Answer:
[tex](0.518,0.790)[/tex]
Step-by-step explanation:
Use the formula [tex]CI=\hat{p}\pm z^*\sqrt{\frac{\hat{p}(1-\hat{p})}{n} }[/tex] where [tex]\hat{p}[/tex] is the sample proportion, [tex]n[/tex] is the sample size, and [tex]z^*[/tex] is the corresponding z-value for a given confidence level.
We know that [tex]\hat{p}=\frac{53}{81}[/tex], [tex]n=81[/tex], and [tex]z^*=2.5758[/tex] for a 99% confidence level.
Therefore, the 99% confidence interval is [tex](0.518,0.790)[/tex]
