(1.28)-PowerPoint Ch 10a商务统计课件

Chapter10,PartA

ComparisonsInvolvingMeans,Experimental

Design,andAnalysisofVariance

InferencesAbouttheDifferenceBetween TwoPopulationMeans:s

1ands

2KnownInferencesAbouttheDifferenceBetweenTwoPopulationMeans:MatchedSamplesInferencesAbouttheDifferenceBetweenTwoPopulationMeans:s

1ands

2UnknownInferencesAbouttheDifferenceBetween

TwoPopulationMeans:s1ands2KnownIntervalEstimationofm

1–m

2HypothesisTestsAboutm

1–m

2EstimatingtheDifferenceBetween

TwoPopulationMeansLet

1equalthemeanofpopulation1and

2equalthemeanofpopulation2.Thedifferencebetweenthetwopopulationmeansis

1-

2.Toestimate

1-

2,wewillselectasimplerandomsampleofsizen1frompopulation1andasimplerandomsampleofsizen2frompopulation2.Letequalthemeanofsample1andequalthemeanofsample2.Thepointestimatorofthedifferencebetweenthe meansofthepopulations1and2is.ExpectedValueSamplingDistributionofStandardDeviation(StandardError)where:

1=standarddeviationofpopulation1

2=standarddeviationofpopulation2

n1=samplesizefrompopulation1

n2=samplesizefrompopulation2IntervalEstimateIntervalEstimationof

1-

2:

s1ands2Knownwhere: 1-

istheconfidencecoefficientIntervalEstimationof

1-

2:

s1ands2KnownInatestofdrivingdistanceusingamechanicaldrivingdevice,asampleofPargolfballswascomparedwithasampleofgolfballsmadebyRap,Ltd.,acompetitor.Thesamplestatisticsappearonthenextslide.Par,Inc.isamanufacturerofgolfequipmentandhasdevelopedanewgolfballthathasbeendesignedtoprovide“extradistance.”Example:Par,Inc.Example:Par,Inc.IntervalEstimationof

1-

2:

s1ands2KnownSampleSizeSampleMeanSample#1Par,Inc.Sample#2Rap,Ltd.120balls

80balls295yards278yardsBasedondatafrompreviousdrivingdistancetests,thetwopopulationstandarddeviationsareknownwiths1=15yardsands2=20yards.IntervalEstimationof

1-

2:

s1ands2KnownExample:Par,Inc.Letusdevelopa95%confidenceintervalestimateofthedifferencebetweenthemeandrivingdistancesofthetwobrandsofgolfball.EstimatingtheDifferenceBetween

TwoPopulationMeansm1–

m2

=differencebetween themeandistancesx1-x2=PointEstimateofm1–

m2

Population1Par,Inc.GolfBallsm1=meandrivingdistanceofPargolfballsPopulation2Rap,Ltd.GolfBallsm2=meandrivingdistanceofRapgolfballsSimplerandomsampleofn2Rapgolfballsx2=samplemeandistancefortheRapgolfballsSimplerandomsampleofn1Pargolfballsx1=samplemeandistanceforthePargolfballsPointEstimateof

1-

2

Pointestimateof

1

-

2=where:

1=meandistanceforthepopulation ofPar,Inc.golfballs

2=meandistanceforthepopulation ofRap,Ltd.golfballs=295-278=17yardsIntervalEstimationof

1-

2:

1and

2KnownWeare95%confidentthatthedifferencebetweenthemeandrivingdistancesofPar,Inc.ballsandRap,Ltd.ballsis11.86to22.14yards.17+5.14or11.86yardsto22.14yardsHypothesisTestsAboutm1

-

m2:

s1ands2KnownHypothesesLeft-tailedRight-tailedTwo-tailedTestStatisticExample:Par,Inc.HypothesisTestsAboutm1

-

m2:

s1ands2KnownCanweconclude,usinga=.01,thatthemeandrivingdistanceofPar,Inc.golfballsisgreaterthanthemeandrivingdistanceofRap,Ltd.golfballs?H0:

1-

2

<0

Ha:

1-

2>0where:

1=meandistanceforthepopulationofPar,Inc.golfballs

2=meandistanceforthepopulationofRap,Ltd.golfballs1.Developthehypotheses.

p–ValueandCriticalValueApproachesHypothesisTestsAboutm1

-

m2:

s1ands2Known2.Specifythelevelofsignificance.a=.013.Computethevalueoftheteststatistic.HypothesisTestsAboutm1

-

m2:

s1ands2Known

p–ValueandCriticalValueApproaches

p–ValueApproach4.Computethep–value.Forz=6.49,thep–value<.0001.HypothesisTestsAboutm1

-

m2:

s1ands2Known5.DeterminewhethertorejectH0.Becausep–value<

a=.01,werejectH0.Atthe.01levelofsignificance,thesampleevidenceindicatesthemeandrivingdistanceofPar,Inc.golfballsisgreaterthanthemeandrivingdistanceofRap,Ltd.golfballs.HypothesisTestsAboutm1

-

m2:

s1ands2Known5.DeterminewhethertorejectH0.Becausez=6.49>2.33,werejectH0.CriticalValueApproachFora=.01,z.01=2.334.Determinethecriticalvalueandrejectionrule.RejectH0ifz

>2.33ThesampleevidenceindicatesthemeandrivingdistanceofPar,Inc.golfballsisgreaterthanthemeandrivingdistanceofRap,Ltd.golfballs.InferencesAbouttheDifferenceBetween

