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GATE 2026 BM – Question 53

Engineering Mathematics · Probability and Statistics · 2 marks · Multiple select

Which changes increase statistical power when comparing two sample means using a t-test, with other assumptions fixed?

  1. Increase both sample sizes from 100 to 1000
  2. Increase significance level α from 0.01 to 0.2
  3. Decrease α from 0.2 to 0.01
  4. Decrease both sample sizes from 1000 to 100

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Show answer and explanation

Correct answer: (A) Increase both sample sizes from 100 to 1000; (B) Increase significance level α from 0.01 to 0.2

Explanation

Increasing sample size reduces standard error and makes a fixed true mean difference easier to detect. Increasing α enlarges the rejection region, raising power at the cost of a higher type-I-error probability. Decreasing either sample size or α has the opposite effect. Thus A,B.

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