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FundamentalsofBusinessStatistics

JianqiangSunPh.D.ofFinancejqsunmath@B5-407Beginwith3QuestionsWhyyoustudyBusinessStatistics?WhyIrecommendthistextbook?Howweconquerthecourse?Assignment20%,Experiment20%,Finalexam60%Courseemail:BS.JQSun@Password:BS.JQSunBS.JQSunSPSS16.0GoodTunesGoodTunes,aprivatelyheldonlineretailerofhomeentertainmentsystemsSeekstoexpanditsbusinessbyopeningseveralstores.GoodTunesneedstoapplyforloansatlocalareabanks.ThemanagersofthefirmagreetodevelopanelectronicslideshowthatwillexplaintheirbusinessandstatethefactsthatwillconvincethebankerstoloanGoodTunesthemoneyitneedsYouhavebeenaskedtoassistintheprocessofpreparingtheslideshow.Whatfactswouldyouinclude?Howwouldyoupresentthosefacts?youshouldproceedwiththereasonableassumptionthatthebankersseektomakeadecisionbasedonthehardfactsyouhelppresent,andnotonotherfactors,suchaswhimsorpersonallikesordislikes.Presentingthewronginformationorthecorrectinformationinthewrongfashioncouldleadthebankerstomakeabadbusinessdecision,whichcouldjeopardizethefutureofGoodTunes.YouneedtoknowsomethingaboutstatisticstoprovidethehardfactsthatarenecessaryTheframeworkTheframeworkofBusinessStatisticsThecontext:Chapter1:DataandStatisticsChapter2:DescriptiveStatisticsChapter3:DescriptiveStatisticsChapter7:SamplingandSamplingDistributionsChapter8:IntervalEstimationChapter9:HypothesisTestChapter10:ComparisonsInvolvingMenasChapter11:TestofIndependenceChapter12:SimpleLinearRegressionChapter13:MultipleRegressionChapter1

DataandStatisticsApplicationsinBusinessandEconomicsDataDataSourcesDescriptiveStatisticsStatisticalInferenceComputersandStatisticalAnalysisApplicationsin

BusinessandEconomicsAccountingEconomicsPublicaccountingfirmsusestatisticalsamplingprocedureswhenconductingauditsfortheirclients.Economistsusestatisticalinformationinmakingforecastsaboutthefutureoftheeconomyorsomeaspectofit.Electronicpoint-of-salescannersatretailcheckoutcountersareusedtocollectdataforavarietyofmarketingresearchapplications.MarketingApplicationsin

BusinessandEconomicsAvarietyofstatisticalqualitycontrolchartsareusedtomonitortheoutputofaproductionprocess.ProductionFinancialadvisorsuseprice-earningsratiosanddividendyieldstoguidetheirinvestmentrecommendations.Finance1.2DataandDataSets

Dataarethefactsandfigurescollected,summarized,analyzed,andinterpreted.Thedatacollectedinaparticularstudyarereferredtoasthedataset.Table1.1showsadatasetcontaininginformationfor25oftheshadowstocktrackedbytheAmericanAssociationofIndividualInvestors.CDfile:shadow02TABLE1.1DATASETFOR25S&P500COMPANIESTheelementsaretheentitiesonwhichdataarecollected.Avariableisacharacteristicofinterestfortheelements.Thesetofmeasurementscollectedforaparticularelementiscalledanobservation.Thetotalnumberofdatavaluesinacompletedatasetisthenumberofelementsmultipliedbythenumberofvariables.Elements,Variables,andObservationsStockAnnualEarn/ExchangeSales($M)Share($)Data,DataSets,

