How does the t-test differ from the z-test?

The t-test and z-test are statistical methods for hypothesis testing about means, but they differ in their application conditions:

• z-test is used when the population variance is known or the sample size is very large (usually >30). It is based on the normal distribution.
• t-test is used when the population variance is unknown and the sample size is small. It uses Student's t-distribution, which accounts for additional uncertainty in estimating the variance.

Example: if you have a small dataset and want to check if the mean differs from a specified value, use the t-test. If the sample size is large and the variance is known, the z-test is suitable.