大学课件商务与经济统计习题答案(第8版,中文版)

21-1LearningObjectives1.Learnwhatasamplesurveyisandhowitdiffersfromanexperimentasamethodofcollectingdata.2.Knowaboutthemethodsofdatacollectionforasurvey.3.Knowthedifferencebetweensamplingandnonsamplingerror.4.Learnaboutfoursampledesigns:(1)simplerandomsampling,(2)stratifiedsimplerandomsampling,(3)clustersampling,and(4)systematicsampling.5.Leanhowtoestimateapopulationmean,apopulationtotal,andapopulationproportionusingtheabovesampledesigns.6.Understandtherelationshipbetweensamplesizeandprecision.7.Learnhowtochoosetheappropriatesamplesizeusingstratifiedandsimplerandomsampling.8.Learnhowtoallocatethetotalsampletothevariousstratausingstratifiedsimplerandomsampling.21-2Chapter21Solutions:1.a.x=215isanestimateofthepopulationmean.800-50bs=2.7386x50800c.215士2(2.7386)or209.5228to220.47722.a.Estimateofpopulationtotal=Nx=400(75)=30,000b.EstimateofStandardError=Ns(8)400-80Ns=400||=320x(80)400c.30,000士2(320)or29,360to30,6403.a.p=.30isanestimateofthepopulationproportion(1000-100)((.3)(.7))p(1000)(99)b.s=p(1000)(99)c..30士2(.0437)or.2126to.38744.B=154900Asamplesizeof73willprovideanapproximate95%confidenceintervalofwidth30.5.a.x=149,670ands=73,420771-50(73,420)s=||=10,040.83x771(50)approximate95%confidenceinterval149,670士2(10,040.83)or$129,588.34to$169,751.66b.X=Nx=771(149,670)=115,395,570s=Ns=771(10,040.83)=7,741,479.93xx21-3SampleSurveyapproximate95%confidenceinterval93)or$99,912,810.14to$130,878,729.86(771-50)((.36)(.64))p(771)(49)c.p=18/50=0.36andsp(771)(49)approximate95%confidenceinterval0.36土2(0.0663)or0.2274to0.4926Thisisaratherlargeinterval;samplesizesmustberatherlargetoobtaintightconfidenceintervalsonapopulationproportion.6.B=5000/2=2500Usethevalueofsforthepreviousyearintheformulatodeterminethenecessarysamplesize.(31.3)2979.69n===336.00519157Asamplesizeof337willprovideanapproximate95%confidenceintervalofwidthnolargerthan$5000.7.a.Stratum1:=138Stratum2:x=1032Stratum3:x=2103b.Stratum1x=1381(30)200-20s=||=6.3640x1(20)200or125.272to150.728Stratum2x=103221-4(200)(250)((200)(250)(100)x=(25)250-30s=||=4.2817x2(30)250or94.4366to111.5634 Stratum3 x=2103(50)100-25s=||=8.6603x3(25)100210土2(8.6603)or192.6794to227.3206st(550)(550)(550)st(550)(550)(550)=50.1818+46.8182+38.1818=135.1818((1)((30)2(25)2(50)2) ((550)2)(203025)((1) ((550)2)135.1818土2(3.4092)or128.3634to142.00028.a.Stratum1:Nx=200(138)=27,60011Stratum2:Nx=250(103)=25,75022Stratum3:Nx=100(210)=21,00033b.Nx=27,600+25,750+21,000=74,350Note:thesumoftheestimateforeachstratumtotalequalsNxc.Nx=550(3.4092)=1875.06(see7c)21-5cdSampleSurveycdapproximate95%confidenceinterval74,350土2(1875.06)or70,599.88to78,100.129.a.Stratum1p=.501(200-20)((.50)(.50))p1(200)(19)s=p1(200)(19)or.2824to.7176Stratum2p=.782(250-30)((.78)(.22))p2(250)(29)sp2(250)(29)or.6356to.9244Stratum3p=.213(100-25)((.21)(.79))p3(100)(24)sp3(100)(24)or.066to.354( | (( | (( | (( | (.p192924)1)==(550)2).approximate95%confidenceinterval.21-6土2(.0530)or.4685to.680500)2(300(150))1(140,000)1(140,000)(600(75))140,000)140,000)(500(100))(140,000)(140,000)b.WithB=10,thefirstterminthedenominatorintheformulafornchanges.Roundingup,weseethatasamplesizeof306isneededtoprovidethislevelofprecision.