Problem 2BSC

Freshman 15For the matched pairs listed in Exercise,identify the following components used in the Wilcoxon signed-ranks test:

a.Differencesd

b.The ranks corresponding to the nonzero values of |d |

c.The signed ranks

d.The sum of the positive ranks and the sum of the absolute values of the negative ranks

e.The value ofT

f.The critical value ofT(assuming a 0.05 significance level in a test of no difference between September weights and April weights)

Exercise

Wilcoxon Signed-Ranks Test for Freshman 15The following table lists some of the weights from Data Set 4 in Appendix B. Those weights were measured from college students in September and later in April of their freshman year. Assume that we plan to use the Wilcoxon signed-ranks test to test the claim of no difference between September weights and April weights. What requirements must be satisfied for this test? Is there any requirement that the populations must have a normal distribution or any other specific distribution? In what sense is this Wilcoxon signed-ranks test a “distribution-free test”?

Solution 2BSC

The Interpretetion is as follows:

Here the P-value of 0.0023 is less than the Level of Significance of 0.05 so there is sufficient evidence to reject the Null Hypothesis and the claim of no difference.

Thus we conclude that the median is less than 98.6°F. Here we observe that different approaches to perform the sign test can lead to different results as indicated by the value of the test statistic given by -4.61, -4.29 , -2.82. But the conclusions come out to be the same in this case , there can be different conclusions in different cases observed.