APPENDIX A Tables and Formulas 745 Formulas by Mario F. Triola Copyright 2022 Pearson Education, Inc. Ch. 3: Descriptive Statistics x = Σx n Mean x = Σ1f # x2 Σf Mean (frequency table) s = BΣ1x - x22 n - 1 Standard deviation s = Bn 1Σx22 - 1Σx22 n 1n - 12 Standard deviation (shortcut) s = Bn 3Σ1f # x224 - 3Σ1f # x242 n 1n - 12 Standard deviation (frequency table) variance = s2 Ch. 4: Probability P1A or B2 = P1A2 + P1B2 if A, B are mutually exclusive P1A or B2 = P1A2 + P1B2 - P1A and B2 if A, B are not mutually exclusive P1A and B2 = P1A2 # P1B2 if A, B are independent P1A and B2 = P1A2 # P1B0 A2 if A, B are dependent P1A2 = 1 - P1A2 Rule of complements nPr = n! 1n - r2! Permutations (no elements alike) n! n1! n2! c nk! Permutations (n1 alike, c) nCr = n! 1n - r2! r! Combinations Ch. 5: Probability Distributions m = Σ3x # P1x24 Mean (prob. dist.) s = 2Σ3x 2 # P1x24 - m 2 Standard deviation (prob. dist.) P1x2 = n! 1n - x2! x! # px # qn-x Binomial probability m = n# p Mean (binomial) s 2 = n# p# q Variance (binomial) s = 1n # p # q Standard deviation (binomial) P1x2 = mx # e-m x! Poisson distribution where e = 2.71828 Ch. 6: Normal Distribution z = x - m s or x - x s Standard score mx = m Central limit theorem sx = s2 n Central limit theorem (Standard error) Ch. 7: Confidence Intervals (one population) pn - E 6 p 6 pn + E Proportion where E = za>2Bpnqn n x - E 6 m 6 x + E Mean where E = ta>2 s1 n (s unknown) or E = za>2 s1 n (s known) 1n - 12s2 x2 R 6 s 2 6 1n - 12s2 x2 L Variance Ch. 7: Sample Size Determination n = 3za>24 20.25 E2 Proportion n = 3za>24 2pnqn E2 Proportion (pn and qn are known) n = J za>2s E R 2 Mean Ch. 8: Test Statistics (one population) z = pn - p Bpq n Proportion—one population t = x - m s1 n Mean—one population (s unknown) z = x - m s1 n Mean—one population (s known) x2 = 1n - 12s2 s 2 Standard deviation or variance— one population
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