Let X1, ,X9 be a random sample from the N(, 1) distribution To test the hypothesis H0 0 against H1 0, one uses the test reject H0 if 3 X 5 Find the power function and show that this is a bad test

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Question: Let X1, ...,X9 be a random sample from the N(, 1) distribution. To test the hypothesis H0 : 0 against H1 :

Let X1, ...,X9 be a random sample from the N(μ, 1) distribution. To test the hypothesis H0 : μ ≤ 0 against H1 : μ > 0, one uses the test “reject H0 if 3 ≤ X ≤ 5.” Find the power function and show that this is a bad test.

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