Let U1,U2 . . . , U\" be iid copies of Unif(0, 9). We are interested in testing H0 : 9 = l and Ha : 9 > 1. Suppose we have two test statistics and two corresponding rules to reject the null hypothesis as follows: - T1 2 U1, reject H0 if T1 > 0.95. - T2 = max{U1,...,Un}, reject H0 if T2 > 0951/". (a) (5 points) What are the Type I error probabilities of those two rules? (b) (5 points) Calculate the number of replications needed to estimate the power of the test with a margin of error of at most 0.01 at the conservative approximate 95% condence level. (c) (5 points) Using the number of replications computed above to produce a simulation-based power curve for the two rules using n = 20, 9 E {1, 1.04, 1.08, . . . ,2}. Comment and compare the two plots. (d) (5 points) Using the number of replications computed above to produce a simulation-based power curve for the two rules using 9 : 1.1,n : {20, 30,40, . . . 500}. Comment and compare the two plots