Statisticsfor

BusinessandEconomics(14e)

MetricVersionAnderson,Sweeney,Williams,Camm,Cochran,Fry,Ohlmann?2020CengageLearning?2020Cengage.Maynotbescanned,copiedorduplicated,orpostedtoapubliclyaccessiblewebsite,inwholeorinpart,exceptforuseaspermittedinalicensedistributedwithacertainproductorserviceorotherwiseonapassword-protectedwebsiteorschool-approvedlearningmanagementsystemforclassroomuse.1Chapter22-SampleSurvey22.1-TerminologyUsedinSampleSurveys22.2-TypesofSurveysandSamplingMethods22.3-SurveyErrors22.4-SimpleRandomSampling22.5-StratifiedSimpleRandomSampling22.6-ClusterSampling22.7-SystematicSampling2TerminologyUsedinSampleSurveys(1of2)Anelementistheentityonwhichdataarecollected.Apopulationisthecollectionofallelementsofinterest.Asampleisasubsetofthepopulation.Thetargetpopulation

isthepopulationwewanttomakeinferencesabout.Thesampledpopulation

isthepopulationfromwhichthesampleisactuallyselected.Thesetwopopulationsarenotalwaysthesame.Ifinferencesfromasamplearetobevalid,thesampledpopulationmustberepresentativeofthetargetpopulation.3TerminologyUsedinSampleSurveys(2of2)Thepopulationisdividedintosamplingunits

whicharegroupsofelementsortheelementsthemselves.Alistofthesamplingunitsforaparticularstudyiscalledaframe.Thechoiceofaparticularframeisoftendeterminedbytheavailabilityandreliabilityofalist.Thedevelopmentofaframecanbethemostdifficultandimportantstepsinconductingasamplesurvey.4TypesofSurveys(1of2)SurveysInvolvingQuestionnairesThreecommontypesaremailsurveys,telephonesurveys,andpersonalinterviewsurveys.Surveycostsarelowerformailandtelephonesurveys.Withwell-trainedinterviewers,higherresponseratesandlongerquestionnairesarepossiblewithpersonalinterviews.Thedesignofthequestionnaireiscritical.5TypesofSurveys(2of2)SurveysNotInvolvingQuestionnairesOften,someonesimplycountsormeasuresthesampleditemsandrecordstheresults.Anexampleissamplingacompany’sinventoryofpartstoestimatethetotalinventoryvalue.6SamplingMethodsSamplesurveyscanalsobeclassifiedintermsofthesamplingmethodused.Thetwocategoriesofsamplingmethodsare:NonprobabilisticsamplingProbabilisticsampling7NonprobabilisticSamplingMethods(1of2)Theprobabilityofobtainingeachpossiblesamplecannotbecomputed.Statisticallyvalidstatementscannotbemadeabouttheprecisionoftheestimates.Samplingcostislowerandimplementationiseasier.Methodsincludeconvenienceandjudgmentsampling.8NonprobabilisticSamplingMethods(2of2)ConvenienceSamplingTheunitsincludedinthesamplearechosenbecauseofaccessibility.Insomecases,conveniencesamplingistheonlypracticalapproach.JudgmentSamplingAknowledgeablepersonselectssamplingunitsthathe/shefeelsaremostrepresentativeofthepopulation.Thequalityoftheresultisdependentonthepersonselectingthesample.Generally,nostatisticalstatementshouldbemadeabouttheprecisionoftheresult.9ProbabilisticSamplingMethodsTheprobabilityofobtainingeachpossiblesamplecanbecomputed.Confidenceintervalscanbedevelopedwhichprovideboundsonthesamplingerror.Methodsincludesimplerandom,stratifiedsimplerandom,cluster,andsystematicsampling.10SurveyErrors(1of6)Twotypesoferrorscanoccurinconductingasurvey:SamplingerrorNonsamplingerror11SurveyErrors(2of6)SamplingErrorItisdefinedasthemagnitudeofthedifferencebetweenthepointestimate,developedfromthesample,andthepopulationparameter.Itoccursbecausenoteveryelementinthepopulationissurveyed.Itcannotoccurinacensus.Itcannotbeavoided,butitcanbecontrolled.12SurveyErrors(3of6)NonsamplingErrorItcanoccurinbothacensusandasamplesurvey.Examplesinclude:MeasurementerrorErrorsduetononresponseErrorsduetolackofrespondentknowledgeSelectionerrorProcessingerror13SurveyErrors(4of6)NonsamplingError-MeasurementErrorMeasuringinstrumentsarenotproperlycalibrated.Peopletakingthemeasurementsarenotproperlytrained.NonsamplingError-ErrorsDuetoNonresponseTheyoccurwhennodatacanbeobtained,oronlypartialdataareobtained,forsomeoftheunitssurveyed.Theproblemismostseriouswhenabiasiscreated.14SurveyErrors(5of6)NonsamplingError-ErrorsDuetoLackofRespondentKnowledgeTheseerrorsarecommonintechnicalsurveys.Somerespondentsmightbemorecapablethanothersofansweringtechnicalquestions.NonsamplingError-SelectionErrorAninappropriateitemisincludedinthesurvey.Forexample,inasurveyof“smalltruckowners,”someinterviewersincludeSUVownerswhileotherinterviewersdonot.15SurveyErrors(6of6)NonsamplingError-ProcessingErrorDataisincorrectlyrecorded.Dataisincorrectlytransferredfromrecordingformstocomputerfiles.16SimpleRandomSampling

