# 4.6.2 - The t-distribution

4.6.2 - The t-distributionIn 1908, William Sealy Gosset from Guinness Breweries discovered the t-distribution. His pen-name was Student and thus it is called the "Student's t-distribution."

The t-distribution is different for different sample size, n. Thus, tables, as detailed as the standard normal table, are not provided in the usual statistics books. The graph below shows the t-distribution for degrees of freedom of 10 (blue) and 30 (red dashed).

## Properties of the t-distribution

- t is symmetric about 0
- t-distribution is more variable than the Standard Normal distribution
- t-distributions are different for different degrees of freedom (d.f.).
- The larger \(n\) gets (or as \(n\) goes to infinity), the closer the \(t\)-distribution is to the \(z\).
- The meaning of \(t_\alpha\) is the \(t\)-value having the area "\(\alpha\)" to the right of it.