Whenever you come throughout the term **zα/2** in statistics, it is ssuggest referring to the**z instrumental 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 using a z table.How to uncover zα/2 making use of a calculator.The many widespread values forzα/2.Let’s jump in!

**How to discover zα/2 making use of a z table**

Suppose we desire to discover zα/2 for some test that is utilizing a 90% confidence level.

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

To find the corresponding z important worth, we would ssuggest look for **0.05** in a z table:

Notice that the precise value of **0.05**doesn’t show up in the table, yet it would certainly be directly in between the values**.0505**and**.0495**. The corresponding z important worths on the external of the table are **-1.64** and**-1.65**.

By separating the distinction, we see that the z crucial worth would certainly be **-1.645**. And generally when we usage zα/2 we take the absolute worth. Therefore, z.01/2 = **1.645**.

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

We have the right to additionally usage a Critical Z Value Calculator todiscover zα/2 for some test.

For instance, for some test that is utilizing a 90% confidence level we have the right to sindicate enter **0.1**as the meaning level and the calculator will automatically rerotate the value of**1.645 **as the corresponding critical z value:

**Common Values for zα/2**

The following table display screens the most widespread critical values for different values of α:

The way to interpret this table is as follows:

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

**1.96**.For a test using a 99% confidence level (e.g. α = 0.01), the z instrumental worth is

**5.576**.

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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**