AP Statistics FRQ Strategy Reference Cheat Sheet

Key Facts

• For any inference procedure, identify the parameter, state the method, check conditions, calculate the statistic, and write a conclusion in context.
• A confidence interval has the general form $\text{statistic} \pm \text{critical value}\times \text{standard error}$.
• A significance test uses the test statistic $z=\frac{\text{statistic}-\text{parameter}}{\text{standard error}}$ or $t=\frac{\text{statistic}-\text{parameter}}{\text{standard error}}$.
• The one-proportion standard error for a confidence interval is $SE=\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$.
• The two-sample difference in means standard error is $SE=\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}$ when using sample standard deviations.
• A $p$-value is the probability, assuming $H_0$ is true, of getting a result as extreme as or more extreme than the observed result.
• A Type I error means rejecting a true $H_0$, and a Type II error means failing to reject a false $H_0$.
• For probability FRQs, define events clearly and use rules such as $P(A\cup B)=P(A)+P(B)-P(A\cap B)$ and $P(A\mid B)=\frac{P(A\cap B)}{P(B)}$.

Vocabulary

Free-response question

A written AP Statistics problem that requires calculations, explanations, and statistical conclusions in context.

Parameter

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

Statistic

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

Conditions

The required assumptions that justify using a statistical method, such as randomness, independence, and approximate normality.

Standard error

The estimated standard deviation of a sampling distribution, used to measure typical sampling variability.

Conclusion in context

A final statement that answers the original question using the problem setting, statistical evidence, and appropriate uncertainty language.