Proportion

Prerequisites
Introduction to the Normal Distribution, Normal Approximation to the Binomial, Sampling Distribution of the Mean, Sampling Distribution of a Proportion, Confidence Intervals, Confidence Interval on the Mean

Learning Objectives

  1. Estimate the population proportion from sample proportions
  2. Apply the correction for continuity
  3. 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