When determining sample size for a proportion, the farther that p is from 0.5, the smaller the resulting sample size will be.

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When estimating a proportion, the formula for determining sample size includes the term p(1-p), which reaches its maximum value when p = 0.5. As p moves away from 0.5, the value of p(1-p) decreases, resulting in a smaller required sample size to achieve the same level of statistical precision.

When Determining Sample Size for a Proportion, the Farther That