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

Estimate ± (Critical Value) * (Standard Error)

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

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.

Sample Proportion: Calculated from a subset of the population, used to estimate the population proportion. | Population Proportion: The true proportion for the entire population, usually unknown.

Confidence Interval: Provides a range of plausible values for the true difference. | Hypothesis Test: Determines whether there is sufficient evidence to reject the null hypothesis based on the interval.

Null Hypothesis: Assumes no difference between population proportions. | Alternative Hypothesis: Suggests there is a significant difference between population proportions.