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.

$t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}$ 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

For a large enough sample size (n ≥ 30), the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

Ensures independence when sampling without replacement; population size must be at least 10 times the sample size.

It means we don't have enough evidence to say the null hypothesis is false, not that it's true.

To challenge a claim about a population mean using sample data.

Use when the population standard deviation (σ) is unknown and you are working with means.