A vice president in charge of sales for a large corporation claims that salespeople are averaging no more than 15 sales contracts per week. As a check on his claim, n = 36 salespeople are selected at random, and the number of contracts made by each is recorded for a single randomly selected week. The sample mean was 17 and sample variance was 9. (a) With a = 0.05, perform an large sample Z hypothesis test to determine if the evidence contradicts the vice president's claim. (b) Suppose that / is actually 16. What is the value for 8, the probability of making a type II error, in this case? And, what is the power of this test for this value of (c) Again suppose that / = 16. If we set o = = 0.05, what size sample should be used? You can assume that o' = 9