Key Concepts

• There are two types of errors that can happen in hypothesis testing: Type I and Type II.
• A Type I error is rejecting the null hypothesis when the null hypothesis is true.
• The probability of a Type I error is called alpha, [latex]\alpha[/latex].
• A Type II error is not rejecting the null hypothesis when the null hypothesis is false.
• The probability of a Type II error is called beta, [latex]\beta[/latex].

Power is the ability of a test to correctly reject a false null hypothesis.  Power equals [latex]1 - \beta[/latex].

Glossary

Level of Significance of the Test: Probability of a Type I error (reject the null hypothesis when it is true). Notation: [latex]\alpha[/latex]. In hypothesis testing, the Level of Significance is called the preconceived [latex]\alpha[/latex] or the preset [latex]\alpha[/latex].

Type 1 Error: The decision is to reject the null hypothesis when, in fact, the null hypothesis is true.

Type 2 Error: The decision is not to reject the null hypothesis when, in fact, the null hypothesis is false.