What is Z-test?

Definition Z-test


Definition of Z-test

A statistical test which compares the sample and population means to find out if there is a significant difference. A-test requires a simple random sample with normal distribution and mostly used for dealing large samples i.e. when n ≥ 30.

Explanation of Z-test

Hypothesis testing is one of the key purpose of statistics. Hypothesis testing is used to check that whether the results from a test are valid or not. Example of it can be that a person says that he/she has made a new drug that can cure cancer, in order to find out if the person is telling the truth or a lie, a hypothesis test is used. Z-test is the type of hypothesis test, and used when data is normally distributed or fits in the shape of a bell curve.

For different purposes, different types of Z-test are used:

1.            Z-test for a single proportion: It is used to test a hypothesis on a definite value of the population quantity.

A null hypothesis HO: p = p0 is tested against the alternative hypothesis H1: p><p0.

p = population

p0 = Specific value of population

2.            Z-test for difference of proportions: The test is for testing the hypothesis that two populations have the same proportion. For example if one has to find out that whether there is a difference in the habit of sleeping between female and male then this test can be applied.  For this test two independent samples; one of male and other of female must be collected.


3.            Z-test for single mean:  This type of Z-test is used for testing a hypothesis on a particular value of the population mean.

In this type, a null hypothesis H0: μ = μ0 is tested against alternative hypothesis H1: μ >< μ0

μ = population mean

μ0 = specific value of the population


4.       Z-test for single variance: When a hypothesis for a specific value of population variance is to be tested, Z-test for a single variance is used.

Null hypothesis H0: σ = σ0 is tested against H1: σ >< σ0 which is an alternative hypothesis. Where σ = population mean σ0 = specific value of the population variance


5.       Z-test for testing equality of variance: This type of Z-test is used to test the hypothesis of equality of two population variances when the sample size of each sample is 30 or larger.

Steps to run Z-test

There are 5 step of Z-test.

1.            Create the null hypothesis as well as alternate hypothesis.

2.            Select an alpha value.

3.            In Z-table, find a critical value.

4.            Compute the z test value.

5.            Compare the test value to the critical z value and decide if you should support or reject the null hypothesis.

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