is the Wilcoxon signed-ranks test a “distribution-free test”?

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Friday 6th Friday 13th 9 13 6 12 11 14 11 10 3 4 5 12