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6. MINITAB QUESTION. Hypothesis testing for u when o is known. Imagine choosing n = 16 women at random from a large population and measuring their heights. Assume that the heights of the women in this population are normally distributed with u = 63.8 inches and G = 3 inches. Suppose you then test the null hypothesis Ho: H - 63.8 versus the alternative that He: u # 63.8, using a = 0.10. Simulate the results of doing this test 100 times by entering the following commands: random 16 cl-c100; normal 63.8 3. ztest 63.8 3 cl-c100 (A) In how many of these hypothesis tests did you reject Ho? In how many of these hypothesis tests did you expect to reject Ho? (B) Are the p-values all the same for the 100 tests? Why or why not? (C) Suppose you used a = 0.01 instead of a = 0.10. Does this change any of your decisions to reject or not? In how many of these hypothesis tests did you expect to reject Ho? In general, should the number of rejections increase or decrease if a = 0.01 is used instead of a = 0.10? (D) Now assume that the population really has a mean of u = 63 instead of 63.8. Carry out the above 100 simulations again by changing the command "normal 63.8 3." to "normal 63 3." Once again, using a =0.10, in how many tests did you reject the null hypothesis Ho: ( =63.8? In how many of these hypothesis tests did you expect to reject Ha? (E) Is a rejection of Ho in part (A) a correct decision? If not, what type of error are you making in rejecting Ho? (F) Is a rejection of Ho in part (D) a correct decision? If not, what type of error are you making in rejecting Ho