Answer
$22.83\lt\mu\lt58.16$
Work Step by Step
1. From the data set we get $\bar X=40.494, s=31.897 , n=15 $
2. At a 95% confidence and $df=14$, the critical t-value is $t_{\alpha/2}=2.145 $ (use table F)
3. The margin of error can be found as $E=2.145\times\frac{31.897}{\sqrt {15}}=17.666$
4. Thus, the interval of the true mean can be estimated as $\bar X-E\lt\mu\lt\bar X+E$ which gives
$22.83\lt\mu\lt58.16$
