GATE 2022 ST – Question 60

Testing of Hypotheses · Most Powerful and Uniformly Most Powerful Tests · 2 marks · Numerical answer

Four iid Bernoulli(θ) observations test θ=1/4 against θ>1/4 by rejecting when ΣX_i>2. Let α be type-I error and γ(θ) the power. Find 16α+7γ(1/2),as an integer.

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Correct answer: 3 to 3

Explanation

The rejection probability is γ(θ)=4θ³(1−θ)+θ⁴. At θ=1/4,this is (12+1)/256=13/256. At θ=1/2,it is 5/16. Therefore 16α+7γ(1/2)=13/16+35/16=**3**.

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