In $2011,$ a U$.$S$.$ Census report determined that $71\%$ of college students work. A researcher thinks this percentage has changed since then. A survey of $110$ college students reported that $91$ of them work. Is there evidence to support the reasearcher's claim at the $1\%$ significance level? A normal probability plot indicates that the population is normally distributed.

a$)$ Determine the null and alternative hypotheses.

$H_0$:$p=$

$H_a$:$p$

$($Put in the correct symbol and value$)$

b$)$ Determine the test statistic. Round to two decimals.

$z=$

c$)$ Find the p$-$value. Round to $4$ decimals.

P$-$value $=$

d$)$ Make a decision.

Reject the null hypothesis

Fail to reject the null hypothesis

e$)$ Write the conclusion.

There is sufficient evidence to support the claim that the percentage of college students who work is different than $71\%.$

There is not sufficient evidence to support the claim that the percentage of college students who work is different than $71\%.$