(50 points) Suppose Y1,...,Y, is a random sample of size n = 10 from a normal population with mean O and variance o2 (un

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50 Points Suppose Y1 Y Is A Random Sample Of Size N 10 From A Normal Population With Mean O And Variance O2 Un 1 (45 KiB) Viewed 20 times

(50 points) Suppose Y1,...,Y, is a random sample of size n = 10 from a normal population with mean O and variance o2 (unknown). (a) Find the most powerful test with significance level 0.05 to test Ho : o2 = 2 vs. He : 02 = 1. (b) Under the alternative hypothesis in (a), find B, the probability of the type II error. Further, find the power of the test in this situation. (c) Suppose that we observe Di=ı y = 4. Is there enough evidence to conclude that the random sample is drawn from a standard normal distribution at the significance level a = 0.05? (d) Find a when the rejection region in (a) is RR = {C}=1y<6), n = 10. i=