Answer Happy

3. Let X1, X2, X, be iid N(44,0%). Here we assume that he is known and is equal to n. Consider the hypothesis test: HO 0 = 2 H: 0=1 We denote s2 := (x-), (8)2 := 2.6%:--) (a) (10 points) Which of the following rejection regions: Ci = {s? > K},C2 = {82 SK) C3 {(s)? 2 K),Cs = {(8') < K} is most appropriate for this hypothesis test? Explain your reason (the right reasoning is worth 5 points with the right region, picking the wrong region results in 0 point without any consideration of the reason.) (b) (10 points) Decide K so that the region you pick in part a is of size a ( this question is graded independently of part a, as long as the calculation in this part is correct). (c) (10 points) Use Neyman Pearson to show that the region you pick in part a is a most powerful rejection region of size a (this part is tied to part a. If you got part a wrong you cannot get this right, which will also result in 0 point here. So consider both carefully).