Whenever you come throughout the term zα/2 in statistics, it is ssuggest referring to thez instrumental valuefrom 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:

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Notice that the precise value of 0.05doesn’t show up in the table, yet it would certainly be directly in between the values.0505and.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 0.1as the meaning level and the calculator will automatically rerotate the value of1.645 as the corresponding critical z value:

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Common Values for zα/2

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

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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 is1.645.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