Exercise

# Cutoffs under the t-distribution

We can use the `qt()`

function to find cutoffs under the t-distribution. For a given probability `p`

and a given degrees of freedom `df`

, `qt(p, df)`

gives us the cutoff value for the t-distribution with `df`

degrees of freedom for which the probability under the curve is `p`

. In other words, if \(P(t_{df} < T) = p\), then \(T\) = `qt(p, df)`

. For example, if \(T\) corresponds to the 95th percentile of a distribution, \(p = 0.95\). The "middle 95%" means from `p = 0.025`

to `p = 0.975`

.

Instructions

**100 XP**

- Find the 95th percentile of the t-distribution with 10 degrees of freedom.
- Find the cutoff value that bounds the upper end of the middle 95th percent of the t-distribution with 10 degrees of freedom.
- Find the cutoff value that bounds the upper end of the middle 95th percent of the t-distribution with 100 degrees of freedom.
*How do the last values probabilities compare? Based on your findings, is the middle 95% of the t-distribution wider for lower or higher degrees of freedom?*