# 4.6.2 - The t-distribution

In 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 Section

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