Inferential Statisticshard
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Consider the Neyman-Pearson lemma. For testing H0:θ=θ0H_0: \theta=\theta_0 vs H1:θ=θ1H_1: \theta=\theta_1, if the likelihood ratio Λ(x)=L(θ0x)L(θ1x)\Lambda(x) = \frac{L(\theta_0|x)}{L(\theta_1|x)} is used to define the rejection region R={x:Λ(x)<k}R = \{x : \Lambda(x) < k\}, what is the property of this test?