Confidence interval for binomial data in R?

Question

I know that I need mean and s.d to find the interval, however, what if the question is:

A survey of 1000 randomly chosen workers, 520 of them are female. Create a 95% confidence interval for the proportion of wokrers who are female based on survey.

How do I find mean and s.d for that?

Answer 1

You can also use prop.test from package stats, or binom.test

prop.test(x, n, conf.level=0.95, correct = FALSE)

        1-sample proportions test without continuity correction

data:  x out of n, null probability 0.5
X-squared = 1.6, df = 1, p-value = 0.2059
alternative hypothesis: true p is not equal to 0.5
95 percent confidence interval:
 0.4890177 0.5508292
sample estimates:
   p 
0.52 

You may find interesting this article, where in Table 1 on page 861 are given different confidence intervals, for a single proportion, calculated using seven methods (for selected combinations of n and r). Using prop.test you can get the results found in rows 3 and 4 of the table, while binom.test returns what you see in row 5.