### 9.9: Errors In Hypothesis Tests

When performing a hypothesis test, there are four possible outcomes depending on the actual truth (or falseness) of the null hypothesis and the decision to reject or not.

- The decision is not to reject null hypothesis when it is true (correct decision).
- The decision is to reject the null hypothesis when it is true (incorrect decision known as a Type I error).
- The decision is not to reject the null hypothesis when, in fact, it is false (incorrect decision known as a Type II error).
- The decision is to reject the null hypothesis when it is false (correct decision whose probability is called the Power of the Test).

Each of the errors occurs with a particular probability. The Greek letters *α* and *β* represent the probabilities.

*α* = probability of a Type I error = *P*(Type I error) = probability of rejecting the null hypothesis when the null hypothesis is true.

*β* = probability of a Type II error = *P*(Type II error) = probability of not rejecting the null hypothesis when the null hypothesis is false.

*α* and *β* should be as small as possible because they are probabilities of errors. They are rarely zero.

The Power of the Test is 1 – *β*. Ideally, we want a high power that is as close to one as possible. Increasing the sample size can increase the Power of the Test.

*This test is adapted from *Openstax, Introductory Statistics, Section 9.2 Outcomes of Type I and Type II Errors**.**