Answer
$226.3\lt\mu\lt260.1$
Work Step by Step
1. Based on the data set we can find $\bar X=243.2, s=23.8 , n=14 $
2. At the 98% confidence and $df=13$, the critical t-value is $t_{\alpha/2}=2.65$ (use table F)
3. The margin of error can be found as $E=2.65\times\frac{23.8}{\sqrt {14}}=16.9$
4. Thus, the interval of the true mean can be estimated as
$\bar X-E\lt\mu\lt\bar X+E$ which gives $226.3\lt\mu\lt260.1$
