Unformatted text preview: the hypothesis H : θ ≥ θ v.s. the alternative H A : θ < θ at level of signiﬁcance α . [Hint: Question 7.10 in LNp.23, and notice that X 1 + ··· + X n follows a Gamma distribution] 7. Let X 1 ,X 2 ,X 3 be i.i.d. from Binomial B (1 ,p ). Derive the uniformly most powerful unbiased (UMPU) test for testing the hypothesis H : p = 0 . 25 v.s. the alternative H A : p 6 = 0 . 25 at level of signiﬁcance α . Determine the test for α = 0 . 05. [Hint: Let Y ∼ B (3 , . 25), then P ( Y = 0) = 0 . 42, P ( Y = 1) = 0 . 42, P ( Y = 2) = . 14, and P ( Y = 3) = 0 . 02] 1...
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 Spring '11
 lisa
 Probability theory, Randomness, Statistical power, alternative Ha, neymanpearson lemma

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