*37*

Whenever you come across the term **z _{Î±/2}** in statistics, it is simply referring to theÂ

**z critical valueÂ**from the z table that corresponds to Î±/2.

This tutorial explains the following:

- How to find z
_{Î±/2}using a z table. - How to find z
_{Î±/2}using a calculator. - The most common values forÂ z
_{Î±/2}.

Letâ€™s jump in!

**How to find z**_{Î±/2} using a z table

_{Î±/2}using a z table

Suppose we want to find z_{Î±/2} for some test that is using a 90% confidence level.

In this case, Î± would be 1 â€“ 0.9 =Â **0.1**. Thus, Î±/2 = 0.1/2 =Â **0.05**.

To find the corresponding z critical value, we would simply look for **0.05** in a z table:

Notice that the exact value of **0.05Â **doesnâ€™t appear in the table, but it would be directly between the valuesÂ **.0505Â **andÂ **.0495**. The corresponding z critical values on the outside of the table are **-1.64** andÂ **-1.65**.

By splitting the difference, we see that the z critical value would be **-1.645**. And typically when we use z_{Î±/2} we take the absolute value. Thus, z_{.01/2} = **1.645**.

**How to find z**_{Î±/2} using a calculator

_{Î±/2}using a calculator

We can also use a Critical Z Value Calculator toÂ find z_{Î±/2} for some test.

For example, for some test that is using a 90% confidence level we can simply enter **0.1Â **as the significance level and the calculator will automatically return the value ofÂ **1.645 **as the corresponding critical z value:

**Common Values for z**_{Î±/2}

_{Î±/2}

The following table displays the most common critical values for different values of Î±:

The way to interpret this table is as follows:

- For a test using a 90% confidence level (e.g. Î± = 0.1), the z critical value isÂ
**1.645**. - For a test using a 95% confidence level (e.g. Î± = 0.05), the z critical value is
**1.96**. - For a test using a 99% confidence level (e.g. Î± = 0.01), the z critical value is
**5.576**.

And so on.

**Additional Resources**

How to use the Z Table (With Examples)

How to Find the Z Critical Value on a TI-84 Calculator