An R Introduction to Statistics

Student t Distribution

Assume that a random variable Z has the standard normal distribution, and another random variable V has the Chi-Squared distribution with m degrees of freedom. Assume further that Z and V are independent, then the following quantity follows a Student t distribution with m degrees of freedom.

t = ∘-Z-- ~ t(m )
     V ∕m

Here is a graph of the Student t distribution with 5 degrees of freedom.

PIC

Problem

Find the 2.5th and 97.5th percentiles of the Student t distribution with 5 degrees of freedom.

Solution

We apply the quantile function qt of the Student t distribution against the decimal values 0.025 and 0.975.

> qt(c(.025, .975), df=5)   # 5 degrees of freedom 
[1] -2.5706  2.5706

Answer

The 2.5th and 97.5th percentiles of the Student t distribution with 5 degrees of freedom are -2.5706 and 2.5706 respectively.