商业应用统计英文版ch10

1、AppliedBusinessStatistics,7thed.byKenBlack,Chapter10StatisticalInferencesAboutTwoPopulations,LearningObjectives,TesthypothesesandconstructconfidenceintervalsaboutthedifferenceintwopopulationmeansusingtheZstatistic.Testhypothesesandconstructconfidenceintervalsaboutthedifferenceintwopopulationmeansusi

2、ngthetstatistic.,LearningObjectives,Testhypothesesandconstructconfidenceintervalsaboutthedifferenceintworelatedpopulations.Testhypothesesandconstructconfidenceintervalsaboutthedifferencesintwopopulationproportions.TesthypothesesandconstructconfidenceintervalsabouttwopopulationvariancesusingtheFstati

3、stic.,CalculatingtwosamplemeansandusingthedifferenceinthetwosamplemeansisusedtotestthedifferenceinthepopulationThecentrallimittheoremstatesthatthedifferenceintwosamplemeansisnormallydistributedforlargesamplesizes(bothn1andn2)30)regardlessoftheshapeofthepopulation,HypothesisTesting;ConfidenceInterval

4、s-DifferenceinMeansusingzStatistic(PopulationVariancesKnown),ZFormularforDifferencesBetweenTwoSampleMeans,HypothesisTestingforDifferencesBetweenMeans:TheWageExamplePart3,Asaspecificexample,supposewewanttoconductahypothesistesttodeterminewhethertheaverageannualwageforanadvertisingmanagerisdifferentfr

5、omtheaverageannualwageofanauditingmanager.Becausewearetestingtodeterminewhetherthemeansaredifferent,itmightseemlogicalthatthenullandalternativehypotheseswouldbeHo:1=2Ha:12whereadvertisingmanagersarepopulation1andauditingmanagersarepopulation2.,HypothesisTestingforDifferencesBetweenMeans:TheWageExamp

6、le,=0.05,/2=0.025,z0.025=1.96,HypothesisTestingforDifferencesBetweenMeans:TheWageExamplePart1,Thehypothesescanalsobeexpressedas:,Analysisistestingwhetherthereisadifferenceintheaveragewage.Thisisatwotailedtest.,HypothesisTestingforDifferencesBetweenMeans:WageExamplePart2,HypothesisTestingforDifferenc

7、esBetweenMeans:TheWageExamplePart3,Sincetheobservedvalueof2.35isgreaterthan1.96,rejectthenullhypothesis.Thatis,thereisasignificantdifferencebetweentheaverageannualwageofadvertisingmanagersandtheaverageannualwageofanauditingmanager.,HypothesisTestingforDifferencesBetweenMeans:WageExamplePart4,Differe

8、nceBetweenMeans:UsingExcel,Asampleof87professionalworkingwomenshowedthattheaverageamountpaidannuallyintoaprivatepensionfundperpersonwas$3352.Thepopulationstandarddeviationis$1100.Asampleof76professionalworkingmenshowedthattheaverageamountpaidannuallyintoaprivatepensionfundperpersonwas$5727,withapopu

9、lationstandarddeviationof$1700.Awomensactivistgroupwantsto“prove”thatwomendonotpayasmuchperyearasmenintoprivatepensionfunds.Iftheyuse=.001andthesesampledata,willtheybeabletorejectanullhypothesisthatwomenannuallypaythesameasormorethanmenintoprivatepensionfunds?Usetheeight-stephypothesis-testingproces

10、s.,DemonstrationProblem10.1,DemonstrationProblem10.1(Step1),DemonstrationProblem10.1(Steps2-7),Theevidenceissubstantialthatwomen,onaverage,paylessthanmenintoprivatepensionfundsannually.Theprobabilityofobtaininganobservedzvalueof-10.42isvirtuallyzero.,DemonstrationProblem10.1(Step8BusinessImplication

11、s),ConfidenceInterval,Sometimesthesolution(s)is/aretotakearandomsamplefromeachofthetwopopulationsandstudythedifferenceinthetwosamples.Formulaforconfidenceintervaltoestimate(1-2).Designatingagroupasgroupone,andanotherasgrouptwoisanarbitrarydecision.,Aconsumertestgroupwantstodeterminethedifferenceinga

12、solinemileageofcarsusingregularunleadedgasandcarsusingpremiumunleadedgas.Researchersforthegroupdividedafleetof100carsofthesamemakeinhalfandtestedeachcarononetankofgas.Fiftyofthecarswerefilledwithregularunleadedgasand50werefilledwithpremiumunleadedgas.Thesampleaveragefortheregulargasolinegroupwas21.4

