I 1. [15 points] Suppose that X1,..., Xn come from a random sample from a normal...

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I 1. [15 points] Suppose that X1,..., Xn come from a random sample from a normal distribution with known mean and unknown variance T. We wish to test the following simple hypotheses: Ho: T = 2 vs HT=3. (a) Find the uniformly most powerful size-a test of these hypotheses. (b) Find a formula to compute the P-value for this test if the observed data is equal to t. I 1. [15 points] Suppose that X1,..., Xn come from a random sample from a normal distribution with known mean and unknown variance T. We wish to test the following simple hypotheses: Ho: T = 2 vs HT=3. (a) Find the uniformly most powerful size-a test of these hypotheses. (b) Find a formula to compute the P-value for this test if the observed data is equal to t.