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

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

\alpha&=&\mbox{Probability of making a Type I error} \\
...nce}}) \\
\beta&=&\mbox{Probability of making a Type II error} \\