Chapter 7 - Confidence Intervals and Sample - 7-2 Confidence Intervals for the Mean When σ Is Unknown - Exercises 7-2 - Page 387: 14

$9.7\lt\mu\lt16.5$

Given $n=8, \bar X=13.1, s=4.1$, at a 95% confidence and $df=7$, the critical t-value is $t_{\alpha/2}=2.37 $ (use table F) The margin of error can be found as $E=2.37\times\frac{4.1}{\sqrt {8}}=3.4$ Thus, the interval of the true mean can be estimated as $\bar X-E\lt\mu\lt\bar X+E$ which gives $9.7\lt\mu\lt16.5$