3. Suppose {Xi, i = 1...n} is a random sample from N(u, 02) where both u and op > 0 are unknown. Consider testing hypoth

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3 Suppose Xi I 1 N Is A Random Sample From N U 02 Where Both U And Op 0 Are Unknown Consider Testing Hypoth 1 (70.59 KiB) Viewed 47 times

3. Suppose {Xi, i = 1...n} is a random sample from N(u, 02) where both u and op > 0 are unknown. Consider testing hypotheses THỊo := 0%, vs. H :040% = using data {X;, i = 1...n}. = (a) Let S = noget , where ô2 = 2?=1(X; – Xn)?, Xn = + 2?=X;. Propose a test to control 21-1; 2 i nô2 i= size at a based on test statistic S. (b) Find the likelihood ratio statistic LRn. (c) Show LRn > c for some c is equivalent to S > b for some b. Thus in this case likelihood ratio test is equivalent to the test in (a).