Question: Question 1 (20 points) Suppose X1,X2, . . . ,Xn is a random sample from a normal population N (p, 1). Consider the following hypotheses

Question 1 (20 points) Suppose X1,X2, . . . ,Xn is

Question 1 (20 points) Suppose X1,X2, . . . ,Xn is a random sample from a normal population N (p, 1). Consider the following hypotheses Ha : p=2 v.s. H1 :p=3, and the rejection region given by {5: 2 2.6}. (a) If n = 20, nd the type-I error ad the type-II error. (b) If we want the type-II error to be smaller than 0.01, i.e., ,6 5 0.01, what is the minimum value of the sample size 1;? You may directly use the CDF of the standard normal distribution @(z) = P(Z <_: z without calculating its value>

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