Problem 3 (16 points ) Answer the following questions: a. Suppose X ,, X 2, X; are i.i.d. N (u, v13.5). We are interested in the following test: H. : u = 15 against / = 16. The following plot is the graph of the Neyman-Pearson lemma ratio against values of x. Neyman-Pearson lemma test: Mo = 15 against Ha = 16 Neyman-Pearson lemma ratio Suppose k = 0.7. What is the exact significance level o? Note: You must find the exact value of a first that corresponds to the critical region for the given k. b. Suppose X, , ..., Xis are i.i.d. N (u, 4). We are interested in the following test: Ho : A = 100 against u = 100 . The following plot is the graph of the likelihood ratio test against values of i . Likelihood ratio test : Mo = 100 against Ho * 100 95 100 105 110 Suppose k = 0.2. What is the rejection region and the significance level o? Note: You must find the exact values of a first that correspond to the critical region for the given k