All units covered · Exam-style difficulty · Instant feedback with detailed explanations
Always describe Shape, Center, Spread, and Outliers (SOCS). Use mean & SD for symmetric distributions; median & IQR for skewed data.
A z-score tells how many standard deviations a value is from the mean. Use Table A or calculator to find area (probability).
The LSRL minimizes the sum of squared residuals. The slope b tells the predicted change in ŷ per unit increase in x. Always check the residual plot for linearity.
SRS: every sample of size n equally likely. Stratified: random sample within groups. Cluster: randomly select groups entirely. Voluntary response and convenience samples produce bias.
Control, Randomize, Replicate. A well-designed experiment can establish causation. Observational studies can only show association. Placebo effect requires a control group; blinding prevents bias.
Addition rule (general): P(A∪B) = P(A)+P(B)−P(A∩B). Multiplication rule: P(A∩B) = P(A)·P(B|A). Independent if P(A∩B) = P(A)·P(B).
Expected value E(X) = Σ x·P(x). For independent random variables: μ(X±Y) = μX ± μY and σ²(X±Y) = σ²X + σ²Y (variances always add).
Binomial BINS: Binary, Independent, Number fixed, Same p. Geometric: counts trials until first success.
For large n, the sampling distribution of x̄ is approximately Normal regardless of population shape. Typically n ≥ 30 is sufficient; smaller n OK if population is roughly Normal.
CI = statistic ± (critical value)(SE). A 95% CI means: if we repeated sampling many times, 95% of such intervals would capture the true parameter. P-value = probability of observing our result or more extreme, given H₀ is true.