Suppose that X follows a distribution with probability density function f θ (x) &prop; x θ-1 (1 - x) θ-1 ; 0 0. The uniformly most powerful critical region for testing H 0 : θ = 1 against H 1 : θ > 1 based on a single observation is of the form:

Mathematics · Statistical Inference

Suppose that X follows a distribution with probability density function f θ (x) &prop; x θ-1 (1 - x) θ-1 ; 0 < x < 1, θ > 0. The uniformly most powerful critical region for testing H 0 : θ = 1 against H 1 : θ > 1 based on a single observation is of the form:

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Correct answer

[0, α 2 ) ∪ (1 - α 2 , 1]

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