GATE 2022 ST – Question 20

Testing of Hypotheses · Most Powerful and Uniformly Most Powerful Tests · 1 mark · Multiple choice

Six iid Bernoulli(θ) observations are used to test θ=1/2 against θ>1/2 via Y=ΣX_i. Observed Y=4. Find the p-value.

Show answer and explanation

Correct answer: (C) 11/32

Explanation

Under H₀,Y∼Binomial(6,1/2). A larger Y favors the alternative,so p=P(Y≥4)=[binom(6,4)+binom(6,5)+binom(6,6)]/64=(15+6+1)/64=**11/32, C**.

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