GATE 2021 ST – Question 63

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

X takes 7,8,9,10. Under p₀ the probabilities are .90,.05,.04,.01;under p₁ they are .69,.10,.16,.05. Find the power of the most-powerful size-.05 test of p=p₀ against p=p₁ from one observation,to two decimals.

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Correct answer: 0.20 to 0.22

Explanation

The p₁/p₀ ratios at 7,8,9,10 are .7667,2,4,5. Neyman–Pearson rejects at the largest ratios:first 10 consumes null probability .01,then 9 consumes .04,total .05 exactly. Under the alternative,the rejection probability is .05+.16=**0.21**.

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