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Unformatted text preview: Sample problems 3 1. In the backward elimination algorithm, Minitab ended up with 7 variables. How many partial f-tests did it perform if the number of candidate variables was 12? Solution: 12 + 11 + 10 + 9 + 8 + 7 = 57. 2. Using the sign test on equality of two medians against a two-sided alternative at = 0 . 05, the null hypothesis was rejected on the basis of a sample of size 10. The Wilcoxon sign rank test of the same hypothesis based on the same sample led to an acceptance of H . It is also known that the number of positive differences was smaller than the number of negative differences. What are the possible values of r + and w + in these two tests based on the above information? Solution: Since sign test led to a rejection, r + had be either 1 or 0. If it were 0, w + would have to be 0 as well, and the Wilcoxon test would result in a rejection as well. Therefore r + = 1. Since the Wilcoxon test resulted in an acceptance, w + has to be larger than 8. But since we know that there was only one positive difference, it could have been equal only to...
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- Spring '08