A range of values that likely contains the true population parameter, calculated from sample data and a chosen confidence level. It provides a measure of uncertainty around a point estimate.

A procedure to assess the evidence against a null hypothesis. It involves calculating a test statistic and p-value to determine if the observed data is statistically significant.

The probability of observing a sample statistic as extreme as, or more extreme than, the one observed if the null hypothesis is true. A small p-value suggests evidence against the null hypothesis.

Random sampling ensures that the sample is representative of the population, reducing bias and allowing for valid generalizations from the sample to the population.

Larger sample sizes lead to narrower confidence intervals because they reduce the standard error of the sample proportion, providing a more precise estimate of the population proportion.

A Type I error occurs when we reject the null hypothesis when it is actually true. The probability of making a Type I error is equal to the significance level (alpha).

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.

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.