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(Solved): Given H_(0):\theta =kH_(1):\theta =2x>(1)/(2)\alpha \beta \alpha (\beta )/(64)=1f(x)=(1 \theta ) ...



Given

H_(0):\theta =kH_(1):\theta =2x>(1)/(2)\alpha \beta \alpha (\beta )/(64)=1f(x)=(1 \theta )x^(\theta ),\theta >0,0. You are testing the hypothesis H_(0):\theta =k against the H_(1):\theta =2, and you use x>(1)/(2) as a critical region in this one sided test. If the Type I error is \alpha and Type II error is \beta such that \alpha (\beta )/(64)=1 what is k ?


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