Sample size for a binomial confidence interval (October 3, 2005)

This page is moving to a new website.

Someone asked me for some help with a homework question. I hesitate to offer too much advice in these situations because I don't want to disrupt the teacher's efforts to get the students to think on their own.

If it is not too much trouble, I would really appreciate your kind assistance on how best to determine and calculate for sample size if the only information given to me is the estimate (i.e. 10% of all male patient in the study population likely to be screened for prostate cancer at the medical clinic) and the precision of this estimate (i.e. 5%).

This sure sounds like they want a sample size that will produce a 95% confidence interval that has a width of plus or minus 5%. The confidence interval is based on a single binomial distribution, I suspect, rather than a difference in two binomial proportions. There's a bit of ambiguity in the wording, so it always helps to get a bit of clarification.

I have a spreadsheet that does confidence interval calculations for a single binomial proportion and you can play some "what-if" games to arrive at an appropriate sample size. But there are also formulas that you can use. Here are two web sites that provide simple and easy to follow guidance.