The confidence interval on the difference between proportions is based on the same general formula as are other confidence intervals. A confidence interval on the difference between two proportions is computed in the following situation: There are two populations and the members of each population can be classified as falling into one of two categories. For example, the categories might be such things as whether or not one has a high-school degree or whether or not one has ever been arrested.

Consider a researcher interested in whether people who majored in psychology are more or less likely than physics majors to solve a problem that involves a certain type of statistical reasoning. The researcher is interested in estimating the difference in the proportions of people in the two populations that can solve the problem and in computing a 99% confidence interval on the difference. Random samples of 100 psychology majors and 110 physics majors are taken and each person is given a chance to solve the problem. Of the 100 psychology majors, 65 solve the problem; of the 110 physics majors only 45 solve it.