大学课件-商务与经济统计习题答案（第8版，中文版）SBE8-SM07

7-1Chapter7SamplingandSamplingDistributionsLearningObjectives1.Understandtheimportanceofsamplingandhowresultsfromsamplescanbeusedtoprovideestimatesofpopulationcharacteristicssuchasthepopulationmean,thepopulationstandarddeviationand/orthepopulationproportion.2.Knowwhatsimplerandomsamplingisandhowsimplerandomsamplesareselected.3.Understandtheconceptofasamplingdistribution.4.Knowthecentrallimittheoremandtheimportantroleitplaysinsampling.5.Specificallyknowthecharacteristicsofthesamplingdistributionofthesamplemean(x)andthesamplingdistributionofthesampleproportion(p).6.Becomeawareofthepropertiesofpointestimatorsincludingunbiasedness,consistency,andefficiency.7.Learnaboutavarietyofsamplingmethodsincludingstratifiedrandomsampling,clustersampling,systematicsampling,conveniencesamplingandjudgmentsampling.8.Knowthedefinitionofthefollowingterms:simplerandomsamplingfinitepopulationcorrectionfactorsamplingwithreplacementstandarderrorsamplingwithoutreplacementunbiasednesssamplingdistributionconsistencypointestimatorefficiencyChapter77-2Solutions:1.a.AB,AC,AD,AE,BC,BD,BE,CD,CE,DEb.With10samples,eachhasa1/10probability.c.EandCbecause8and0donotapply.;5identifiesE;7doesnotapply;5isskippedsinceEisalreadyinthesample;3identifiesC;2isnotneededsincethesampleofsize2iscomplete.2.Usingthelast3-digitsofeach5-digitgroupingprovidestherandomnumbers:601,022,448,147,229,553,147,289,209Numbersgreaterthan350donotapplyandthe147canonlybeusedonce.Thus,thesimplerandomsampleoffourincludes22,147,229,and289.3.459,147,385,113,340,401,215,2,33,3484.a.6,8,5,4,1IBM,Microsoft,Intel,GeneralElectric,AT&Tb.!10!3,628,500252!()!5!(105)!(120)(120)NnNn5.283,610,39,254,568,353,602,421,638,1646.2782,493,825,1807,2897.108,290,201,292,322,9,244,249,226,125,(continuingatthetopofcolumn9)147,and113.8.13,8,23,25,18,5Thesecondoccurrencesofrandomnumbers13and25areignored.Washington,Clemson,Oklahoma,Colorado,USCandWisconsin9.511,791,99,671,152,584,45,783,301,568,754,75010.finite,infinite,infinite,infinite,finite11.a.xxni/5469b.sxxni()21()xxi2=(-4)2+(-1)2+12(-2)2+12+52=48s=486131.SamplingandSamplingDistributions7-312.a.p=75/150=.50b.p=55/150=.366713.a.xxni/465593b.xi()xxi()xxi294+11100+74985-86494+1192-11Totals4650116sxxni().21116453914.a.149/784=.19b.251/784=.32c.Totalreceivingcash=149+219+251=619619/784=.7915.a.700/710ixxnyearsb.2()20.21.51101ixxsnyears16.p=1117/1400=.8017.a.595/1008=.59b.332/1008=.33c.81/1008=.0818.a.Ex()200b.xn//501005c.NormalwithE(x)=200andx=5Chapter77-4d.Itshowstheprobabilitydistributionofallpossiblesamplemeansthatcanbeobservedwithrandomsamplesofsize100.Thisdistributioncanbeusedtocomputetheprobabilitythatxiswithinaspecifiedfrom19.a.ThesamplingdistributionisnormalwithE(x)==200xn//501005For5,(x-)=5zxx551Area=.3413x2.6826b.For10,(x-)=10zxx1052Area=.4772x2.954420.xn/xxxx2550354251002502515020425200177/./././.Thestandarderrorofthemeandecreasesasthesamplesizeincreases.21.a.xn//.1050141b.n/N=50/50,000=.001Usexn//.1050141c.n/N=50/5000=.01Usexn//.1050141d.n/N=50/500=.10UsexNnNn15005050011050134.UseSamplingandSamplingDistributions7-5xn//.5030913xxNote:Onlycase(d)wheren/N=.10requirestheuseofthefinitepopulationcorrectionfactor.Notethatxisapproximatelythesameeventhoughthepopulationsizevariesfrominfiniteto500.22.a.Usingthecentrallimittheorem,wecanapproximatethesamplingdistributionofxwithanormalprobabilitydistributionprovidedn30.b.n=30n=4023.a.xn//.1650226For2,()x2zxx2226088..Area=.3106x2.6212b.x16100160.zxx2160125..Area=.3944x2.7888c.x16200113.400400xn//.5040791Chapter77-6xn//.40006051640xxn//.40006051640zxx2113177..Area=.4616x2.9232d.x16400080.zxx2080250..Area=.4938x2.9876e.Thelargersampleprovidesahigherprobabilitythatthesamplemeanwillbewithin2of.24.a.ThenormaldistributionisbasedontheCentralLimitTheorem.b.Forn=120,E(x)remains$51,800andthesamplingdistributionofxcanstillbeapproximatedbyanormaldistribution.However,xisreducedto4000120/=365.15.c.Asthesamplesizeisincreased,thestandarderrorofthemean,x,isreduced.Thisappearslogicalfromthepointofviewthatlargersamplesshouldtendtoprovidesamplemeansthatareclosertothepopulationmean.Thus,thevariabilityinthesamplemean,measuredintermsofx,shoulddecreaseasthesamplesizeisincreased.25.a.51,800E(x)51,80051,30052,300SamplingandSamplingDistributions7-7z=52,300-51,800516.40=+.97Area=.3340x2.6680b.xn//.400012036515z=52,300-51,800365.15=+1.37Area.4147x2.829426.a.AnormaldistributionExnx()././.120010500014b.z1221200014141....Area=0.4207z1181200014141....Area=0.4207probability=0.4207+0.4207=0.8414c.z1211200014071....Area=0.2612z1191200014071....Area=0.2612probability=0.2612+0.2612=0.522427.a.E(x)=1017xn//.100751155b.102710170.8711.55zArea=0.3078100710170.8711.55zArea=0.3078probability=0.3078+0.3078=0.6156c.103710171.7311.55zArea=0.4582xChapter77-899710171.7311.55zArea=0.4582probability=0.4582+0.4582=0.916428.a.34,000/xz