(1of12)

17SimpleRandomSampling(2of12)Wewillseeintheupcomingslideshowto:Estimatethefollowingpopulationparameters:PopulationmeanPopulationtotalPopulationproportionDeterminetheappropriatesamplesize18SimpleRandomSampling(3of12)

19SimpleRandomSampling(4of12)PopulationMeanPointEstimator: EstimateoftheStandardErroroftheMean:IntervalEstimate:Approximate95%ConfidenceIntervalEstimate: 20SimpleRandomSampling(5of12)PopulationTotalPointEstimator:EstimateoftheStandardErroroftheTotal:IntervalEstimate:Approximate95%ConfidenceIntervalEstimate: 21SimpleRandomSampling(6of12)PopulationProportionPointEstimator: EstimateoftheStandardErroroftheProportion:IntervalEstimate:Approximate95%ConfidenceIntervalEstimate:22DeterminingtheSampleSize

23SimpleRandomSampling(7of12)NecessarySampleSizeforEstimatingthePopulationMean24SimpleRandomSampling(8of12)NecessarySampleSizeforEstimatingthePopulationTotalNecessarySampleSizeforEstimatingthePopulationProportion25SimpleRandomSampling(9of12)Example:SteddyInvestmentsBenSteddyisafinancialadvisorfor200clients.Asampleof40clientshasbeentakentoobtainvariousdemographicdataandinformationabouttheclients’investmentobjectives.Statisticsofparticularinterestaretheclients’networthandtheproportionfavoringfixedincomeinvestments.Forthesample,themeannetworthwas$480,000(withastandarddeviationof$120,000),andtheproportionfavoringfixed-incomeinvestmentswas0.30.26SimpleRandomSampling(10of12)PointEstimateofTotalNetWorth(TNW)EstimateofStandardErrorofTNWApproximate95%ConfidenceIntervalforTNW27SimpleRandomSampling(11of12)PointEstimateofPopulationProportionFavoringFixed-IncomeInvestmentsEstimateofStandardErrorofProportionApproximate95%ConfidenceInterval28SimpleRandomSampling(12of12)Example:SteddyInvestmentsOneyearlater,Steddywantstoagainsurveyhisclients.Henowhas250clientsandwantstosetaboundof$30,000ontheerroroftheestimateoftheirmeannetworth.Whatisthenecessarysamplesize?Steddywillneedasamplesizeof51.29StratifiedSimpleRandomSampling

