Suppose that X1, , Xn form a random sample from the normal distribution with known mean and unknown variance 2, and the following simple hypotheses are to be tested H0 2 2, H1 2 3 a Show that among all test procedures for which () 0 05, the value of () is minimized by a procedure that rejects H0 when b For n 8, find the value of the constant c that appears in part (a)

Question: Suppose that X1, . . . , Xn form a random sample from the normal distribution with known mean and unknown variance 2, and

Suppose that X1, . . . , Xn form a random sample from the normal distribution with known mean μ and unknown variance σ2, and the following simple hypotheses are to be tested:
H0: σ2 = 2,
H1: σ2 = 3.
a. Show that among all test procedures for which α(δ) ≤ 0.05, the value of β(δ) is minimized by a procedure that rejects H0 when
b. For n = 8, find the value of the constant c that appears in part (a).

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a By the NeymanPearson lemma H 0 should be rejected if f 1 Xf 0 ... View full answer

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