Problem 1. (a) Simulate <= Y; in problem 10.102, with n = 100 and p =.55 in R. Does your simulation lead to a rejection

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Problem 1 A Simulate Y In Problem 10 102 With N 100 And P 55 In R Does Your Simulation Lead To A Rejection 1 (37.65 KiB) Viewed 27 times

PROBLEM 10.102:

Problem 1 A Simulate Y In Problem 10 102 With N 100 And P 55 In R Does Your Simulation Lead To A Rejection 2 (66.72 KiB) Viewed 27 times

Problem 1 A Simulate Y In Problem 10 102 With N 100 And P 55 In R Does Your Simulation Lead To A Rejection 3 (90.16 KiB) Viewed 27 times

Problem 1. (a) Simulate <= Y; in problem 10.102, with n = 100 and p =.55 in R. Does your simulation lead to a rejection of Ho : p= Po, with po = .5 at an a = .05 level? (b) Repeat the simulation in the previous part 1000 times. What proportion of the time was Ho rejected? How is this proportion related to the power of the test?

10.102 Let Yı, Y2, ..., Y, denote a random sample from a Bernoulli-distributed population with parameter p. That is, p(yi|p) = pº (1 – p) –» Y; = 0,1. a Suppose that we are interested in testing Ho: p = po versus Ha: p = Pa, where po < Pa. i Show that L(po) po(1 – Pa) 1 ) Σή Po L(pa) (1 – popa n - = La )" = [ ( - )". - 1- Pa

ii Argue that L(po)/L(pa) <k if and only if i=1 Y> k* for some constant k*. iii Give the rejection region for the most powerful test of H, versus Ha. b Recall that =1 Y; has a binomial distribution with parameters n and p. Indicate how to determine the values of any constants contained in the rejection region derived in part [a(iii)] c Is the test derived in part (a) uniformly most powerful for testing Ho: p = po versus H:p > po? Why or why not? с