13、5milespergallon(mpg),andthesampleaverageforthepremiumgasolinegroupwas24.6mpg.Assumethatthepopulationstandarddeviationoftheregularunleadedgaspopulationis3.46mpg,andthatthepopulationstandarddeviationofthepremiumunleadedgaspopulationis2.99mpg.Constructa95%confidenceintervaltoestimatethedifferenceinthem

14、eangasmileagebetweenthecarsusingregulargasolineandthecarsusingpremiumgasoline.,DemonstrationProblem10.2,DemonstrationProblem10.2,HypothesisTesting(PopulationVariancesUnknownandAssuming12=22),Hypothesistest-comparesthemeansoftwosamplestoseeifthereisadifferenceinthetwopopulationmeansfromwhichthesample

15、comes.T-testisusedwhen2isunknownandsamplesareindependent,andthemeasurementisnormallydistributed.,tFormulatoTesttheDifferenceinMeansAssuming12=22,Aswelearnedbefore,whenisknown.Thedifferenceinmeanscanbeanalyzedbyzformula,tFormulatoTesttheDifferenceinMeansAssuming12=22,If12=22,zformulacanberewrittenas,

16、tFormulatoTesttheDifferenceinMeansAssuming12=22,Ifisunknown,itcanbeestimatedbypoolingthetwosamplevariancesandcomputingapooledsamplestandarddeviation,tFormulatoTesttheDifferenceinMeansAssuming12=22,Finallywegetthetformula,tTestforDifferencesinPopulationMeans,Thefollowingconditionsshouldbemet:Eachofth

17、etwopopulationsisnormallydistributed.Thetwosamplesareindependent.Thevaluesofthepopulationvariancesareunknown.Thevariancesofthetwopopulationsareequal,i.e.12=22,AttheHernandezManufacturingCompany,anapplicationofthistestarises.Newemployeesareexpectedtoattendathree-dayseminartolearnaboutthecompany.Atthe

18、endoftheseminar,theyaretestedtomeasuretheirknowledgeaboutthecompany.Thetraditionaltrainingmethodhasbeenlectureandaquestion-and-answersession.Managementdecidedtoexperimentwithadifferenttrainingprocedure,whichprocessesnewemployeesintwodaysbyusingDVDsandhavingnoquestion-and-answersession.,HernandezManu

19、facturingCompany,Ifthisprocedureworks,itcouldsavethecompanythousandsofdollarsoveraperiodofseveralyears.However,thereissomeconcernabouttheeffectivenessofthetwo-daymethod,andcompanymanagerswouldliketoknowwhetherthereisanydifferenceintheeffectivenessofthetwotrainingmethods.TrainingMethodATrainingMethod

20、B565052445259545565474753454852576453425142434453565357,HernandezManufacturingCompanyContd,HernandezManufacturingCompany(Steps14),HernandezManufacturingCompany(Step5),HernandezManufacturingCo.(Steps6-7),HernandezManufacturingCo.BusinessImplications(Step8),Theconclusionisthatthereisasignificantdiffer

21、enceintheeffectivenessofthetrainingmethods.GiventhattrainingmethodBscoresaresignificantlyhigherandthefactthattheseminarisadayshorterthanmethodA(savingtimeandmoney),itmakesbusinesssensetoadoptmethodBasthestandardtrainingmethod.,TwosampleTformethodAvs.methodBNMeanStDevSEMeanmethodA1547.734.421.1method

22、B1256.604.271.295%C.I.formumethodA-mumethodB:(-12.2,-5.3)T-TestmumethodA=mumethodB(vs.not=):T=-5.20P=0.0000DF=25BothusePooledStDev=4.35,MINITABOutputforHernandezNew-EmployeeTrainingProblem,EXCELOutputforHernandezNew-EmployeeTrainingProblem,ConfidenceIntervaltoEstimate1-2when12and22areunknownand12=22

23、,Acoffeemanufacturerisinterestedinestimatingthedifferenceintheaveragedailycoffeeconsumptionofregular-coffeedrinkersanddecaffeinated-coffeedrinkers.Itsresearcherrandomlyselects13regular-coffeedrinkersandaskshowmanycupsofcoffeeperdaytheydrink.Herandomlylocates15decaffeinated-coffeedrinkersandaskshowma

24、nycupsofcoffeeperdaytheydrink.Theaveragefortheregular-coffeedrinkersis4.35cups,withastandarddeviationof1.20cups.Theaverageforthedecaffeinated-coffeedrinkersis6.84cups,withastandarddeviationof1.42cups.Theresearcherassumes,foreachpopulation,thatthedailyconsumptionisnormallydistributed,andheconstructsa

