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Formulas for the Final Exam Five number summary Minimum Q1 Median Q 3 Maximum InterQuartile Range : IQR Q 3 Q1 Range Maximum Minimum Mean x x n y y n Standard Deviation sx sy x x 2 n 1 y y 2 n 1 Standardized Score zx xx sx zy y y sy Correlation Coefficient z x z y x x y y r n 1s x s y n 1 Slope br sy sx Intercept a y bx Prediction Equation yˆ a bx residual y yˆ R 2 r 2 1 np 15 and n1 p 15 Sampling Distribution of y : Shape: normal if population has a normal shape, otherwise approximately normal Mean: p Mean: μ Sampling Distribution of p̂ : Shape: Approximately normal if Standard Deviation: SD pˆ p1 p n Standard Error: SE y s n Single sample (Categorical Variable) Confidence interval for p : pˆ z * pˆ 1 pˆ to pˆ z * n Confidence z* Test Statistic: pˆ 1 pˆ n 80% 1.282 90% 1.645 z 95% 2 or 1.96 pˆ po p0 1 p0 n 98% 2.326 99% 2.576 Single sample (Numerical Variable) Confidence interval for μ: y t* s s to y t * n n df = n – 1 Test Statistic: t y o s n df = n – 1 2