Let X 1 ,X 2 , , X n be a random sample from the normal distribution N(,1) Show that the likelihood ratio principle for testing H 0 ' where ' is specified, against H 1 ' leads to the inequality x ' c (a) Is this a uniformly most powerful test of H 0 against H 1 (b) Is this a uniformly most powerful unbiased test of H 0 against H 1

Question: Let X 1 ,X 2 , . . . , X n be a random sample from the normal distribution N(,1). Show that the likelihood

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?

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