We have a single formula for a confidence interval for a population proportion, which is valid when the sample is large. The condition that a sample be large is not that its size n be at least 30, but...We have a single formula for a confidence interval for a population proportion, which is valid when the sample is large. The condition that a sample be large is not that its size n be at least 30, but that the density function fit inside the interval [0,1].