The test of a given statistical hypothesis in which a value of the statistic that is either sufficiently small or sufficiently large will lead to rejection of the hypothesis tested.

The statistical tables for Z and for t provide criticaal values for both one and two tailed tests. That is, they provide the critical values that cut off an entire alpha region at one or the other end of the sampling distribution as well as the critical vfalues that cut off the 1/2 alpha regions at both ends of the sampling distribution.