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

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Corrections and comments to discussion on 11/01/2011 1. Let X 1 , X 2 , …, X n be a random sample from the distribution with p.d.f ( ) , We wish to test H 0 : θ ≥ 2 vs. H 1 : 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 H 0 be rejected? ( ) ( )∑ Since θ < 2 then Λ increases as decreases so we have that our uniformly most powerful rejection region is: The distribution of we have found a few times before and you can do for example using the CDF method: ( ) ( ) ( ) ( ) ( ) , x,θ ( ) ( , ) α ( | ) (∑ ≥ | )
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