(300(150))1(140,000)n1(140,000)(600(75))2(140,000)2(140,000)(500(100))3(140,000)3(140,000)Duetorounding,thetotaloftheallocationstoeachstrataonlyaddto305.Notethateventhoughthesamplesizeislarger,theproportionallocatedtoeachstratumhasnotchanged.4Roundingup,weseethatasamplesizeof275willprovidethedesiredlevelofprecision.Theallocationstothestrataareinthesameproportionasforpartsaandb.21-7(300(150)n=275||=981140,000(600(75)n=275||=882140,000(500(100)n=275||=983140,000Again,duetorounding,thestratumallocationsdonotaddtothetotalsamplesize.Anotheritemcouldbesampledfrom,say,stratum3ifdesired.11.a.11.a.x1=29.5333264.775x=45.2125x=53.030034b.Indianapolis629.53310.9086(.9177)or19.5222to39.5438 Louisville 864.77517.7248(.9068)or48.7022to80.8478St.Louis845.2125(13.7238)(.9487)or32.1927to58.2323Memphis53.03001053.030018.7719(.9258)or35.6510to70.409021-8Chapter21(38)(1)(45)(5)(80)(3)(70)(5)(38)(1)(45)(5)(80)(3)(70)(5)111n-151222n-172333n-173444n-194pst((233)2)(233)2approximate95%confidenceinterval土2(.0857)or.2555to.598312.a.St.Louistotal=Nx=80(45.2125)=3617Indollars:$3,617,000b.Indianapolistotal=Nx=38(29.5333)=1122.2654Indollars:$1,122,265(38)(45)(80)(70)(38)(45)(80)(70)s2(13.3603)2N(N-n)1=38(32)=36,175.517111n61s2(25.0666)2N(N-n)2=45(37)=130,772.1222n8221-9x1x12s2(19.4084)2N(N-n)3=80(72)=271,213.91333n83s2(29.6810)2N(N-n)4=70(60)=370,003.94444n104 ((233)2)approximate95%confidenceintervalstx48.7821士2(3.8583)or41.0655to56.4987Indollars:$41,066to$56,499d.dapproximate95%confidenceintervalstx233(48.7821)士2(233)(3.8583)or9,568.2612to13,164.197Indollars:$9,568,261to$13,164,197Roundingupweseethatasamplesizeof28isnecessarytoobtainthedesiredprecision.(50(80))(38(150))n=28||(35(45))(11,275)(11,275)21-10Chapter21bn==33bn==33(50(100))1(12,300)1(12,300)(38(100))2(12,300)n2(12,300)(35(100))(12,300)(12,300)Thisisthesameasproportionalallocation.Notethatforeachstratum(N)nh=n|()|xx750cxM5014.a.x=cxM50iX=Mx=300(15)=4500cxa15cxM50p=icxM50ib.x(x-xM)2=[95-15(7)]2+[325-15(18)]2+[190-15(15)]2+[140-15(10)]2ici=(-10)2+(55)2+(-35)2+(-10)2=4450(25-4)(4450)s=Ms=300(1.4708)=441.24cXxcx(a-pM)2=[1-.3(7)]2+[6-.3(18)]2+[6-.3(15)]2+[2-.3(10)]2ici=4.82(25-4)(4.82)c.approximate95%confidenceIntervalforPopulationMean:)or12.0584to17.941621-11SampleSurveyd.approximate95%confidenceIntervalforPopulationTotal:4500土2(441.24)or3617.52to5382.48e.approximate95%confidenceIntervalforPopulationProportion:or.2032to.396840015.a.x==80c130X=Mx=600(80)=48,000cp==.10b.x(x-xM)2=[3500-80(35)]2+[965-80(15)]2+[960-80(12)]2ici+[2070-80(23)]2+[1100-80(20)]2+[1805-80(25)]2=(700)2+(-235)2+(0)2+(230)2+(-500)2+(-195)2=886,150(30-6)(886,150)capproximate95%confidenceIntervalforPopulationMean:861)or64.6278to95.3722c.s=600(7.6861)=4611.66Xapproximate95%confidenceIntervalforPopulationTotal:48,000土2(4611.66)or38,776.68to57,223.32x(a-pM)2=[3-.1(35)]2+[0-.1(15)]2+[1-.1(12)]2+[4-.1(23)]2ici+[3-.1(20)]2+[2-.1(25)]2=(-.5)2+(-1.5)2+(-.2)2+(1.7)2+(1)2+(-.5)2=6.6821-12Chapter21(30-6)(6.68)approximate95%confidenceIntervalforPopulationProportion:or.0578to.1422xc50Estimateofmeanageofmechanicalengineers:40yearsc.x(x-xM)2=[520-40(12)]2+···+[462-40(13)]2ici=(40)2+(-7)2+(-10)2+(-11)2+(30)2+(9)2+(22)2+(8)2+(-23)2+(-58)2=7292(120-10)(7292)approximate95%confidenceIntervalforMeanage:40土2(2.0683)or35.8634to44.1366d.x(a-pM)2=[8-.7(12)]2+···+[12-.7(13)]2ici=(-.4)2+(-.7)2+(-.4)2+(.3)2+(-1.2)2+(-.1)2+(-1.4)2+(.3)2+(.7)2+(2.9)2=13.3(120-10)(13.3)approximate