Z-Test Vs T-Test

What is the main difference between a Z-test and a T-test?

• Z-Test: Used when the sample size is large (n > 30) and the population standard deviation is known.
• T-Test: Used when the sample size is small (n < 30) and the population standard deviation is unknown.

When should I use a Z-test instead of a T-test?

Use a Z-test when you have a large sample size and the population standard deviation is known. It’s often used for hypothesis testing about means when these conditions are met.

When should I use a T-test instead of a Z-test?

Use a T-test when the sample size is small and the population standard deviation is unknown. It’s also used when comparing the means of two samples or paired observations.

How do I interpret the results of a Z-test or T-test?

Compare the test statistic (Z or t) to the critical value from the Z or t distribution table, or compare the P-value to your significance level (e.g., 0.05). If the test statistic exceeds the critical value or the P-value is less than the significance level, reject the null hypothesis.

Can I use a Z-test for small samples?

Generally, no. Z-tests are not recommended for small samples because the Z distribution assumes a large sample size for the Central Limit Theorem to hold. For small samples, use a T-test.

Z-tests are used when the population variance is known and the sample size is large, while t-tests are used when the population variance is unknown and the sample size is small.

This article explains the differences between Z-tests and T-tests, detailing their purposes, assumptions, sample size requirements, and applications in statistical hypothesis testing.