Hypothesis Errors - Two types of errors can result from any decision rule (test): rejecting the null hypothesis when it is true (a type i error), and failing to reject the null hypothesis when it is false (a type ii error). For any hypothesis, it is possible to develop many different decision rules (tests). Typically, one specifies ahead of time the chance of a type i error one is willing to allow. That chance is called the significance level of the test or decision rule. For a given significance level, one way of deciding which decision rule is best is to pick the one that has the smallest chance of a type ii error when a given alternative hypothesis is true. The chance of correctly rejecting the null hypothesis when a given alternative hypothesis is true is called the power of the test against that alternative.