A hypothesis test might make one of two types of errors.  These two types of errors traditionally have been given the names "Type I Error," and "Type II Error."  If the parameter has a value that is in the null parameter space, but the test incorrectly rejects the null hypothesis, then the test has made a Type I Error. If on the other hand, the parameter has a value that is in the alternative parameter space, but the test decides to accept the null hypothesis, a Type II Error has been made.  In this lesson, the process for constructing a test with the smallest possible Type II Error probability for a fixed and small Type I Error probability is described and illustrated.