Let X₁,X₂, . . . , X_n be a random sample from the normal distribution N(θ,1). Show that the likelihood ratio principle for testing H₀ : θ = θ' where θ' is specified, against H₁ : θ ≠ θ' leads to the inequality |‾x − θ'| ≥ c.
(a) Is this a uniformly most powerful test of H₀ against H₁?

(b) Is this a uniformly most powerful unbiased test of H₀ against H₁?