95%confidenceIntervalforProportionAttendingLocalUniversity:21-13SampleSurveyor.5234to.876640Estimateofmeanage:36.9737yearsb.ProportionofCollegeGraduates:128/304=.4211ProportionofMales:112/304=.3684c.x(x-xM)2=[17(37)-(36.9737)(17)]2+···+[57(44)-(36.9737)(44)]2ici=(.4471)2+(-174.0795)2+(-25.3162)2+(-460.2642)2+(173.1309)2+(180.3156)2+(-94.7376)2+(400.4991)2=474,650.68(150-8)(474,650.68)xc((150)(8)(40)2)(7)sxc((150)(8)(40)2)(7)approximate95%confidenceIntervalforMeanAgeofAgents:36.9737士2(2.2394)or32.4949to41.4525d.x(a-pM)2=[3-.4211(17)]2+···+[25-.4211(57)]2ici=(-4.1587)2+(-.7385)2+(-2.9486)2+(10.2074)2+(-.1073)2+(-3.0532)2+(-.2128)2+(.9973)2=141.0989(150-8)(141.0989)pc((150)(8)(40)2)(7)spc((150)(8)(40)2)(7)approximate95%confidenceIntervalforProportionofAgentsthatareCollegeGraduates:士2(.0386)or.3439to.4983e.x(a-pM)2=[4-.3684(17)]2+···+[26-.3684(57)]2ici=(-2.2628)2+(-.8940)2+(-2.5784)2+(3.6856)2+(-3.8412)2+(1.5792)2+(-.6832)2+(5.0012)2=68.878721-14Chapter21150-8(68.8787s=|approximate95%confidenceIntervalforProportionofAgentsthatareMale:.36842(.0270)or.3144to.422418.a.p=0.19(0.19)(0.81)s==0.0206p363Approximate95%ConfidenceInterval:0.192(0.0206)or0.1488to0.2312b.p=0.31(0.31)(0.69)s==0.0243p363Approximate95%ConfidenceInterval:0.312(0.0243)or0.2615to0.3585c.p=0.17(0.17)(0.83)s==0.0197p373Approximate95%ConfidenceInterval:0.172(0.0197)or0.1306to0.2094d.Thelargeststandarderroriswhenp=.50.Atp=.50,weget(0.5)(0.5)sp=363=0.026221-15SampleSurveyMultiplyingby2,wegetaboundofB=2(.0262)=0.0525Forasampleof363,then,theyknowthatintheworstcase(p=0.50),theboundwillbeapproximately5%.e.Ifthepollwasconductedbycallingpeopleathomeduringthedaythesampleresultswouldonlyberepresentativeofadultsnotworkingoutsidethehome.ItislikelythattheLouisHarrisorganizationtookprecautionsagainstthisandotherpossiblesourcesofbias.19.a.Assume(N-n)/N1p=.55(0.55)(0.45)s==0.0222p504b.p=.31(0.31)(0.69)s==0.0206p504c.Theestimateofthestandarderrorinpart(a)islargerbecausepiscloserto.50.d.Approximate95%Confidenceinterval:or.5056to.5944e.Approximate95%Confidenceinterval:.2688to.3512a.s==204.9390x200Approximate95%ConfidenceIntervalforMeanAnnualSalary:23,200士2(204.9390)or$22,790to$23,610b.Nx=3000(23,200)=69,600,000s=3000(204.9390)=614,817x21-16(380)(10)(380)(10)(760)(19)(260)(7)Approximate95%ConfidenceIntervalforPopulationTotalSalary:69,600,000土2(614,817)or$68,370,366to$70,829,634c.p=.73(3000-200)((.73)(.27))p(3000)(199)s=p(3000)(199)Approximate95%ConfidenceIntervalforProportionthatareGenerallySatisfied:or.6692to.7908d.Ifmanagementadministeredthequestionnaireandanonymitywasnotguaranteedwewouldexpectadefiniteupwardbiasinthepercentreportingtheyweregenerallysatisfiedwiththeirob.Aprocedureforguaranteeinganonymityshouldreducethebias.21.a.p=1/3(380-30)((1/3)(2/3))p(380)(29)sp(380)(29)Approximate95%ConfidenceInterval:土2(.0840)or.1653to.5013b.X2=760(19/45)=320.8889c.p=19/45=.4222(760-45)((19/45)(26/45))p(760)(44)s=p(760)(44)Approximate95%ConfidenceInterval:土2(.0722)or.2778to.5666st(1400)(30)(1400)(45)(1400)(25)st(1400)(30)(1400)(45)(1400)(25)21-17SampleSurvey4424=1019.1571+3012.7901+513.2400=4545.1892(1)s=||4545.1892=.0482pst((1400)2)Approximate95%ConfidenceInterval:土2(.0482)or.2753to.468122.a.X=380(9/30)+760(12/45)+260(11/25)=431.0667Estimateapproximately431deathsduetobeating.xN(N-n)xN(N-