TwoPopulationMeans:s1ands2UnknownIntervalEstimationofm

1–m

2HypothesisTestsAboutm

1–m

2IntervalEstimationof

1-

2:

s1ands2Unknown Whens1ands2areunknown,wewill:replaceza/2withta/2.usethesamplestandarddeviationss1ands2 asestimatesofs1ands2,andWherethedegreesoffreedomforta/2are:IntervalEstimationof

1-

2:

s1ands2UnknownIntervalEstimateExample:SpecificMotors

DifferenceBetweenTwoPopulationMeans:s1ands2UnknownSpecificMotorsofDetroithasdevelopedanewautomobileknownastheMcar.24Mcarsand28Jcars(fromJapan)wereroadtestedtocomparemiles-per-gallon(mpg)performance.Thesamplestatisticsareshownonthenextslide.Letusdevelopa90%confidenceintervalestimateofthedifferencebetweenthempgperformancesofthetwomodelsofautomobile.DifferenceBetweenTwoPopulationMeans:s1ands2UnknownExample:SpecificMotorsSampleSizeSampleMeanSampleStd.Dev.Sample#1MCarsSample#2JCars24cars 28cars29.8mpg27.3mpg2.56mpg1.81mpgPointestimateof

1

-

2=PointEstimateofm1

-

m2where:

1=meanmiles-per-gallonforthe populationofMcars

2=meanmiles-per-gallonforthe populationofJcars=29.8-27.3=2.5mpgIntervalEstimationofm1

-

m2:

s1ands2UnknownThedegreesoffreedomforta/2are:Witha/2=.05anddf=24,ta/2=1.7109IntervalEstimationofm1

-

m2:

s1ands2UnknownWeare90%confidentthatthedifferencebetweenthemiles-per-gallonperformancesofMcarsandJcarsis1.431to3.569mpg.2.5+1.069or1.431to3.569mpgHypothesisTestsAboutm1

-

m2:

s1ands2UnknownHypothesesLeft-tailedRight-tailedTwo-tailedTestStatisticExample:SpecificMotors

HypothesisTestsAboutm1

-

m2:

s1ands2UnknownCanweconclude,usinga.05levelofsignificance,thatthemiles-per-gallon(mpg)performanceofMcarsisgreaterthanthemiles-per-gallonperformanceofJcars?H0:

1-

2

<0

Ha:

1-

2>0where:

1=meanmpgforthepopulationofMcars

2=meanmpgforthepopulationofJcars1.Developthehypotheses.

p–ValueandCriticalValueApproachesHypothesisTestsAboutm1

-

m2:

s1ands2Unknown2.Specifythelevelofsignificance.3.Computethevalueoftheteststatistic.a=.05

p–ValueandCriticalValueApproachesHypothesisTestsAboutm1

-

m2:

s1ands2UnknownHypothesisTestsAboutm1

-

m2:

s1ands2Unknown

p–ValueApproach4.Computethep–value.Thedegreesoffreedomfortaare:Becauset=4.003>t.05

=1.6839,thep–value<.005.5.DeterminewhethertorejectH0.Weareatleast95%confidentthatthemiles-per-gallon(mpg)performanceofMcarsisgreaterthanthemiles-per-gallonperformanceofJcars?.

p–ValueApproachBecausep–value<

a=.05,werejectH0.HypothesisTestsAboutm1

-

m2:

s1ands2Unknown4.Determinethecriticalvalueandrejectionrule.CriticalValueApproachHypothesisTestsAboutm1

-

m2:

s1ands2UnknownFora=.05anddf=40,t.05=1.6839RejectH0ift

>

1.68395.DeterminewhethertorejectH0.Because4.003>1.683,werejectH0.Weareatleast95%confidentthatthemiles-per-gallon(mpg)performanceofMcarsisgreaterthanthemiles-per-gallonperformanceofJcars?.Withamatched-sampledesigneachsampleditemprovidesapairofdatavalues.Thisdesignoftenleadstoasmallersamplingerrorthantheindependent-sampledesignbecausevariationbetweensampleditemsiseliminatedasasourceofsamplingerror.InferencesAbouttheDifferenceBetween

TwoPopulationMeans:MatchedSamplesExample:ExpressDeliveriesInferencesAbouttheDifferenceBetween

TwoPopulationMeans:MatchedSamplesAChicago-basedfirmhasdocumentsthatmustbequicklydistributedtodistrictofficesthroughouttheU.S.Thefirmmustdecidebetweentwodeliveryservices,UPX(UnitedParcelExpress)andINTEX(InternationalExpress),totransportitsdocuments.Example:ExpressDeliveriesInferencesAbouttheDifferenceBetween

TwoPopulationMeans:MatchedSamplesIntestingthedeliverytimesofthetwoservices,thefirmsenttworeportstoarandomsampleofitsdistrictofficeswithonereportcarriedbyUPXandtheotherreportcarriedbyINTEX.Dothedataonthenextslideindicateadifferenceinmeandeliverytimesforthetwoservices?Usea.05levelofsignificance.3230191615181410716252415151315158911UPXINTEXDifferenceDistrictOfficeSeattleLosAngelesBostonClevelandNewYorkHoustonAtlantaSt.LouisMilwaukeeDenverDeliveryTime(Hours)764123-12-25InferencesAbouttheDifferenceBetween

TwoPopulationMeans:MatchedSamplesH0:

d=0

Ha:

d

Let

d=themeanofthedifferencevaluesforthetwodeliveryservicesforthepopulationofdistrictoffices1.Developthehypotheses.InferencesAbouttheDifferenceBetween

TwoPopulatio