What is the difference between Z test and T test? - ProProfs Discuss
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# What is the difference between Z-test and T-test?

Asked by Lysa , Last updated: Aug 04, 2020

#### W. Pratt

Want to learn new things and share my knowledge

W. Pratt, Marketing Analyst, MBA, Lincoln

T-test and Z-test are two known tests for statistical hypotheses, which are used in solving problems. Let's discuss further. A T-test is actually a statistical hypothesis test. In this kind of text, the student's t-distribution determines the test statistics if the null hypothesis is true. Gossett W. S was the man that primarily introduced the T-statistics under the name "Student."

This, the T-test statistics, is also known as the student T-test. This test is easy to use and also straight forward, which makes it seem to be the most widely used procedure for statistical data analysis testing hypothesis. The Z-test, on the other hand, is usually employed when the standard deviation of the population is known.

The Z-test usually helps to discover if there is any significant difference between the sample and population means. The Z-test is usually used in large samples where n is greater than 30. And some tangible conditions need to have been met before you can use the Z-test.

#### A. Samuel

Writing quality content for contentment has been my passion since i was 21. I've been pursuing it as a Content Manager and Producer.

A. Samuel, Content Manager, Masters in Marketing and accounting, Florida

Z-test and T-test are two statistical hypothesis tests out of many other statistical methods that are used to test hypotheses. One of the major differences between the Z-test and T-test is that the former uses a normal distribution, whereas the latter uses a Student's T-distribution.

Z-test is used mostly to compare population and sample and to find out if there is any difference between them. At times, the standard deviation can be used together with Z-tests provided if it is known. T-test seems to be a better statistical method for small samples, i.e., samples less than 30 (n < 30).

In contrast, Z-test is used mostly when the samples to be handled are more than 30, i.e. (n > 30). However, this does not mean that the T-test cannot be used for large samples, just that it is the most suitable statistical method for small samples. In fact, the use of a T-test for large samples makes it look like you are using Z-test.