# 95% confidence interval for the proportion and population size

A simple random sample responses from n = 271 residents of a province. Of these, 57 report being current members of a club.

Give a 95% confidence interval for the proportion of residents who are club members. Also there are totally 800,000 club members, obtain a 95% confidence interval for the population size of the province.

My answer (16.181, 25.885) for the first part is incorrect, is it because my answer shouldn't be in percentage? Any thoughts on the second part?

Thanks!

• Probably. The crude normal approximation gives about $0.2588$ for the upper number. – André Nicolas Sep 17 '15 at 18:03

It should be a proportion, which it is $phat=0.2103$ plus or minus $0.048$ which gives the interval $[0.1623,0.2585]$ You are close to these values, but don't use percentages.