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.

Assumptions:

1. The samples are independently and randomly selected from their respective populations.
2. The samples are sufficiently large. A common rule of thumb is that np and n(1-p) should both be greater than or equal to 10 for each sample.
3. The populations from which the samples are drawn are at least 10 times as large as the respective samples.