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.