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.
\[
\begin{array}{l}
H_{0}: p \neq 0.52 \\
H_{1}: p=0.52
\end{array}
\]
B. $H_{0}: p> 0.52$
\[
H_{1}: p=0.52
\]
D.
\[
\begin{array}{l}
H_{0}: p< 0.52 \\
H_{1}: p=0.52
\end{array}
\]
E
\[
\begin{array}{l}
H_{0}: p=0.52 \\
H_{1}: p< 0.52
\end{array}
\]
\[
\begin{array}{l}
H_{0}: p=0.52 \\
H_{1}: p \neq 0.52 \\
H_{0}: p=0.52 \\
H_{1}: p=0.52
\end{array}
\]
Find the test statistic for this hypothesis test.
$z=1.24$ (Round to two decimal places as needed.)
Determine the P-value for this hypothesis test.
P-value $=0.107$ (Round to three decimal places as needed.)
State the conclusion for this hypothesis test.
A. Reject $\mathrm{H}_{0}$. There is sufficient evidence at the $\alpha=0.05$ level of significance to conclude that the proportion of voters who approve of the job the president is doing is significantly higher than the original level.
B. Reject $\mathrm{H}_{0}$. There is not sufficient evidence at the $\boldsymbol{\alpha}=0.05$ level of significance to conclude that the proportion of voters who approve of the job the president is doing is significantly higher than the original level.
C. Do not reject $\mathrm{H}_{0}$. There is not sufficient evidence at the $\alpha=0.05$ level of significance to conclude that the proportion of voters who approve of the job the president is doing is significantly higher than the original level.
D. Do not reject $\mathrm{H}_{0}$. There is sufficient evidence at the $\alpha=0.05$ level of significance to conclude that the proportion of voters who approve of the job the president is doing is significantly higher than the original level.
Answer
The correct null and alternative hypotheses for this test are: \[\boxed{H_{0}: p=0.52} \] \[\boxed{H_{1}: p \neq 0.52}\]
Step 1 ：Identify the null and alternative hypotheses for this test. The null hypothesis is a statement of no effect or no difference and is assumed to be true until we have evidence to suggest otherwise. The alternative hypothesis is a statement of an effect or difference. In this case, we are testing whether the proportion of voters who approve of the job the president is doing is significantly higher than the original level. So, the null hypothesis should be that the proportion is not higher than the original level, and the alternative hypothesis should be that the proportion is higher than the original level. Looking at the options, the correct null and alternative hypotheses should be: \[H_{0}: p \leq 0.52\] \[H_{1}: p > 0.52\] However, this option is not provided in the question. The closest option to this would be: \[H_{0}: p=0.52\] \[H_{1}: p \neq 0.52\] This option suggests that the null hypothesis is that the proportion is equal to the original level, and the alternative hypothesis is that the proportion is not equal to the original level. This would be a two-tailed test, which is not exactly what we want, but it's the closest option available.
Step 2 ：The correct null and alternative hypotheses for this test are: \[\boxed{H_{0}: p=0.52} \] \[\boxed{H_{1}: p \neq 0.52}\]
