Formulas and Tablesfor Elementary Statistics, Tenth Edition, by Mario F. TriolaCopyright 2006 Pearson Education, Inc.Ch. 3: Descriptive Statistics! Mean! Mean (frequency table)s ! Standard deviations !s !variance ! s2Ch. 4: Probabilityif A, B are mutually exclusiveif A, B are not mutually exclusiveif A, B are independentif A, B are dependentRule of complementsPermutations (no elements alike)Permutations (n1alike, ...)CombinationsCh. 5: Probability DistributionsMean (prob. dist.)Standard deviation (prob. dist.)Binomial probabilityMean (binomial)Variance (binomial)Standard deviation (binomial)Ch. 6: Normal DistributionStandard scoreCentral limit theoremCentral limit theorem(Standard error)"x#!"!n$x#!$z !x # xs or x #$"Poisson Distributionwhere e " 2.71828P(x)!$x . e#$x!"!!n . p . q"2! n . p . q$! n . pP(x) !n!(n # x)! x! . px . qn#x"!![%x2 . P(x)] #$2$!%x . P(x)nCr5n!(n 2 r)! r!n!n1! n2! . . . nk!nPr5n!(n 2 r)!P(A) 5 1 2 P(A)P(A and B) 5 P(A) . P(B 0A)P(A and B) 5 P(A) . P(B)P(A or B) 5 P(A) 1 P(B) 2 P(A and B)P(A or B) 5 P(A) 1 P(B)Standard deviation(frequency table)Ån3S(f . x2)42 3S(f . x)42n(n 2 1)Standard deviation(shortcut)Ån(Sx2) 2 (Sx)2n(n 2 1)ÅS(x 2 x)2n 2 1Sf . xSfxSxnxCh. 7: Confidence Intervals (one population)ˆp # E & p &ˆp ' E Proportionwhere Meanwhere (s known )or (s unknown)VarianceCh. 7: Sample Size DeterminationProportionProportion (ˆp and ˆq are known)MeanCh. 9: Confidence Intervals (two populations)where (Indep.)where (s1and s2unknown and not assumed equal)(s1and s2unknown but assumed equal)(s1, s2known) (Matched Pairs)where (df ! n # 1)E 5 ta>2sd!nd 2 E ,md, d 1 EE 5 za>2Ås21n11s22n2s2p5(n12 1)s211 (n22 1)s22(n12 1) 1 (n22 1)E 5 ta>2Ås2pn11s2pn2(df 5 n11 n22 2)(df ! smaller of n1# 1, n2# 1)E 5 ta>2Ås21n11s22n2(x12 x2) 2 E , (m12m2) , (x12 x2) 1 EE 5 za>2Åpˆ1qˆ1n11pˆ2qˆ2n2(pˆ12 pˆ2) 2 E , (p12 p2) , (pˆ12 pˆ2) 1 En 5 Bza>2sER2n 53za>242pˆqˆE2n 53za>242 . 0.25E2(n 2 1)s2x2R,s2,(n 2 1)s2x2LE 5 ta>2s!nE 5 za>2s!nx 2 E ,m,x 1 EE 5 za>2Åpˆqˆn‹‹‹5014_Triola_Pullout Card 11/14/05 5:35 PM Page 2Copyright 2007 Pearson Education, publishing as Pearson Addison-Wesley.Formulas and Tablesfor Elementary Statistics, Tenth Edition, by Mario F. TriolaCopyright 2006 Pearson Education, Inc.Ch. 8: Test Statistics (one population)Proportion—one populationCh. 9: Test Statistics (two populations)Two proportionsTwo means—independent; s1and s2unknown, andnot assumed equal.Two means—independent; s1and s2unknown, butassumed equal.Ch. 11: Multinomial and Contingency Tableswhere McNemar’s testfor matched pairs(df ! 1)x25( 0b 2 c 0 2 1)2b 1 cE 5(row total) (column total)(grand total)Contingency table[df ! (r # 1)(c # 1)]x25 g(O 2 E)2EMultinomial(df ! k # 1)x25 g(O 2 E)2EStandard deviation or variance—two populations (where s21( s22)F 5s21s22Two means—matched pairs(df ! n # 1)t 5d2mdsd>!nTwo means—independent;"1, "2known.z 5(x12 x2) 2 (m12m2)Ås21n11s22n2s2p5(n12 1)s211 (n22 1)s22n11 n22 2(df ! n1' n2# 2)t 5(x12 x2) 2 (m12m2)Ås2pn11s2pn2df ! smaller ofn1# 1, n2# 1 t 5(x12 x2) 2 (m12m2)Ås21n11s22n2z 5(pˆ12 pˆ2) 2 (p12 p2)Åpqn11pqn2Standard deviation or variance—one populationx25(n 2 1)s2s2Mean—one population(" unknown)t 5x2ms>!nMean—one population(" known)z 5x 2ms>!nz 5pˆ2 pÅpqnCh. 