AP Statistics
Master Quiz

Describe distributions using SOCS: Shape, Outliers, Center, Spread. Symmetric distributions → mean/SD; skewed → median/IQR.

• Right-skewed: mean > median; left-skewed: mean < median
• Adding constant c: mean/median/percentiles shift by c; SD unchanged
• Multiplying by k: mean, SD both scale by |k|

LSRL: $\hat{y} = b_0 + b_1 x$, where $b_1 = r \cdot \dfrac{s_y}{s_x}$. The line passes through $(\bar{x}, \bar{y})$.

• −1 ≤ r ≤ 1; r has no units; correlation ≠ causation
• Random scatter in residual plot → linear model is appropriate
• Curved pattern in residual plot → linear model NOT appropriate

Only randomized experiments allow causal conclusions. Observational studies show association only.

• SRS: every set of n individuals equally likely to be selected
• Stratified: divide into strata, SRS from each stratum
• Cluster: divide into clusters, randomly select entire clusters
• Blocking: group similar units to reduce variability (like stratifying in experiments)
• Confounding variable: related to both explanatory and response variables

• Var(X±Y) = Var(X) + Var(Y) when X, Y independent (variances always ADD)
• Normal approx to binomial: np ≥ 10 and n(1−p) ≥ 10
• Geometric: # trials until first success; μ = 1/p

• CLT: x̄ is approx Normal when n ≥ 30 (or population is Normal)
• Larger n → smaller SE → estimates closer to true parameter

• Type I error (α): reject true H₀; Type II error (β): fail to reject false H₀
• Power = 1 − β; increases with larger n, larger effect, larger α
• p-value: P(data this extreme | H₀ true); reject H₀ if p-value < α
• Halve CI width: multiply n by 4
• Chi-square df: goodness-of-fit = k−1; independence = (r−1)(c−1)