Whenever you come throughout the ax zα/2 in statistics, it is simply referring to thez vital 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 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 0.05doesn’t appear in the table, however it would be directly in between the values.0505and.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 0.1as the definition level and also the calculator will instantly return the value of1.645 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 is1.645.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