If the test is twotailed, H1: μ ≠ μ_{0} then the test is called twotailed test and in such a case the critical region lies in both the right and left tails of the sampling distribution of the test statistic, with total area equal to the level of significance as shown in diagram.
If the test is onetailed either righttailed or lefttailed), then the test is called a onetailed test.
For example, to test whether the population mean μ = μ_{0} , we may have the Alternative Hypothesis H1 given by H1: μ < μ_{0} (Lefttailed) or H1: μ > μ_{0} (Righttailed). In this case, the test is a singletailed or onetailed test. In the righttailed test where H1:
μ > μ_{0} , the critical region (or rejection region) z > z_{α} lies entirely in the right tail of the sampling distribution of sample statistic with area equal to the level of significance a. Similarly, in the lefttailed (H1: μ < μ_{0} ), the critical region z <  z_{α} lies entirely in the left tail of the sampling distribution of q with area equal to the level of significance α is shown.
Figure
The type of the tests to be applied depends on the nature of the Alternative Hypothesis H_{1}. We apply onetailed or twotailed test accordingly as Alternate Hypothesis is onetailed or twotailed.
Critical values of z for both twotailed and onetailed tests at 10%, 5% and 1% level of significance are given below.
Critical Values of Z
Level of significance (a)

10%

5%

1%

Critical values for Twotailed tests

1.64

1.96

2.58

Critical values for Lefttailed tests

1.28

1.64

2.33

Critical values for Righttailed tests

1.28

1.64

2.33

For large samples (n > 30), the sampling distributions of many statistics are approximately normal distribution. In such cases, we can use the results of the table given above to formulate decision rules. We will focus primarily on large samples.