It was reported that in a survey of 4782 American youngsters

It was reported that in a survey of 4782 American youngsters aged 6 to 19, 12% were seriously overweight (a body mass index of at least 30; this index is a measure of weight relative to height). Calculate a confidence interval using a 99% confidence level for the proportion of all American youngsters who are seriously overweight. (Round your answers to three decimal places.) Interpret the resulting interval.

Solution

Given a=0.01, |Z(0.005)|=2.58 (check standard normal table)

So 99% CI is
p±Z*[p*(1-p)/n]

--> 0.18±2.58*sqrt(0.18*(1-0.18)/4792)

--> (0.1656813, 0.1943187)