Whenever you come throughout the ax **zα/2** in statistics, it is simply referring to the**z vital value**from the z table that corresponds to α/2.

You are watching: Compute the critical value za/2

This tutorial explains the following:

How to find zα/2 making use of a z table.How to discover zα/2 utilizing a calculator.The most common values forzα/2.Let’s jump in!

**How to find zα/2 using a z table**

Suppose we desire to find zα/2 for some test the is making use of a 90% to trust level.

In this case, α would be 1 – 0.9 =**0.1**. Thus, α/2 = 0.1/2 =**0.05**.

To uncover the matching z crucial value, us would simply look for **0.05** in a z table:

Notice the the precise value of **0.05**doesn’t appear in the table, however it would be directly in between the values**.0505**and**.0495**. The equivalent z vital values top top the external of the table room **-1.64** and**-1.65**.

By dividing the difference, we see that the z critical value would be **-1.645**. And also typically as soon as we use zα/2 we take the absolute value. Thus, z.01/2 = **1.645**.

**How to discover zα/2 making use of a calculator**

We can likewise use a an important Z value Calculator tofind zα/2 for some test.

For example, for some test that is making use of a 90% to trust level we can simply enter **0.1**as the definition level and also the calculator will instantly return the value of**1.645 **as the corresponding vital z value:

**Common worths for zα/2**

The following table screens the most common critical values for various values the α:

The way to interpret this table is together follows:

For a test utilizing a 90% to trust level (e.g. α = 0.1), the z vital value is**1.645**.For a test using a 95% to trust level (e.g. α = 0.05), the z critical value is

**1.96**.For a test utilizing a 99% trust level (e.g. α = 0.01), the z an important value is

**5.576**.

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And for this reason on.

**Additional Resources**

How to usage the Z Table (With Examples)**How to uncover the Z crucial Value ~ above a TI-84 Calculator**