Answer :
Answer:
99.7% confidence interval is [tex][0.4162,0.7437][/tex]
Step-by-step explanation:
The formula for a confidence interval for a population proportion is [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 critical score for the desired confidence level.
We are given a sample size of [tex]n=80[/tex] and a sample proportion of [tex]\hat{p}=0.58[/tex]. Our critical score for a 99.7% confidence level would be [tex]z^*=normalcdf(0.9985,0,1)=2.9677[/tex]
Therefore, the approximate 99.7% confidence interval for the population parameter is [tex]CI=\hat{p}\pm z^*\sqrt{\frac{\hat{p}(1-\hat{p})}{n} }=0.58\pm 2.9677\sqrt{\frac{0.58(1-0.58)}{80} }=[0.4162,0.7438][/tex]
So we are 99.7% confident that the true population proportion is contained within the interval [tex][0.4162,0.7437][/tex]