25、95%confidenceintervaltoestimatethedifferenceintheaveragesofthetwopopulations.,DemonstrationProblem10.4,DemonstrationProblem10.4,Theresearcheris95%confidentthatthedifferenceinpopulationaveragedailyconsumptionofcupsofcoffeebetweenregular-anddecaffeinated-coffeedrinkersisbetween1.46cupsand3.52cups.,Dem

26、onstrationProblem10.4,StatisticalInferencesforTwoRelatedPopulations,DependentsamplesUsedinbeforeandafterstudiesAftermeasurementisnotindependentofthebeforemeasurement,HypothesisTesting,ResearchermustdetermineifthetwosamplesarerelatedtoeachotherThetechniqueforrelatedsamplesisdifferentfromthetechniqueu

27、sedtoanalyzeindependentsamplesMatchedpairstestrequiresthetwosamplesbethesamesize,MatchedPairSample,BeforeandaftermeasurementsonthesameindividualStudiesoftwinsStudiesofspouses,HypothesisTesting,Thefollowingttestfordependentmeasuresusesthesampledifference,d,betweenindividualmatchedsamplesasthebasicmea

28、surementofanalysisAnanalysisofdconvertstheproblemfromatwosampleproblemtoasinglesampleofdifferences,FormulasforDependentSamples,HypothesisTesting,Analysisofdatabythismethodinvolvescalculatingatvaluewithacriticalvalueobtainedfromthetableninthedegreesoffreedom(n1)isthenumberofmatchedpairsofscores,Suppo

29、seastockmarketinvestorisinterestedindeterminingwhetherthereisasignificantdifferenceintheP/E(pricetoearnings)ratioforcompaniesfromoneyeartothenext.Inanefforttostudythisquestion,theinvestorrandomlysamplesninecompaniesfromtheHandbookofCommonStocksandrecordstheP/Eratiosforeachofthesecompaniesattheendofy

30、ear1andattheendofyear2.,P/ERatiosforNineRandomlySelectedCompanies,P/ERatiosforNineRandomlySelectedCompanies,HypothesisTestingwithDependentSamples:P/ERatiosforNineCompanies,H0:D=0H1:D0,HypothesisTestingwithDependentSamples:P/ERatiosforNineCompanies,HypothesisTestingwithDependentSamples:P/ERatiosforNi

31、neCompanies,HypothesisTestingwithDependentSamples:P/ERatiosfor9CompaniesComputerOutput,ConfidenceIntervals,ResearchercanbeinterestedinestimatingthemeandifferenceintwopopulationsforrelatedsamplesThisrequiresaconfidenceintervalofD(themeanpopulationdifferenceoftworelatedsamples)tobeconstructed,Confiden

32、ceIntervalsforMeanDifferenceforRelatedSamples,DifferenceinNumberofNew-HouseSales,ConfidenceIntervalforMeanDifferenceinNumberofNew-HouseSales,Theanalystestimateswitha99%levelofconfidencethattheaveragedifferenceinnew-housesalesforarealestatecompanyinIndianapolisbetween2005and2006isbetween-5.62and-1.16

33、houses.,ConfidenceIntervals-MINITABSolution,StatisticalInferenceabouttwoPopulationProportions(),Sampleproportionusedis(),HypothesisTesting,Becausepopulationproportionsareunknown,anestimateoftheStdDevofthedifferenceintwosampleproportionsismadebyusingsampleproportionsaspointofestimatesofthepopulationp

34、roportion,ZFormulatoTesttheDifferenceinPopulationProportions,Astudyoffemaleentrepreneurswasconductedtodeterminetheirdefinitionofsuccess.Thewomenwereofferedoptionalchoicessuchashappiness/self-fulfillment,sales/profit,andachievement/challenge.Thewomenweredividedintogroupsaccordingtothegrosssalesofthei

35、rbusinesses.Asignificantlyhigherproportionoffemaleentrepreneursinthe$100,000to$500,000categorythaninthelessthan$100,000categoryseemedtoratesales/profitasadefinitionofsuccess.Supposeyoudecidetotestthisresultbytakingasurveyofyourownandidentifyfemaleentrepreneursbygrosssales.Youinterview100femaleentrep

36、reneurswithgrosssalesoflessthan$100,000,and24ofthemdefinesales/profitassuccess.Youtheninterview95femaleentrepreneurswithgrosssalesof$100,000to$500,000,and39citesales/profitasadefinitionofsuccess.Usethisinformationtotesttodeterminewhetherthereisasignificantdifferenceintheproportionsofthetwogroupsthatdefinesuccessassales/profit.Use=0.01.,DemonstrationProblem10.6,TestingtheDifferenceinPopulationProportions(DemonstrationProblem10.6),Testing