You can simulate the coverage of the small sample confidence intervals for \(\mu\) by generating 20 samples of size 10 from a normal distribution with \(\mu=20\) and \(\sigma=5\) and computing the \(95 \%\) confidence intervals according to the formula on page 231.

Using MINITAB:

(a) From your output, determine the proportion of the 20 intervals that cover the true mean \(\mu=20\)

(b) Repeat with 20 samples of size 5 .

Calc Random Data > Normal Type 10 in Generate, C1-C20 in Store, 20 in Mean, and 5 in standard deviation. Click OK. Stat > Basic Statistics > 1-sample t, Click on box and Type C1 C20. Click OK.