6.4.8—Proportion confidence intervals

For a population proportion p, estimate with p̂=x/n and use p̂±critical value√[p̂(1−p̂)/n] when the normal approximation is justified.

Check that expected successes and failures are sufficiently large, keep the interval within [0,1] in interpretation, and state the confidence level.

If p̂=0.40 and n=100, the estimated standard error is √(0.24/100)≈0.049.

A proportion is not a mean of arbitrary measurements, and the normal interval can be poor for small counts or extreme p̂.