t-test Hypothesis Testing for Means with Unknown Variance

In the situation where you have a sample and would like to know if the population represented by the sample has a mean different than some specification, then this is the test for you. In this case, you do not know the actual variance of the population, you just have a sample.

This test is often the second one in a textbook that describes hypothesis testing. It is a useful hypothesis test and applies in many situations as we rarely know the population variance.