When finding a confidence interval for the difference between two population proportions we use a pooled estimate of the proportion.

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When finding a confidence interval for the difference between two population proportions, we do not use a pooled estimate of the proportion if we are not assuming that the population proportions are equal. The use of a pooled estimate is specific to certain hypothesis tests (like the two-proportion z-test under the assumption of equal proportions) but not generally used for confidence intervals for the difference between two independent proportions.

When Finding a Confidence Interval for the Difference Between Two