Elements,Variables,andObservationsCompanyDataram EnergySouthKeystoneLandCarePsychemedicsNQ 73.10 0.86N 74.00 1.67N 365.70 0.86NQ 111.40 0.33N 17.60 0.13VariablesElementNamesDataSetObservationScalesofMeasurementThescaleindicatesthedatasummarizationandstatisticalanalysesthataremostappropriate.Thescaledeterminestheamountofinformationcontainedinthedata.Scalesofmeasurementinclude:NominalOrdinalIntervalRatioScalesofMeasurementNominalAnonnumericlabelornumericcodemaybeused.Dataarelabelsornamesusedtoidentifyanattributeoftheelement.Example:StudentsofauniversityareclassifiedbytheschoolinwhichtheyareenrolledusinganonnumericlabelsuchasBusiness,Humanities,Education,andsoon.Alternatively,anumericcodecouldbeusedfortheschoolvariable(e.g.1denotesBusiness,2denotesHumanities,3denotesEducation,andsoon).Example:

Table1.1,scaleofmeasurementfortheexchangevariable.ScalesofMeasurementNominalScalesofMeasurementOrdinalAnonnumericlabelornumericcodemaybeused.Thedatahavethepropertiesofnominaldataandtheorderorrankofthedataismeaningful.ScalesofMeasurementOrdinalExample:StudentsofauniversityareclassifiedbytheirclassstandingusinganonnumericlabelsuchasFreshman,Sophomore,Junior,orSenior.Alternatively,anumericcodecouldbeusedfortheclassstandingvariable(e.g.1denotesFreshman,2denotesSophomore,andsoon).ScalesofMeasurementIntervalIntervaldataarealwaysnumeric.Thedatahavethepropertiesofordinaldata,andtheintervalbetweenobservationsisexpressedintermsofafixedunitofmeasure.ThedifferencesaremeaningfulNoabsolute“zero”valueScalesofMeasurementIntervalExample:MelissahasanSATscoreof1205,whileKevinhasanSATscoreof1090.Melissascored115pointsmorethanKevin.ScalesofMeasurementRatioThedatahaveallthepropertiesofintervaldataandtheratiooftwovaluesismeaningful.Variablessuchasdistance,height,weight,andtimeusetheratioscale.Thisscalemustcontainazerovaluethatindicatesthatnothingexistsforthevariableatthezeropoint.ScalesofMeasurementRatioExample:Melissa’scollegerecordshows36credithoursearned,whileKevin’srecordshows72credithoursearned.KevinhastwiceasmanycredithoursearnedasMelissa.Datacanbefurtherclassifiedasbeingqualitativeorquantitative.Thestatisticalanalysisthatisappropriatedependsonwhetherthedataforthevariablearequalitativeorquantitative.Ingeneral,therearemorealternativesforstatisticalanalysiswhenthedataarequantitative.QualitativeandQuantitativeDataQualitativeData

LabelsornamesusedtoidentifyanattributeofeachelementOftenreferredtoascategoricaldataUseeitherthenominalorordinalscaleofmeasurementCanbeeithernumericornonnumericAppropriatestatisticalanalysesareratherlimitedQuantitativeDataQuantitativedataindicatehowmanyorhowmuch:

discrete,ifmeasuringhowmany

continuous,ifmeasuringhowmuchQuantitativedataarealwaysnumeric.Ordinaryarithmeticoperationsaremeaningfulforquantitativedata.ScalesofMeasurementQualitativeQuantitativeNumericalNumericalNon-numericalDataNominalOrdinalNominalOrdinalIntervalRatioCross-SectionalData

Cross-sectionaldataarecollectedatthesameorapproximatelythesamepointintime.

Example:datadetailingthenumberofbuildingpermitsissuedinJune2007ineachofthecountiesofOhio

Example:Table1.125shadowstocksTimeSeriesData

Timeseriesdataarecollectedoverseveraltimeperiods.

