The LRT rejects for |(X₁+X₂)/√2|>z_.975. For a shifted unit normal, the two-sided rejection probability is minimized at mean zero and increases with the absolute mean, so its power is at least .05 everywhere: it is unbiased. No UMP two-sided test exists because positive and negative alternatives favor opposite one-sided tails. Symmetry gives E₀[X₁φ]=0. **B**.
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