Question: Let X be distributed according to P, , and let T be sufficient for . If (X) is any test of a hypothesis

Let X be distributed according to Pθ, θ ∈ , and let T be sufficient for θ. If ϕ(X) is any test of a hypothesis concerning θ, then ψ(T ) given by ψ(t) =

E[ϕ(X) | t] is a test depending on T only, and its power function is identical with that of ϕ(X).

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