GATE 2023 ST – Question 42

Testing of Hypotheses · Most Powerful and Uniformly Most Powerful Tests · 2 marks · Multiple choice

For (X,Y)∈{0,1}²,P(0,0)=P(1,1)=θ and P(1,0)=P(0,1)=1/2−θ,0≤θ≤1/2. Test θ=1/4 against θ=1/3 using n iid pairs. If m counts equal pairs,which likelihood-ratio rejection form is correct?

m>c
m<c
c₁<m<c₂
m<c₁ or m>c₂

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Show answer and explanation

Correct answer: (A) m>c

Explanation

The alternative/null ratio is (4/3)^m(2/3)^(n−m)=(2/3)^n2^m,strictly increasing in m. Neyman–Pearson rejects for large ratio,therefore large m. **A**,with boundary randomization if an exact unattainable discrete size is required.

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