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.
\[
H_{0}: p=
\]
\[
H_{\mathrm{a}}: p \text { Select an answer } v
\]
(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.
\[
P \text {-value }=
\]
d) Make a decision.
Fail to reject the null hypothesis
Reject the null hypothesis
Answer
\(H_{\mathrm{a}}: p \neq 0.71\)
Step 1 ：State the null and alternative hypotheses. The null hypothesis is that the proportion of college students who work is still 71%, or 0.71. The alternative hypothesis is that the proportion has changed, which means it could be either less than or greater than 0.71. Therefore, this is a two-tailed test.
Step 2 ：\(H_{0}: p=0.71\)
Step 3 ：\(H_{\mathrm{a}}: p \neq 0.71\)
