In determining the sample size requirement for an application involving the estimation of the proportion of department store customers who pay using the store's credit card, the closer the true proportion is to .5, the larger will be the required sample size for a given margin of error and confidence level.

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The sample size required for estimating a proportion with a given margin of error and confidence level increases as the estimated proportion approaches 0.5 because the variance of a binomial distribution (which underlies the proportion) is maximized when the proportion is 0.5, leading to the largest possible sample size requirement for the same level of precision.

In Determining the Sample Size Requirement for an Application Involving