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Avimehenwal · Answer 1 · 2023-03-23T13:35:13+0000

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:

$\hat{p}=(x)/(n)$

By replacing the known values, we obtain:

$\hat{p}=(571)/(1086)=0.526$

Now, the confidence interval is given by:

$\begin{gathered} \hat{p}-E<p>Where z* is the z-value for the confidence level. As the C.L=99%, then z is:</p>[tex]\begin{gathered} z^*_{(\alpha)/(2)}\rightarrow(\alpha)/(2)=0.99+(1-0.99)/(2)=0.99+(0.01)/(2)=0.995 \\ \\ And\text{ z for 0.995 is} \\ z^*=2.576 \end{gathered}$

Now, replace this value into the formula and solve:

$\begin{gathered} E=2.576\sqrt{(0.526(1-0.526))/(1086)} \\ \\ E=2.576\sqrt{(0.249)/(1086)} \\ \\ E=2.576√(0.0002) \\ \\ E=2.576*0.015 \\ \\ E=0.039 \end{gathered}$

The confidence interval is then:

[tex]\begin{gathered} 0.526-0.039

The answer is above.

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