Suppose that a single observation X is taken from the normal distribution with unknown mean and known variance is 1. Suppose that it is known that the value of must be 5, 0, or 5, and it is desired to test the following hypotheses at the level of significance 0.05: H0: = 0, H1: = 5 or = 5. Suppose also that the test procedure to be used specifies rejecting H0 when |X| > c, where the constant c is chosen so that Pr(|X| > c| = 0) = 0.05. a. Find the value of c, and show that if X = 2, then H0 will be rejected. b. Show that if X = 2, then the value of the likelihood function at = 0 is 12.2 times as large as its value at = 5 and is 5.9 109 times as large as its value at = 5.

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