Chapter 7 - Confidence Intervals and Sample - 7-2 Confidence Intervals for the Mean When σ Is Unknown - Exercises 7-2 - Page 388: 17

$32.0\lt\mu\lt71.0$

1. The data set gives $\bar X=51.5, s=45.98 , n=17 $ 2. At a 90% confidence and $df=16$, the critical t-value is $t_{\alpha/2}=1.75 $ (use table F) 3. The margin of error can be found as $E=1.75\times\frac{45.98}{\sqrt {17}}=19.5$ 4. Thus, the interval of the true mean can be estimated as $\bar X-E\lt\mu\lt\bar X+E$ which gives $32.0\lt\mu\lt71.0$