A decade$-$old study found that the proportion, $p,$ of high school seniors who believed that "getting rich" was an important personal goal was $80\%.$ A researcher decides to test whether or not that percentage still stands. He finds that, among the $235$ high school seniors in his random sample, $200$ believe that "getting rich" is an important goal. Can he conclude, at the $0\mathrm{.}01$ level of significance, that the proportion has indeed changed?

Perform a two$-$tailed test. Then complete the parts below.

Carry your intermediate computations to three or more decimal places. $($If necessary, consult a list of formulas.$)$

$($a$)$ State the null hypothesis $H_0$ and the alternative hypothesis $H_1$

$H_0$:$$

$H_1$:$$

$($b$)$ Determine the type of test statistic to use.

$($c$)$ Find the value of the test statistic. $($Round to three or more decimal places.$)$

$($d$)$ Find the p$-$value. $($Round to three or more decimal places.$)$

$($e$)$ Can we conclude that the proportion of high school seniors who believe that "getting rich" is an important goal has changed?