A range of plausible values for the true difference between two population proportions.

The true proportion of individuals with a certain characteristic in the entire group of interest.

The probability that a confidence interval will contain the true population parameter if repeated samples are taken.

A statement of no effect or no difference that we aim to disprove with statistical evidence.

A statement that contradicts the null hypothesis, suggesting a specific effect or difference.

Extraneous factors that can influence the results of a study, potentially leading to incorrect conclusions about the relationship between variables.

State the confidence level, refer to the population parameter (difference in population proportions), and relate the interpretation to the specific scenario.

If the confidence interval contains zero, we fail to reject the null hypothesis. If it does not contain zero, we reject the null hypothesis.

If we were to take many samples and build a confidence interval from each sample, then approximately 95% of those intervals would contain the true population difference.

We are 95% confident that the true difference in population proportions lies between -0.1 and 0.2. Because the interval contains 0, there may be no difference between the two population proportions.

Zero represents the absence of a difference between the two proportions. Its inclusion or exclusion from the confidence interval determines whether we reject the null hypothesis.

$SE = \sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}$

Estimate ± (Critical Value) * (Standard Error)

$(\hat{p}_1 - \hat{p}_2) \pm z^* \sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}$