Of 125 adults selected randomly from one town,28 of them smoke.Construct a 99% confidence interval for the percentage of all adults in the town who smoke.
A)(15.1%,29.7%)
B)(13.7%,29.7%)
C)(12.8%,30.3%)
D)(16.2%,28.6%)
E)(13.7%,31.1%)

Question

Quizplus · Accepted Answer

We need to use the formula for the confidence interval of a proportion:
p̂ ± z*√(p̂(1-p̂)/n)
where p̂ is the sample proportion (28/125), n is the sample size (125), and z* is the appropriate z-score for the desired confidence level. 
For a 99% confidence level, the corresponding z-score is 2.576. 
Calculating the interval:
28/125 ± 2.576*√((28/125)*(1-28/125)/125) 
gives us (12.8%,30.3%). Therefore, the answer is choice C.

Of 125 Adults Selected Randomly from One Town,28 of Them