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).

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.