Correct answer: (A) (S−1)/S if S>1, zero otherwise
Explanation
Given S=s, X₁ is uniform on (0,s). Hence E(φ|S=s)=P(X₁>1|S=s)=(s−1)/s for s>1, zero otherwise. Iterated expectation shows this conditional test has exactly the same rejection probability for every θ. **A**.
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