# Sample size for a binomial confidence interval

## 2005-10-03

[StATS]: Sample size for a binomial confidence interval (October 3, 2005)

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.

You can also browse for pages similar to this one at Category: Sample size justification.

You can find an earlier version of this page on my website.