The GATE Grind

GATE 2021 MN – Question 46

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

Test H₀:mean Fe=62% against Hₐ:mean Fe<62%. A sample of five grades is 58%, 56%, 60%, 64%, 62%. Find the one-sample t statistic.

  1. −3.000
  2. 1.414
  3. −1.414
  4. 3.000

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Correct answer: (C) −1.414

Explanation

Sample mean is 60. Squared deviations from 60 sum 40, so unbiased sample variance is 40/4=10. Standard error is√10/√5=√2. Thus t=(60−62)/√2=−1.4142, C. Use n−1 in the sample variance and preserve the signed deviation.

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