Estimate the population proportion from sample proportions

Apply the correction for continuity

Compute a confidence interval

The confidence interval for a proportion is computed
based on the mean and standard deviation of the sampling distribution of a proportion. The formulas for these
two parameters are shown below

μp = π

Since we do not know the population parameter π, we use
the sample proportion p as an estimate. The estimated standard error of p is therefore

To correct for the fact that we are approximating
a discrete
distribution with a continuous
distribution (the normal distribution), we subtract 0.5/N from
the lower limit and add 0.5/N to the upper limit of the interval.
Therefore the confidence interval is