Type I and Type II Errors

The kind of errors we can make are

1. Type I:/ Reject when is really true.
2. Type II:/ Fail to reject when is really false.

It is important to emphasize that we can either reject / or fail to reject/ (in the same sense, a jury can only find someone ``guilty'' or ``not guilty,'' not ``innocent''). Some books will call the latter accepting , but we will try to be careful in using terminology.

In the one and two sample situation, we will always have three forms of :

Note that hypotheses are always about population parameters. The first hypothesis above, , is called a two-sided/ or two-tailed/ test, while the second and third tests are one-sided/ or one-tailed/ hypotheses.