Discussion11.01Corrections - Corrections and comments to...

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Unformatted text preview: Corrections and comments to discussion on 11/01/2011 1. Let X1, X2,…, Xn be a random sample from the distribution with p.d.f () , We wish to test H0: θ ≥ 2 vs. H1: θ < 2. a) If n=5, find a uniformly most powerful rejection region with the significance level α=0.1 that is based on the statistic ∑ . That is, for which values of ∑ should H0 be rejected? ∏ () ∏ Since θ < 2 then Λ increases as ∑ most powerful rejection region is: ( )∑ decreases so we have that our uniformly ∑ ≥ The distribution of ∑ we have found a few times before and you can do for example using the CDF method: () ( ) ( ) ( ) ( ( ( ∑ ( α (∑ ( | ≥ | ) ) , x,θ ) ) , (∑ (∑ ) ≥| ≥ | ) ) ( ( )≥ ) θ = “λ” = 2 “θ” = 1/θ = 1/2 ) ∑ ≥ b) Find the power of the test in part (a) if θ ( | ( ), , ) (∑ (λ ≥ | ) ) θ = “λ” = 1/2 “θ” = 1/θ = 2 8.1-1 No errors. A For problem A where we tested if the distribution was a Poisson(λ ) the test statistic was wrong. I gave you 7.16189 and it should have been 4.53416. My analysis of the results was based on the former value so technically I wrongfully rejected the hypothesis. However I intended to design the problem so we would reject to point out the fact that if we reject H0 there is no alternative hypothesis that we look to. B No errors. ...
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This note was uploaded on 11/15/2011 for the course STAT 409 taught by Professor Stephanov during the Fall '11 term at University of Illinois at Urbana–Champaign.

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