GATE 2023 ST – Question 64

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

One observation has CDF F(x)=0 for x<0,1−(1−x)^θ for 0≤x<1,and 1 for x≥1,θ>0. Test θ=1 against θ=2 by rejecting if x<0.5. If α is the level and β the power,find α+β to two decimals.

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Correct answer: 1.20 to 1.30

Explanation

The distribution is continuous,so strict versus non-strict cutoff makes no difference. Under θ=1,α=F₁(.5)=.5. Under θ=2,β=F₂(.5)=1−.5²=.75. Thus α+β=**1.25**; β here denotes power,as specified.

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