Problem
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
Solution
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 ：\(H_{\mathrm{a}}: p \neq 0.71\)
