Confidence Interval for Difference in Proportions

A confidence interval for the difference in proportions provides a range of values that is likely to contain the true difference between two population proportions with a certain level of confidence.

Formula:

Where:

• $\hat p_1$ and $\hat p_2$ are the sample proportions
• $z_{\alpha/2}$ is the critical value from the standard normal distribution
• $n_1$ and $n_2$ are the sample sizes

Interpretation: A 95% confidence interval means that if we repeated this sampling process many times, about 95% of the intervals would contain the true difference between population proportions.