Key Concepts

• The difference of two proportions is approximately normal if there are at least five successes and five failures in each sample.
• When conducting a hypothesis test for a difference of two proportions, the random samples must be independent and the population must be at least ten times the sample size.
• When calculating the standard error for the difference in sample proportions, the pooled proportion must be used.

Glossary

Pooled Proportion: estimate of the common value of $p_1$ and $p_2$ is $p_c$, which is

$p_c = \frac{x_A + x_B}{n_A + n_B}$