Exercise

# Exercise 4 - Sampling from the t-Distribution

\(N=15\) is not that big. We know that heights are normally distributed, so the t-distribution should apply. Repeat the previous Monte Carlo simulation using the t-distribution instead of using the normal distribution to construct the confidence intervals.

What are the proportion of 95% confidence intervals that span the actual mean height now?

Instructions

**100 XP**

- Use the
`replicate`

function to carry out the simulation. Specify the number of times you want the code to run and, within brackets, the three lines of code that should run. - First use the
`sample`

function to randomly sample`N`

values from`x`

. - Second, create a vector called
`interval`

that calculates the 95% confidence interval for the sample. Remember to use the`qt`

function this time to generate the confidence interval. - Third, use the
`between`

function to determine if the population mean`mu`

is contained between the confidence intervals. - Save the results of the Monte Carlo function to a vector called
`res`

. - Use the
`mean`

function to determine the proportion of hits in`res`

.