Answer
$21.2\lt\mu\lt45.6$
see explanations.
Work Step by Step
1. Based on the data set we can find $\bar X=33.4, s=28.7 , n= 17$
2. At the 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 $E=1.75\times\frac{28.7}{\sqrt {17}}=12.2$
4. Thus, the interval of the true mean can be estimated as
$\bar X-E\lt\mu\lt\bar X+E$ which gives $21.2\lt\mu\lt45.6$
5. The population mean (about 32) is close to the point estimate of $\bar X$
and is contained in the confidence interval.
6. One data point (132) is unusual because it is an outlier which
may have shifted the point estimate and the confidence interval higher.
