Hypothesis Testing with One Sample

A type II error occurs when the null hypothesis is false but erroneously fails to be rejected. It is failing to assert what is present, a miss. A type II error may be compared with a so-called false negative (where an actual "hit" was disregarded by the test and seen as a "miss") in a test checking for a single condition with a definitive result of true or false. A type II error is committed when we fail to believe a truth. In terms of folk tales, an investigator may fail to see the wolf ("failing to raise an alarm"). Again, \(\mathrm{H}_{0}:\) no wolf.

The rate of the type II error is denoted by the Greek letter \(\beta\) (beta) and related to the power of a test (which equals \(1-\beta\)).