商务与经济统计习题答案（第8版，中文版）SBE8-SM11

11-1Chapter11InferencesAboutPopulationVariancesLearningObjectives1.Understandtheimportanceofvarianceinadecision-makingsituation.2Understandtheroleofstatisticalinferenceindevelopingconclusionsaboutthevarianceofasinglepopulation.3.Knowthesamplingdistributionof(n-1)s2/2hasachi-squaredistributionandbeabletousethisresulttodevelopaconfidenceintervalestimateof2.4.Knowhowtotesthypothesesinvolving2.5.Understandtheroleofstatisticalinferenceindevelopingconclusionsaboutthevariancesoftwopopulations.6.Knowthatthesamplingdistributionof2212/sshasanFdistributionandbeabletousethisresulttotesthypothesesinvolvingthevariancesoftwopopulations.Chapter1111-2Solutions:1.a.11.0705b.27.4884c.9.59083d.23.2093e.9.390462.s2=25a.With19degreesoffreedom2.05=30.1435and2.95=10.1170219(25)19(25)30.143510.117015.76246.95b.With19degreesoffreedom2.025=32.8523and2.975=8.90655219(25)19(25)32.85238.9065514.46253.33c.3.827.33.With15degreesoffreedom2.05=24.9958RejectH0if224.99582222(1)(161)(8)19.250nsDonotrejectH04.a.n=18s2=.362.05=27.58712.95=8.67176(17degreesoffreedom)217(.36)17(.36)27.58718.67176.222.71InferencesAboutPopulationVariances11-3b..47.845.a.222()31.071xxsn31.075.57sb.2.025=16.01282.975=1.689872(81)(31.07)(81)(31.07)16.01281.6898713.582128.71c.3.6911.346.a.22()176.961ixxsn176.9613.30sb.2.025=11.14332.975=0.4844192(51)(176.96)(51)(176.96)11.14330.48441963.5221461.217.9738.237.a.22()2.621ixxsn2.621.62sb.2.025=16.01282.095=1.689872(81)(2.62)(81)(2.62)16.01281.689871.14210.85c.1.073.298.a.22().0929.008451121ixxsnb..00845.0919sChapter1111-4c.11degreesoffreedom2.025=21.922.975=3.8157522222.025.975(1)(1)nsns2(121).00845(121).0084521.923.81575.00422.0244d..0651.15619.H0:2.0004Ha:2.0004n=302.05=42.5569(29degreesoffreedom)2(29)(.0005)36.25.0004DonotrejectH0;theproductspecificationdoesnotappeartobeviolated.10.H0:2.75Ha:2.752.05=42.5569(29degreesoffreedom)222220(1)(29)(2)206.22(.75)nsSince2=206.2242.5569,rejectH0ThestandarddeviationfortelevisionsetsisgreaterthanthestandarddeviationforVCR’s.11.19degreesoffreedom2.975=8.906552.025=32.8523RejectH0if28.90655orif232.8523InferencesAboutPopulationVariances11-52222(1)(201)(.114)26.79.009216nsDonotrejectH0.Cannotconcludethevarianceininterestrateshaschanged.12.22().81061ixxsnH0:2.94Ha:2.942220(1)(11)(.8106)9.49.94nsWith11degreesoffreedom,rejectif22.975=3.81575or22.025=21.92.Since2=9.49isnotintherejectionregion,wecannotrejectH0.13.a.F.05=2.91b.F.025=2.76c.F.01=4.50d..975.025,20,1011.293.42FFRemembertoreversethedegreesoffreedomintheF.025above.14.F.05,15,19=2.23RejectH0ifF2.2321225.82.422.4sFsRejectH0:conclude221215.Werecommendplacingthelargersamplevarianceinthenumerator.With=.05,F.025,20,24=2.33.RejectifF2.33.F=8.2/4.0=2.05DonotrejectH0OrifwehadthelowertailFvalue,.025,20,24.025,24,2011.412.41FFF=4.0/8.2=.49F.41DonotrejectH0Chapter1111-616.22012H:2212H:aF.01,24,29=2.49RejectH0ifF2.49221222942.6358sFsRejectH0;Concludeadultshaveagreatervarianceinonlinetimesthanteens.17.a.Let21=varianceinrepaircosts(4yearoldautomobiles)22=varianceinrepaircosts(2yearoldautomobiles)22012H:2212H:ab.21s=(170)2=28,90022s=(100)2=10,000212228,9002.8910,000sFsF.01,24,24=2.66RejectH0;concludethat4yearoldautomobileshavealargervarianceinannualrepaircostscomparedto2yearoldautomobiles.Thisisexpectedduetothefactthatolderautomobilesaremorelikelytohavesomeveryexpensiverepairswhichleadtogreatervarianceintheannualrepaircosts.18.22012H:2212H:aF/2=F.025,9,6=5.522212224.273.542.27sFsDonotrejectH0;Cannotconcludeanydifferencebetweenvariancesofthetwoindustries.19.22012H:2212H:aF.025=2.37(Degreesoffreedomare24numerator,21denominator)InferencesAboutPopulationVariances11-7UsingMinitab,Machine1:n1=25s1=.22111x=3.328Machine1:n1=22s1=.07681x=3.278221222(.2211)8.29(.0768)sFsRejectH0;theprocessvariancesaresignificantlydifferent.Machine1offersthebestopportunityforprocessqualityimprovements.Notethatthesamplemeansaresimilarwiththemeanbagweightsofapproximately3.3grams.However,theprocessvariancesaresignificantlydifferent.20.22012H:2212H:aF.025=2.37(Degreesoffreedomare24numerator,24denominator)With11.1thelargersamplevariance,wehaveF=11.1/2.1=5.29RejectH0;thevariancesarenotequalforseniorsandmanagers.21.a.22()1ixxsn2Novs=9663.572Decs=19,237.73b.220NovDecH:22NovDecH:a2Dec2Nov19,237.731.999663.57sFsF.05,9,9=3.18SinceF=1.993.18,donotrejectH0Thereisnoevidencethatthepopulationvariancesdiffer.Chapter1111-822.220wetdryH:22wetdryH:a22wet321024s22dry16256sF.05=2.402wet2dry10244256sFsSinceF=42.40,rejectH0andconcludethatthereisgreatervariabilityinstoppingdistancesonwetpavement.b.Drivecarefullyonwetpavementbecauseoftheuncertaintyinstoppingdistances.23.a.s2=(30)2=900b.2.05=30.1435and2.95=10.1170(19degreesoffreedom)2(19)(900)(19)(900)30.143510.1170567.2921690.22c.23.8241.1124.With12degreesoff