Answer
$25.7\lt\mu\lt33.9$
Work Step by Step
1. Based on the data set we can find $\bar X=29.8, s=6.2 , n=19 $
2. At the 99% confidence and $df=18$, the critical t-value is $t_{\alpha/2}=2.88 $ (use table F)
3. The margin of error can be found as $E=2.88\times\frac{6.2}{\sqrt {19}}=4.1$
4. Thus, the interval of the true mean can be estimated as
$\bar X-E\lt\mu\lt\bar X+E$ which gives $25.7\lt\mu\lt33.9$
