1 50 Points Suppose Y1 Y Is A Random Sample Of Size N 10 From A Normal Population With Mean O And Variance O 1 (32.55 KiB) Viewed 21 times
1 50 Points Suppose Y1 Y Is A Random Sample Of Size N 10 From A Normal Population With Mean O And Variance O 2 (32.55 KiB) Viewed 21 times
1. (50 points) Suppose Y1,...,Y, is a random sample of size n = 10 from a normal population with mean O and variance o? (unknown). (a) Find the most powerful test with significance level 0.05 to test Ho : 02 = 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 -1y? = 4. Is there enough evidence to conclude that the random sample is drawn from a standard niprmal distribution at the significance level a = 0.05? (d) Find a when the rejection region in (a) is RR = {2}=1 41 <6), n = 10.
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