Unformatted text preview: . Let μ = E( X ) . (a) (10 pts) Find the UMP levelα test for testing H : μ ≤ μ versus H 1 : μ > μ , some a given μ > . HINT: Use that if X i have pdf f ( x, θ ) then 2 θ ∑ n i =1 X i ∼ χ 2 2 n . (10 pts extra credit for a proof of this fact.) (b) (10 pts) Find an expression for the power of the UMPtest from part (a) at a given μ 1 with μ 1 > μ . (c) (10 pts) Use the central limit theorem to ±nd approximate values for the critical value of the UMPtest. (d) (10 pts) Use parts (b) and (c) to in order to ±nd the power for n = 22 , μ = 10 , μ 1 = 12 . 5 and α = 0 . 05 ....
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 Spring '07
 Polonik
 Statistics, Normal Distribution, Variance, Probability theory, pts

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