Example:datadetailingthenumberofbuildingpermitsissuedinLucasCounty,Ohioineachofthelast36months

Example:U.S.cityaveragepricepergallonforunleadedregulargasoline.Figure1.1FIGURE1.1

U.S.CITYAVERAGEPRICEPERGALLONFORCONVENTIONALREGULARGASOLINESource:U.S.EnergyInformationAdministration,January2006.1.3DataSourcesExistingSources

Withinafirm–almostanydepartment,Table1.2Businessdatabaseservices–DowJones&Co.,CCERGovernmentagencies-U.S.DepartmentofLabor,Table1.3Industryassociations–TravelIndustryAssociationofAmericaSpecial-interestorganizations–GraduateManagementAdmissionCouncilInternet–moreandmorefirmsTABLE1.2EXAMPLESOFDATAAVAILABLEFROMINTERNALCOMPANYRECORDSTABLE1.3EXAMPLESOFDATAAVAILABLEFROMSELECTEDGOVERNMENTAGENCIESStatisticalStudiesDataSourcesInexperimentalstudiesthevariableofinterestisfirstidentified.Thenoneormoreothervariablesareidentifiedandcontrolledsothatdatacanbeobtainedabouthowtheyinfluencethevariableofinterest.Inobservational(nonexperimental)studiesnoattemptismadetocontrolorinfluencethevariablesofinterest.asurveyisagoodexampleFigure1.3DataCollectingMthodsExperimentalStudiesObservationalstudiesObservationMailSurveyPhoneSurveySymposiumComputerSurveyVisitingSurveyPrivateVisitDataAcquisitionConsiderationsTimeRequirementCostofAcquisitionDataErrorsSearchingforinformationcanbetimeconsuming.Informationmaynolongerbeusefulbythetimeitisavailable.Organizationsoftenchargeforinformationevenwhenitisnottheirprimarybusinessactivity.Blindlyusinganydatathathappentobeavailableorwereacquiredwithlittlecarecanleadtomisleadinginformation.1.4DescriptiveStatisticsDescriptivestatisticsarethetabular,graphical,andnumericalmethodsusedtosummarizeandpresentdata.Example:HudsonAutoRepair ThemanagerofHudsonAutowouldliketohaveabetterunderstandingofthecostofpartsusedintheenginetune-upsperformedintheshop.Sheexamines50customerinvoicesfortune-ups.Thecostsofparts,roundedtothenearestdollar,arelistedonthenextslide.Example:HudsonAutoRepairSampleofPartsCost($)for50Tune-upsTabularSummary:

FrequencyandPercentFrequency50-5960-6970-7980-8990-99100-109

2131677

550426321414

10100(2/50)100Parts

Cost($)Parts

FrequencyPercentFrequencyGraphicalSummary:Histogram24681012141618PartsCost($)Frequency50-5960-6970-79

80-8990-99100-110Tune-upPartsCostNumericalDescriptiveStatisticsHudson’saveragecostofparts,basedonthe50tune-upsstudied,is$79(foundbysummingthe50costvaluesandthendividingby50).Themostcommonnumericaldescriptivestatisticistheaverage(ormean).1.5StatisticalInference

PopulationSampleStatisticalinferenceCensusSamplesurvey-thecollectionofalltheelementsofinterest-asubsetofthepopulation-theprocessofusingdataobtainedfromasampletomakeestimatesandtesthypothesesaboutthecharacteristicsofapopulation-collectingdataforapopulation-collectingdataforasampleFourimportantconcept1.populationApopulationconsistsofallofthemembersofagroupaboutwhichyouwanttodrawaconclusionE.g.Allthefull-timestudentsatacollegeAlltheregisteredvotersinNewYork.Allthepeoplewhowentshoppingatthelocalmallthisweekend.2.sampleAsampleistheportionofthepopulationselectedforanalysisSamplesselectedfromeachofthethreepopulationsmentionedabove.E.g.10full-timestudentsselectedforafocusgroup,500registeredvotersinNewYorkwhowerecontactedviatelephoneforapoliticalpoll,30mallshopperswhowereaskedtocompleteacustomersatisfactionsurvey.Ineachcase,thepeopleinthesamplerepresentaporti

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