Let Tn/ have a 2-distribution with n degrees of freedom. For testing H : = 1

Let Tn/θ have a χ2-distribution with n degrees of freedom. For testing H : θ = 1 at level of significance α = .05, find n so large that the power of the UMP unbiased test is ≥ .9 against both θ ≥ 2 and θ ≤ 1 2 . How large does n have to be if the test is not required to be unbiased?