Problem
b) A poll showed the approval rating to be $0.52(52 \%)$. A second poll based on 1500 randomly selected voters showed that 804 approved of the job the president was doing. Do the results of the second poll indicate that the proportion of voters who approve of the job the president is doing is significantly higher than the original level? Explain. Assume the $\alpha=0.05$ level of significance. Identify the null and alternative hypotheses for this test. A. $H_{0}: p \neq 0.52$ $H_{1}: p=0.52$ D. $H_{0}: p<0.52$ $H_{1}: p=0.52$ B. $\mathrm{H}_{0}: \mathrm{p}>0.52$ $H_{1}: p=0.52$ E. $H_{0}: p=0.52$ $H_{1}: P<0.52$ c. \[ \begin{array}{l} H_{0}: p=0.52 \\ H_{1}: p \neq 0.52 \end{array} \] F. \[ \begin{array}{l} H_{0}: p=0.52 \\ H_{1}: p>0.52 \end{array} \]
Solution
Step 1 ：Identify the null and alternative hypotheses for this test. The null hypothesis should be that the proportion of voters who approve is equal to the original level (52%), and the alternative hypothesis should be that the proportion of voters who approve is greater than the original level.
Step 2 ：Write the null and alternative hypotheses as: \(H_{0}: p=0.52\) and \(H_{1}: p>0.52\)
Step 3 ：Final Answer: \(\boxed{\begin{array}{l} H_{0}: p=0.52 \\ H_{1}: p>0.52 \end{array}}\)
