Wiki Page, Math 13 - Perez Sandbox : Module 24 - Hypothesis Test for a Population Mean (5b of 5)

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2026-01-17T21:15:42-08:00

Review of Type I and Type II Errors

We know that statistical inference is based on probability, so there is always some chance of making a wrong decision. Recall that there are two types of wrong decisions that can be made in hypothesis testing. When we reject a null hypothesis that is true, we commit a Type I error. When we fail to reject a null hypothesis that is false, we commit a Type II error.

The following table summarizes the logic behind Type I and Type II errors.

Type I and Type II errors

We reject .
(accept )

We fail to reject .
(not enough evidence to accept )

is actually true. | Type I Error | Correct Decision

is actually false
( is true.)

Correct Decision

Type II Error

It is possible to have some influence over the likelihoods of committing these errors. But decreasing the chance of a Type I error increases the chance of a Type II error. We have to decide which error is more serious for a given situation. Sometimes a Type I error is more serious. Other times a Type II error is more serious. Sometimes neither is serious.

Recall that if the null hypothesis is true, the probability of committing a Type I error is . Why is this? Well, when we choose a level of significance ( ), we are choosing a benchmark for rejecting the null hypothesis. If the null hypothesis is true, then the probability that we will reject a true null hypothesis is . So the smaller is, the smaller the probability of a Type I error.

It is more complicated to calculate the probability of a Type II error. The best way to reduce the probability of a Type II error is to increase the sample size. But once the sample size is set, larger values of will decrease the probability of a Type II error (while increasing the probability of a Type I error).

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