$$\sqrt{\frac{p_1(1-p_1)}{n_1} + \frac{p_2(1-p_2)}{n_2}}$$

$$\mu = p_1 - p_2$$

Point Estimate ± (Critical Value * Standard Error)

$$\hat{p} = \frac{number \ of \ successes}{sample \ size}$$

$$\sqrt{\frac{\hat{p_1}(1-\hat{p_1})}{n_1} + \frac{\hat{p_2}(1-\hat{p_2})}{n_2}}$$

Distribution of all possible differences in sample proportions you could get if you repeated the study many times.

The standard deviation of a sampling distribution.

A single value estimate for a population parameter.

Bias that occurs when certain groups are more or less likely to respond to a survey.

Condition to confirm normality for proportion inference, verifying that $n_1p_1 ge 10$, $n_1(1 - p_1) ge 10$, $n_2p_2 ge 10$, and $n_2(1 - p_2) ge 10$.

When dealing with differences, variances ALWAYS add. To find the standard deviation, take the square root of the combined variance.

To confirm that the sampling distribution of the difference in sample proportions is approximately normal.

It represents all possible differences in sample proportions you could obtain if you repeated the sampling process many times.

It allows us to make inferences about the true difference in population proportions based on sample data.

With sufficiently large sample sizes, the sampling distribution of the difference in sample proportions will be approximately normal, regardless of the shape of the original populations.