The following two examples show that the assumption of a finitesample space is needed in Problem 8 7 (i) Let X1, , Xn be i i d according to a normal distribution N(, 2) and test H 0 against K 0 (ii) Let X and Y be independent Poisson variables with E(X) and E(Y ) 1, and test H 0 against K 0 In each...

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The following two examples show that the assumption of a finitesample space is needed in Problem 8.7.

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The following two examples show that the assumption of a finitesample space is needed in Problem 8.7.

(i) Let X1, …, Xn be i.i.d. according to a normal distribution N(σ, σ2) and test H : σ = σ0 against K : σ>σ0.

(ii) Let X and Y be independent Poisson variables with E(X) = λ and E(Y ) =

λ + 1, and test H : λ = λ0 against K : λ>λ0. In each case, determine the LMP test and show that it is not LUMP.

[Compare the LMP test with the most powerful test against a simple alternative.]

Section 8.2

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Testing Statistical Hypotheses Volume I

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Authors: E.L. Lehmann, Joseph P. Romano

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The following two examples show that the assumption of a finitesample space is needed in Problem 8.7.

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Testing Statistical Hypotheses Volume I

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