Statistics Formulas for final exam, Cheat Sheet of Statistics

Download Statistics Formulas for final exam and more Cheat Sheet Statistics in PDF only on Docsity! Formula sheet for final exam Stat 201: Formulas for final exam ****Note: You may add notes to the front and back of this formula sheet **** • Sample mean: x̄ = ∑ x n ; Population mean µ = ∑ [xP (x)] • median: the midpoint of the observations when they are ordered from smallest to largest. • z = observation−mean std.dev • Residual = y − ŷ where ŷ = a+ bx • r (correlation coefficient) = (+ or −) √ R2 • P (A) = N(A) N(S) P (Ac) = 1− P (A) P (A or B) = P (A) + P (B)− P (A and B) • P (A|B) = P (A and B) P (B) P (A and B) = P (A|B)P (B) • Mutually exclusive (disjoint) events: P (A and B) = 0 • Independent events: P (A|B) = P (A); P (B|A) = P (B); P (A and B) = P (A)P (B) • Properties of a probability distribution: 1. 0 ≤ P (x) ≤ 1 2. ∑ P (x) = 1 • Binomial probability: P (X = x) = n! x!(n− x)! pxqn−x where x = 0, 1, 2, . . . , n • For Binomial random variable X: µX = np and σX = √ npq • The mean and standard error of a sample proportion is: µp̂ = p and σp̂ = √ p(1− p) n • The mean and standard error of a sample mean is: µx̄ = µ and σx̄ = σ√ n • General way to construct confidence interval: point estimate ± margin of error: – Population proportion: p̂± zα 2 √ p̂(1− p̂) n – One population mean (σ known): x̄± zα 2 σ√ n – One population mean (σ unknown): x̄± tα 2 ,df s√ n where df = n− 1 1