The Zalpha/2 (Z_{α/2}) refers to the critical table value we obtain when conducting a two-tailed Z test at the α% level of significance. The Z_{α/2} value is important because it is used to decide whether we should accept the null hypothesis or reject the null hypothesis.

**Use of Z**** _{α/2}**:

If the absolute value of the calculated Z statistic value exceeds Z_{α/2} (Zalpha/2 or Za/2) in the two-tailed test then we reject the null hypothesis. If the absolute value of the calculated Z statistic value does not exceed Z_{α/2} (Zalpha/2 or Za/2) then we accept the null hypothesis.

This is because Z_{α/2} marks out the two critical regions at α% level of significance in the two-tailed test as shown in the below image.

**Example of how to find Zalpha/2 (Z**** _{α/2})**:

- Given the level of significance α, calculate α/2.
- Find the Z value corresponding to a probability of α/2 in the Z table.
- For example if α=5% we find that for 0.05/2=0.025 in the below table we get that Z
_{α/2}=1.96.