The dean of students of of$$Montclair State University $,$ NJ claims that the average distance commuting students travel to the campus is $32$ miles. The commuting students feel otherwise.

A sample of $64$ students was randomly selected and yielded a mean of $35$ miles and a standard deviation of $5$ miles. Test the dean$$s claim at the $5$ percent level of significance using critical approach. $($Hint; z$\backslash$alpha $/2$

$=1\mathrm{.}96)$

a$.$ What$$s the Ho $($Null$)$ and Ha $($Alternate$)$ Hypothesis for this two$-$tailed test

b$.$ Refute dean$$s claim $($conclusion