Answer
$8.8\lt\mu\lt58.2$
Work Step by Step
1. From the data set we get $\bar X=33.5, s=27.68 , n=10 $
2. At a 98% confidence and $df=9$, the critical t-value is $t_{\alpha/2}=2.82 $ (use table F)
3. The margin of error can be found as $E=2.82\times\frac{27.68}{\sqrt {10}}=24.7$
4. Thus, the interval of the true mean can be estimated as
$\bar X-E\lt\mu\lt\bar X+E$ which gives $8.8\lt\mu\lt58.2$
