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A regional sales manager chooses two similar offices to study the effectiveness of a new training program aimed at increasing sales. One office institutes the training program and the other does not. (Assume that the office staffs are independent of one another). The office that does not institute the training program, office 1, has 31 sales people. The mean sales person over the next month for office 1 turns out to be $3197, with a standard deviation of $102. Office 2, the office that does institute the training program, has 41 sales people; and the mean sales per person over the next month turns out to be $3229, with a standard deviation of $107.
a. at the 5% significance level, does the data provide sufficient evidence to conclude that the training program increases mean sales?
b. use the data given on the previous page to test the conjecture that there is more variability for the sales amounts in office 2, with the training, than there is in office1, without the training. use a 5% significance level.