Question: Thank you for the help. This question pertains to Null Hypothesis, alternative hypothesis, alpha and beta values. Q1: Suppose that Y1, .. . , Yn

Thank you for the help. This question pertains to Null Hypothesis, alternative hypothesis, alpha and beta values.

Q1: Suppose that Y1, .. . , Yn are i.i.d from the N01, 52) distribution, where o2 is known, but u is unknown. Consider testing H0 : u = \"0 against Ha : u > H0 with ct=.05 level of signicance. (40pts) a) Assume that #0 = 0, o2 = 25, and n = 4. What is the probability of type two error when p = 1, when u = 2, and when u = 3? (20pts) b) Repeat part (a) assuming a larger sample size of n = 16. Do you have any comments about the comparison of power for the two sample sizes? (20pts)

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