10: Linear Correlation/RegressionCorrelation Estimated eq. of regression linePrediction intervalwhere Ch. 12: One-Way Analysis of a Variance1. Use software or calculator to obtain results.2. Identify the P-value.3. Form conclusion:If P-value ) a, reject the null hypothesis of equal means.If P * a, fail to reject the null hypothesis of equal means.Ch. 12: Two-Way Analysis of VarianceProcedure:1. Use software or a calculator to obtain results.2. Test H0: There is no interaction between the row factorand column factor.3. Stop if H0 from Step 1 is rejected.If H0from Step 1 is not rejected (so there does notappear to be an interaction effect), proceed with these two tests:Test for effects from the row factor.Test for effects from the column factor.Procedure for testing H0: m15m25m35 cE ! t+#2se $1 '1n'n(x0# x)2n(%x2)# (%x)2yˆ# E & y & yˆ' Ese5ÅS(y 2 yˆ)2n 2 2 or ÅSy22 b0Sy 2 b1Sxyn 2 2r25explained variationtotal variationyˆ5 b01 b1xb05 y 2 b1x or b05(Sy)(Sx2) 2 (Sx)(Sxy)n(Sx2) 2 (Sx)2b15nSxy 2 (Sx)(Sy)n(Sx2) 2 (Sx)2r 5nSxy 2 (Sx)(Sy)"n(Sx2) 2 (Sx)2"n(Sy2) 2 (Sy)2‹‹‹5014_Triola_Pullout Card 11/14/05 5:35 PM Page 3Copyright 2007 Pearson Education, publishing as Pearson Addison-Wesley.TABLE A-6Critical Values of the PearsonCorrelation Coefficient rn a ! .05 a ! .014 .950 .9995 .878 .9596 .811 .9177 .754 .8758 .707 .8349 .666 .79810 .632 .76511 .602 .73512 .576 .70813 .553 .68414 .532 .66115 .514 .64116 .497 .62317 .482 .60618 .468 .59019 .456 .57520 .444 .56125 .396 .50530 .361 .46335 .335 .43040 .312 .40245 .294 .37850 .279 .36160 .254 .33070 .236 .30580 .220 .28690 .207 .269100 .196 .256NOTE: To test H0: r ! 0 against H1: r ! 0,reject H0if the absolute value of r is greaterthan the critical value in the table.Ch. 13: Nonparametric TestsSign test for n * 25Kruskal-Wallis (chi-square df ! k # 1)Rank correlationCh. 14: Control ChartsR chart: Plot sample rangesUCL: Centerline: LCL: chart: Plot sample meansUCL: Centerline: LCL: p chart: Plot sample proportionsUCL: Centerline: LCL: p2 3Åpqnpp 1 3Åpqnxx 2 A2Rxxxx 1 A2RxD3RRD4RRuns testfor n * 20z 5G 2mGsG5G 2 a2n1n2n11 n21 1bÅ(2n1n2)(2n1n22 n12 n2)(n11 n2)2(n11 n22 1)acritical value for n . 30: 6 z!n 2 1brs5 1 26Sd2n(n22 1)H 512N(N 1 1)aR21n11R22n21 . . . 1R2knkb2 3(N 1 1)Wilcoxon rank-sum(two independentsamples)z 5R2mRsR5R2n1(n11 n21 1)2Ån1n2(n11 n21 1)12Wilcoxon signed ranks(matched pairs and n * 30)z 5T 2 n(n 1 1)>4Ån(n 1 1)(2n 1 1)24z 5(x 1 0.5) 2 (n>2)!n>2Formulas and Tablesfor Elementary Statistics, Tenth Edition, by Mario F. TriolaCopyright 2006 Pearson Education, Inc.Control Chart ConstantsSubgroup SizenA2D3D42 1.880 0.000 3.2673 1.023 0.000 2.5744 0.729 0.000 2.2825 0.577 0.000 2.1146 0.483 0.000 2.0047 0.419 0.076 1.9245014_Triola_Pullout Card 11/14/05 5:35 PM Page 4Copyright 2007 Pearson Education, publishing as Pearson Addison-Wesley.Is!the test statistic!to the right or left of!center!?P-value ! twice!the area to the!left of the test!statisticP-value ! area!to the right of the!test statisticP-value ! twice!the area to the!right of the test!statisticP-value ! area!to the left of the!test statisticP-valueP-value is!twice this area.Test statisticTest statistic Test