In hypothesis testing, which of the following defines the size of the power of the test? (A) 1 - (Probability of accepting null hypothesis when it is true) (B) 1 - (Probability of rejecting null hypothesis when it is true) (C) 1 - (Probability of accepting null hypothesis when it is false) (D) 1 + (Probability of rejecting null hypothesis when it is not true)

IIT JAM 2022 Question 8: Hypothesis testing

In hypothesis testing, which of the following defines the size of the power of the test?

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Answer: (C)

Power is the probability of correctly rejecting a false null hypothesis, which equals 1 minus the probability of a Type II error.

A Type II error is accepting the null when it is false, so power = 1 - P(accepting H0 when it is false). The answer is (C).

The trap: (A) 1 - (Probability of accepting null hypothesis when it is true)

Option (A) subtracts the probability of accepting a true null, which relates to the significance level and Type I error, not power.

Hypothesis testing has come up 47 times in 7 exams since 2007.

This question is on Type I and type II errors and power, part of Hypothesis testing in Statistics.

The two ways a test can be wrong and the probability of detecting a real effect.

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Question from the IIT JAM 2022 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.