Chapter 7 - Confidence Intervals and Sample - 7-2 Confidence Intervals for the Mean When σ Is Unknown - Exercises 7-2 - Page 388: 18

$223.2\lt\mu\lt225.6$

1. The data set gives $\bar X=224.4, s=1.43 , n=8 $ 2. At a 95% confidence and $df=7$, the critical t-value is $t_{\alpha/2}=2.37 $ (use table F) 3. The margin of error can be found as $E=2.37\times\frac{1.43}{\sqrt {8}}=1.2$ 4. Thus, the interval of the true mean can be estimated as $\bar X-E\lt\mu\lt\bar X+E$ which gives $223.2\lt\mu\lt225.6$