The given information is:
n=1086
x=571
Confidence level 99%
First, we need to find the sample proportion. It is given by the formula:
[tex]\hat{p}=\frac{x}{n}[/tex]
By replacing the known values, we obtain:
[tex]\hat{p}=\frac{571}{1086}=0.526[/tex]
Now, the confidence interval is given by:
[tex]\begin{gathered} \hat{p}-E
Where z* is the z-value for the confidence level. As the C.L=99%, then z is:
[tex]\begin{gathered} z^*_{\frac{\alpha}{2}}\rightarrow\frac{\alpha}{2}=0.99+\frac{1-0.99}{2}=0.99+\frac{0.01}{2}=0.995 \\ \\ And\text{ z for 0.995 is} \\ z^*=2.576 \end{gathered}[/tex]
Now, replace this value into the formula and solve:
[tex]\begin{gathered} E=2.576\sqrt{\frac{0.526(1-0.526)}{1086}} \\ \\ E=2.576\sqrt{\frac{0.249}{1086}} \\ \\ E=2.576\sqrt{0.0002} \\ \\ E=2.576*0.015 \\ \\ E=0.039 \end{gathered}[/tex]
The confidence interval is then:
[tex]\begin{gathered} 0.526-0.039
The answer is above.
