How are we to test a hypothesis of a sample Mean when the is unknown and the sample size is less than 30?

Enter the t-Distribution.


Properties of the t-Distribution

If a population is essentially normal, then the distribution is:

This is the equation for the Student t-Distribution, or simply t-Distribution, for all samples of size n  less than 30.

To find the Rejection Region, we can use the t-Distribution Table. This table merely requires knowledge of the sample size, which allows us to calculate the Degrees of Freedom, and the Significance Level .

Degrees of Freedom = n - 1

t-Distribution Table

Example: The Height of UCLA Basketball Players