Assessing a summer language institute. Exercise 7.45 (page

Chapter , Problem 16.71

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Assessing a summer language institute. Exercise 7.45 (page 446) gives data on a study of the effect of a summer language institute on the ability of high school language teachers to understand spoken French. This is a matched pairs study, with scores for 20 teachers at the beginning (pretest) and end (posttest) of the institute. We conjecture that the posttest scores are higher on the average. FRENCH (a) Carry out the matched pairs t test. That is, state hypotheses, calculate the test statistic, and give its P-value. (b) Make a Normal quantile plot of the gains: posttest scorepretest score. The data have a number of ties and a low outlier. A permutation test can help check the t test result. (c) Carry out the permutation test for the difference in means in a matched pairs setting, using 9999 resamples. The Normal quantile plot shows that the permutation distribution is reasonably Normal. What is the P-value for the permutation test? Do your tests in parts (a) and (c) lead to the same practical conclusion?