Answer
$13.5\lt\mu\lt15.1$
about 30 minutes
Work Step by Step
Given $n=28, \bar X=14.3, s=2.0$, at the 95% confidence and $df=27$,
the critical t-value is $t_{\alpha/2}=2.05 $ (use table F)
The margin of error can be found as $E=2.05\times\frac{2}{\sqrt {28}}=0.8$
Thus, the interval of the true mean can be estimated as
$\bar X-E\lt\mu\lt\bar X+E$ which gives $13.5\lt\mu\lt15.1$
Since $time(T)=\frac{distance}{speed}$, we have $0.45\lt\bar T\lt0.5$ for an average speed of 30 miles per hour,
and the time the manager would suggest his employees allow for the commute is about 0.5 hour or 30 minutes.
