Question: 8.7-4. Let X1,X2,. . . ,Xn be a random sample of size n from the normal distribution N01, 03), where at? is known but u.

8.7-4. Let X1,X2,. . . ,Xn be a random sample of size n from the normal distribution N01, 03), where at? is known but u. is unknown. (a) Find the likelihood ratio test for H0: (.1. = my against H1: u. 75 110- Show that this critical region for a test with signicance level a is given by |X \"0| > za/Za//- (b) Test H0: is = 59 against H1: [1. 7E 59 when 02 = 225 and a sample of size n = 100 yielded i = 56.13. Let a = 0.05. (c) What is the p-value of this test? Note that H1 is a two-sided alternative

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