Question: I have a question with the following problem: 5. Suppose that we have n independent observations 2:1, ..., son from a normal distribution with unknown

I have a question with the following problem:

5. Suppose that we have n independent observations 2:1, ..., son from a normal distribution with unknown mean ,u and unknown variance 02, and we want to test H0:J2=1 v.s.Ha:02>1 Hint: for the following problems, please rst review Example 8 of the notes for week 2. a. What is the parameter space (denoted as (90) if the null hypothesis is true? What is the parameter space (denoted as 9) if either the null hypothesis or alternative hypothesis is true? . Derive the maximum likelihood estimator when the null hypothesis is true. . Derive the maximum likelihood estimator for (pg?) if either the null hypothesis or alternative hypothesis is true. 0 o L I 2 o o . Compute the test statistics T = 210g (W). Simplify the maxi-L690 LI\") test statistics as a function of the sample variance 32 = w. . Form a rejection region if we use the above test statistics. f. Assume n = 20, 52 = 2 and level a = 0.05. Compute the critical value in the rejection region. Make a decision

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