$t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}$ where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $s$ is the sample standard deviation, and $n$ is the sample size.

df = n - 1, where n is the sample size.

Point estimate ± (Critical value * Standard error)

$t = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}$

Critical Value * Standard Error

The claim being tested, often a statement of no effect or no difference.

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

The probability of observing a sample mean as extreme as ours (or more extreme) if the null hypothesis were true.

A range of values that likely contains the true population mean.

Measures how far our sample mean is from the hypothesized population mean in terms of standard errors.

t-test: σ unknown, uses sample standard deviation (s), t-distribution | z-test: σ known, population normally distributed, uses z-distribution

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

One-sample: Compares the mean of one sample to a known value. | Two-sample: Compares the means of two independent groups.

Confidence intervals: estimate a population parameter | Significance tests: test a claim about a population parameter

Standard deviation: measures the spread of individual data points in a sample. | Standard error: estimates the variability of sample means around the population mean.