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GATE 2025 ST – Question 63

Testing of Hypotheses · Likelihood Ratio and Large Sample Tests · 2 marks · Numerical answer

X~Bin(3,θ),0<θ<1. To test H₀:1/4≤θ≤3/4 against the outside alternatives, reject for X=0 or 3. Find the test size to two decimals.

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Correct answer: 0.42 to 0.46

Explanation

The power is (1−θ)³+θ³=1−3θ+3θ², a convex function. Its maximum over the null interval occurs at either endpoint. At θ=1/4 it equals 27/64+1/64=7/16=.4375. Size=**.44**.

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