商务与经济统计习题答案（第8版，中文版）SBE8-SM08

8-1Chapter8IntervalEstimationLearningObjectives1.Knowhowtoconstructandinterpretanintervalestimateofapopulationmeanand/orapopulationproportion.2.Understandtheconceptofasamplingerror.3.Beabletouseknowledgeofasamplingdistributiontomakeprobabilitystatementsaboutthesamplingerror.4.Understandandbeabletocomputethemarginoferror.5.Learnaboutthetdistributionanditsuseinconstructinganintervalestimateforapopulationmean.6.Beabletodeterminethesizeofasimplerandomsamplenecessarytoestimateapopulationmeanand/orapopulationproportionwithaspecifiedlevelofprecision.7.Knowthedefinitionofthefollowingterms:confidenceintervalprecisionconfidencecoefficientsamplingerrorconfidencelevelmarginoferrordegreesoffreedomChapter88-2Solutions:1.a.xn//.540079b.At95%,zn/.(/).1965401552.a.321.645(/)650321.4(30.6to33.4)b.321.96(/)650321.66(30.34to33.66)c.322.576(/)650322.19(29.81to34.19)3.a.801.96(/)1560803.8(76.2to83.8)b.801.96(/)15120802.68(77.32to82.68)c.Largersampleprovidesasmallermarginoferror.4.1261.96(/)sn16.071.9641.96(16.07)7.874462nnn5.a.1.96/1.96(5.00/49)1.40nb.24.801.40or(23.40to26.20)6.x1.96(/)sn3691.96(/)502503696.20(362.80to375.20)IntervalEstimation8-37.x.025z(/)n3.371.96(.28/120)3.37.05(3.32to3.42)8.a.xzn/212,0001.645(2,200/245)12,000231(11,769to12,231)b.12,0001.96(2,200/245)12,000275(11,725to12,275)c.12,0002.576(2,200/245)12,000362(11,638to12,362)d.Intervalwidthmustincreasesincewewanttomakeastatementaboutwithgreaterconfidence.9.a.Usingacomputer,x=$12.41b.Usingacomputer,s=3.64c.x1.96(/)sn12.411.96(./)3646012.410.92(11.49to13.33)10..025sxzn3.457.751.961807.75.50(7.25to8.25)11.UsingMinitabweobtainedasamplestandarddeviationof2.163.Theconfidenceintervaloutputisshownbelow:THEASSUMEDSIGMA=2.16NMEANSTDEVSEMEAN95.0PERCENTC.I.Miami506.3402.1630.306(5.740,6.940)Chapter88-4The95%confidenceintervalestimateis5.74to6.94.12.a.1143.830ixxnminutesb.2()2.261ixxsnminutesMarginofError=.0252.261.96.8130sznminutesc..025sxzn3.8.81(2.99to4.61)13.a..95b..90c..01d..05e..95f..8514.a.1.734b.-1.321c.3.365d.-1.761and+1.761e.-2.048and+2.04815.a.xxni/80810b.sxxni().2184813464c.With7degreesoffreedom,t.025=2.365xt.025(/)sn102.365(./)34648IntervalEstimation8-5102.90(7.10to12.90)16.a.17.251.729(./)332017.251.28(15.97to18.53)b.17.252.09(./)332017.251.54(15.71to18.79)c.17.252.861(./)332017.252.11(15.14to19.36)17.At90%,80t.05(/)snwithdf=17t.05=1.740801.740(/)1018804.10(75.90to84.10)At95%,802.11(/)1018withdf=17t.05=2.110804.97(75.03to84.97)18.a.18.96$1.5812ixxnb.2().239.14741121ixxsnc.t.025=2.201xt.025(/)sn1.582.201(.1474/12)1.58.09(1.49to1.67)19.xxni/.653minutessxxni().21054minutesxt.025(/)sn6.532.093(./)05420Chapter88-66.53.25(6.28to6.78)20.a.22.41.96(/)56122.41.25(21.15to23.65)b.Withdf=60,t.025=2.00022.42(/)56122.41.28(21.12to23.68)c.xt.025(/)snConfidenceintervalsareessentiallythesameregardlessofwhetherzortisused.21.864$1088ixxn2()6549.6658181ixxsnt.025=2.365xt.025(/)sn1082.365(9.6658/8)1088.08(99.92to116.08)22.a.Usingacomputer,x=6.86s=0.78b.xt.025(/)snt.025=2.064df=246.862.064(./)078256.860.32(6.54to7.18)23.nzEn.(.)().025222222196255960497Use24.a.Planningvalueof=Range/4=36/4=9b.nzEn.(.)().02522222219693345735UseIntervalEstimation8-7c.nn(.)().19692777978222Use25.nn(.)(.)(.).19668215794180222Usenn(.)(.).16456822314732222Use26.a.222222(1.96)(9400)339.44(1000)znEUse340b.222(1.96)(9400)1357.78(500)nUse1358c.22(1.96)(9400)8486.09200nUse848727.a.nn(.)(,)().1962000500614762222Useb.nn(.)(,)().196200020038416385222Usec.nn(.)(,)().19620001001536641537222Use28.a.222222(1.645)(220)52.39(50)znEUse53b.222(1.96)(220)74.37(50)nUse75c.222(2.576)(220)128.47(50)nUse129d.Mustincreasesamplesizetoincreaseconfidence.29.a.nn(.)(.).1966252375238222Useb.nn(.)(.).196625115006151222UseChapter88-830.nn(.)(.).196782584359222Use31.a.p=100/400=0.25b.ppn().(.).102507540000217c.pzppn.()0251.251.96(.0217).25.0424(.2076to.2924)32.a..701.645070030800.(.).70.0267(.6733to.7267)b..701.96070030800.(.).70.0318(.6682to.7318)33.nzppEn.()(.)(.)(.)(.).0252222119603506500534959350Use34.Useplanningvaluep=.50nn(.)(.)(.)(.).196050050003106711106822Use35.a.p=562/814=0.6904b.1645116450690410690481400267.()..(.).ppnc.0.69040.0267(0.6637to0.7171)36.a.p=152/346=.4393b.(1).4393(1.4393).0267346pppnIntervalEstimation8-9.025ppz.43931.96(.0267).4393.0523(.3870to.4916)37.pppn1961.()182.28650p.281.96(.)(.)0280726500.280.0345(0.2455to0.3145)38.a.196119602607440000430.().(.)(.).ppnb.0.260.0430(0.2170to0.3030)c.nn1960260740038212582222.(.)(.)(.).Use39.a.22.02522(1)(1.96)(.33)(1.33)943.75(.03)zppnEUse944b.22.00522(1)(2.576)(.33)(1.33)1630.19(.03)zppnEUse163140.a.p=255/1018=0.2505b.1.96(.)(.)025051025051018=0.026641.(1).16(1.16).01021285pppnMarginofError=1.96p=1.96(.0102)=.02.161.96p.16.02(.14to.18)42.a.(1).50(1.50).0226491pppnChapter88-10.025pz=1.96(.0226)=.0442b.2.0252(1)zpp