(1of16)ThepopulationisfirstdividedintoHgroups,calledstrata.Thenforstratumh,asimplerandomsampleofsizenhisselected.ThedatafromtheHsimplerandomsamplesarecombinedtodevelopanestimateofapopulationparameter.Ifthevariabilitywithineachstratumissmallerthanthevariabilityacrossthestrata,astratifiedsimplerandomsamplecanleadtogreaterprecision.Thebasisforformingthevariousstratadependsonthejudgmentofthedesignerofthesample.30StratifiedSimpleRandomSampling(2of16)Example:ChemTechInternationalChemTechInternationalhasusedstratifiedsimplerandomsamplingtoobtaindemographicinformationandpreferencesregardinghealthcarecoverageforitsemployeesandtheirfamilies.Thepopulationofemployeeshasbeendividedinto3strataonthebasisofage:under30,30-49,and50orover.Someofthesampledataisshownonthenextslide.31StratifiedSimpleRandomSampling(3of16)DemographicDataStratumuppernsubscripthnsubscripthAnnualFamilyDentalExpenseMeanAnnualFamilyDentalExpenseSt.DevProportionMarriedUnder3010030$250$75.6030-4925045400100.7050orOver12530425130.6832StratifiedSimpleRandomSampling(4of16)PopulationMeanPointEstimator33StratifiedSimpleRandomSampling(5of16)PopulationMean-EstimateoftheStandardErroroftheMean34StratifiedSimpleRandomSampling

(6of16)PopulationMeanIntervalEstimate: Approximate95%ConfidenceIntervalEstimate: 35StratifiedSimpleRandomSampling(7of16)PointEstimateofMeanAnnualDentalExpenseEstimateofStandardErrorofMean36StratifiedSimpleRandomSampling(8of16)Approximate95%ConfidenceIntervalforMeanAnnualDentalExpense 37StratifiedSimpleRandomSampling(9of16)PopulationTotalPointEstimator: EstimateoftheStandardErroroftheTotal:IntervalEstimate:Approximate95%ConfidenceIntervalEstimate: 38StratifiedSimpleRandomSampling(10of16)PointEstimateofTotalFamilyExpenseForAllEmployeesApproximate95%ConfidenceInterval39StratifiedSimpleRandomSampling(11of16)PopulationProportionPointEstimator40StratifiedSimpleRandomSampling

(12of16)PopulationProportion-EstimateoftheStandardErroroftheProportion41StratifiedSimpleRandomSampling(13of16)PopulationProportionIntervalEstimate:

Approximate95%ConfidenceIntervalEstimate:42StratifiedSimpleRandomSampling(14of16)PointEstimateofProportionMarriedEstimateofStandardErrorofProportionApproximate95%ConfidenceIntervalforProportion43StratifiedSimpleRandomSampling

(15of16)SampleSizeWhenEstimatingPopulationMeanSampleSizeWhenEstimatingPopulationTotal44StratifiedSimpleRandomSampling(16of16)SampleSizeWhenEstimatingPopulationProportionProportionalAllocationofSamplentotheStrata45ClusterSampling

(1of15)

46ClusterSampling(2of15)

47ClusterSampling(3of15)PopulationMeanPointEstimatorEstimateofStandardErroroftheMean48ClusterSampling(4of15)PopulationMeanIntervalEstimate:

Approximate95%ConfidenceIntervalEstimate: 49ClusterSampling(5of15)PopulationTotalPointEstimator: EstimateoftheStandardErroroftheTotal:IntervalEstimate:Approximate95%ConfidenceIntervalEstimate: 50ClusterSampling(6of15)PopulationProportionPointEstimatorEstimateoftheStandardErroroftheProportion51ClusterSampling(7of15)PopulationProportionIntervalEstimate: Approximate95%ConfidenceIntervalEstimate:52ClusterSampling(8of15)Example:CooperCountySchoolsThereare40highschoolsinCooperCounty.Schoolofficialsareinterestedintheeffectofparticipationinathleticsonacademicpreparationforcollege.