AP Stats Inference Flowchart Cheat Sheet

Key Facts

• Use a one-proportion $z$ procedure when the parameter is $p$ and the data come from one categorical sample with success and failure counts.
• Use a two-proportion $z$ procedure when comparing $p_1 - p_2$ from two independent categorical samples or treatments.
• Use a one-sample $t$ procedure when the parameter is $\mu$ and the data come from one quantitative sample with unknown population standard deviation.
• Use a two-sample $t$ procedure when comparing $\mu_1 - \mu_2$ from two independent quantitative samples or treatments.
• Use a paired $t$ procedure when data are matched pairs or before-and-after measurements, and analyze the differences with $\bar{x}_d$.
• A common test statistic structure is $z \text{ or } t = \frac{\text{statistic} - \text{null value}}{\text{standard error}}$.
• A confidence interval has the general form $\text{estimate} \pm \text{critical value} \cdot \text{standard error}$.
• For chi-square procedures, use $\chi^2 = \sum \frac{(O - E)^2}{E}$ and check that expected counts are usually at least $5$.

Vocabulary

Parameter

A parameter is a numerical value that describes a population, such as $p$, $\mu$, $p_1 - p_2$, or $\mu_1 - \mu_2$.

Statistic

A statistic is a numerical value calculated from sample data, such as $\hat{p}$, $\bar{x}$, $\hat{p}_1 - \hat{p}_2$, or $\bar{x}_1 - \bar{x}_2$.

Null Hypothesis

The null hypothesis $H_0$ states the default claim, usually that there is no difference, no association, or a parameter equals a specific value.

Alternative Hypothesis

The alternative hypothesis $H_a$ states the claim being tested, such as $p > p_0$, $\mu < \mu_0$, or $p_1 - p_2 \neq 0$.

P-value

A $p$-value is the probability, assuming $H_0$ is true, of getting a result as extreme or more extreme than the observed statistic.

Standard Error

Standard error estimates the typical sampling variability of a statistic, such as $\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}$ for one proportion.