IB Maths AI 4.7 Definitions

The claim investigated when sample evidence is strong enough against $H_0$, written as $H_1$.

The number of independent pieces of information used to determine the sampling distribution of a test statistic; for $\chi^2$ independence it is $(\text{rows}-1)(\text{columns}-1)$ and for goodness of fit it is $n-1$.

A statement about a population parameter or about a relationship in a population that can be tested using sample data.

The default claim in a hypothesis test, usually stating no difference, no effect, no association, or that a parameter has a stated value, and written as $H_0$.

A test where $H_1$ is directional (for example, $\mu_1 \gt \mu_2$ or $\mu_1 \lt \mu_2$), so the rejection region is in one tail of the sampling distribution.

The probability of obtaining a result at least as extreme as the sample result, assuming $H_0$ is true; smaller values give stronger evidence against $H_0$.

The chosen cut-off for deciding whether evidence against $H_0$ is strong enough to reject it, usually denoted by $\alpha$.

A test where $H_1$ looks for a difference in either direction (for example, $\mu_1 \neq \mu_2$), so the rejection region is split between both tails.