SE(p̂) = $\sqrt{\frac{p̂(1-p̂)}{n}}$

Estimate ± (Critical Value) * (Standard Error)

z = $\frac{p̂ - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$

SE($p̂_1 - p̂_2$) = $\sqrt{\frac{p̂_1(1-p̂_1)}{n_1} + \frac{p̂_2(1-p̂_2)}{n_2}}$

z = $\frac{(p̂_1 - p̂_2)}{\sqrt{p̂_c(1-p̂_c)(\frac{1}{n_1} + \frac{1}{n_2})}}$ where $p̂_c$ is the combined (pooled) sample proportion.

Confidence Interval: Estimates a range for a population parameter; provides a margin of error. | Significance Test: Tests a claim about a population parameter; determines if there's enough evidence to reject the null hypothesis.

Null Hypothesis: A statement of no effect or no difference; the hypothesis we are trying to disprove. | Alternative Hypothesis: A statement that contradicts the null hypothesis; represents what we suspect to be true.

One-Proportion z-test: Used to test a claim about a single population proportion. | Two-Proportion z-test: Used to compare the proportions of two independent populations.

Type I error: Rejecting a true null hypothesis (false positive). | Type II error: Failing to reject a false null hypothesis (false negative).

Increasing confidence level: Increases the width of the confidence interval, making it more likely to capture the true parameter. | Decreasing significance level: Makes it harder to reject the null hypothesis, reducing the risk of a Type I error.

Using sample data to make educated guesses about a larger population.

Your best guess of the population proportion, calculated from your sample.

How confident you are that the interval contains the true population parameter.

The claim we're trying to disprove in a significance test. We assume it's true until proven otherwise.

What we suspect might be true if the null hypothesis is false.

The probability of observing our sample data (or more extreme) if the null hypothesis were true.