The random variable $\overline{X}$ whose value serves to determine the action is called the test statistic. A testof the null hypothesis is a course of action specifying the set of values of a test statistic $\overline{X}$, for which H0 is to be rejected. This set is called the rejection region of the test. A test is completely specified by a test statistic and the rejection region.

Two types of error

$\begin{array}{c\vert cc} \hline &\multicolumn{2}{c}{\mbox{Unknown True Situatio... ...ox{Wrong retention of } H_0 \\ &&(\mbox{Type II error}) \\ \hline \end{array}$

Type I error: Rejection of H0 when H0 is true.
Type II error: Nonrejection of H0 when H1 is true.

$\begin{array}{rcl} \alpha&=&\mbox{Probability of making a Type I error} \\ &&(... ...nce}}) \\ \beta&=&\mbox{Probability of making a Type II error} \\ \end{array}$