Problem 1. (a) Simulate <= Y; in problem 10.102, with n = 100 and p =.55 in R. Does your simulation lead to a rejection
Posted: Wed May 11, 2022 7:11 am
- 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 28 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 2 (66.72 KiB) Viewed 28 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 28 times
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