The GATE Grind

GATE 2024 ST – Question 25

Testing of Hypotheses · Likelihood Ratio and Large Sample Tests · 1 mark · Multiple choice

Which statement about hypothesis-test errors is true?

  1. Type-I probability cannot exceed Type-II probability.
  2. Type-II error accepts the null when it is false.
  3. Type-I error rejects the null when it is false.
  4. Type-I and Type-II probabilities must sum to 1.

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Show answer and explanation

Correct answer: (B) Type-II error accepts the null when it is false.

Explanation

Type II means failing to reject (the question says “accepting”) a false null; Type I means rejecting a true null. Their probabilities concern different underlying hypotheses and have no universal ordering or sum constraint. **B**.

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