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The probability of type one error is :

  • A.Probability of rejecting null hypothesis (accepting alternative hypothesis) when null hypothesis is true
  • B.Probability of accepting null hypothesis (rejecting alternative hypothesis) when null hypothesis is false
  • C.Probability of rejecting null hypothesis (accepting alternative hypothesis) when null hypothesis is false
  • D.Probability of accepting null hypothesis (rejecting) alternative hypothesis) when null hypothesis is true

Answer: A

The probability of a type one error is the probability of rejecting the null hypothesis when it is true.

A type I error is a false rejection: the null hypothesis is actually true, but the sample leads us to reject it (and accept the alternative). Its probability is the significance level \(\alpha\) chosen for the test.

Accepting a false null hypothesis (B) is a type II error, with probability \(\beta\). Rejecting a false null (C) is a correct decision, the power of the test, and accepting a true null (D) is also a correct decision.

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