英文商务统计学ppt-第10章Ch10

BusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap10-1Chapter10Two-SampleTests&One-WayANOVABusinessStatistics:AFirstCourseFifthEditionBusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap10-2LearningObjectivesInthischapter,youlearn:HowtousehypothesistestingforcomparingthedifferencebetweenThemeansoftwoindependentpopulationsThemeansoftworelatedpopulationsTheproportionsoftwoindependentpopulationsThevariancesoftwoindependentpopulationsHowtouseone-wayanalysisofvariance(ANOVA)totestfordifferencesamongthemeansofseveralpopulationsHowtoperformmultiplecomparisonsinaone-wayanalysisofvariance.BusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap10-3Two-SampleTestsTwo-SampleTestsPopulationMeans,IndependentSamplesPopulationMeans,RelatedSamplesPopulationVariancesMean1vs.Mean2Samegroupbeforevs.aftertreatmentVariance1vs.Variance2Examples:PopulationProportionsProportion1vs.Proportion2BusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap10-4DifferenceBetweenTwoMeansPopulationmeans,independentsamplesGoal:Testhypothesisorformaconfidenceintervalforthedifferencebetweentwopopulationmeans,μ1–μ2ThepointestimateforthedifferenceisX1–X2*σ1andσ2unknown,assumedequalσ1andσ2unknown,notassumedequalBusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap10-5DifferenceBetweenTwoMeans:IndependentSamplesPopulationmeans,independentsamples*UseSptoestimateunknownσ.UseaPooled-Variancettest.σ1andσ2unknown,assumedequalσ1andσ2unknown,notassumedequalUseS1andS2toestimateunknownσ1andσ2.UseaSeparate-variancettestDifferentdatasourcesUnrelatedIndependentSampleselectedfromonepopulationhasnoeffectonthesampleselectedfromtheotherpopulationBusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap10-6HypothesisTestsforTwoPopulationMeansLower-tailtest:H0:μ1μ2H1:μ1μ2i.e.,H0:μ1–μ20H1:μ1–μ20Upper-tailtest:H0:μ1≤μ2H1:μ1μ2i.e.,H0:μ1–μ2≤0H1:μ1–μ20Two-tailtest:H0:μ1=μ2H1:μ1≠μ2i.e.,H0:μ1–μ2=0H1:μ1–μ2≠0TwoPopulationMeans,IndependentSamplesBusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap10-7TwoPopulationMeans,IndependentSamplesLower-tailtest:H0:μ1–μ20H1:μ1–μ20Upper-tailtest:H0:μ1–μ2≤0H1:μ1–μ20Two-tailtest:H0:μ1–μ2=0H1:μ1–μ2≠0aa/2a/2a-ta-ta/2tata/2RejectH0iftSTAT-taRejectH0iftSTATtaRejectH0iftSTAT-ta/2ortSTATta/2Hypothesistestsforμ1–μ2BusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap10-8Populationmeans,independentsamplesHypothesistestsforµ1-µ2withσ1andσ2unknownandassumedequalAssumptions:SamplesarerandomlyandindependentlydrawnPopulationsarenormallydistributedorbothsamplesizesareatleast30Populationvariancesareunknownbutassumedequal*σ1andσ2unknown,assumedequalσ1andσ2unknown,notassumedequalBusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap10-9Populationmeans,independentsamples•Thepooledvarianceis:•Theteststatisticis:•WheretSTAThasd.f.=(n1+n2–2)(continued)1)n(nS1nS1nS212222112p()1*σ1andσ2unknown,assumedequalσ1andσ2unknown,notassumedequalHypothesistestsforµ1-µ2withσ1andσ2unknownandassumedequal212p2121STATn1n1SμμXXtBusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap10-10Populationmeans,independentsamples212p/221n1n1SXXαtTheconfidenceintervalforμ1–μ2is:Wheretα/2hasd.f.=n1+n2–2*Confidenceintervalforµ1-µ2withσ1andσ2unknownandassumedequalσ1andσ2unknown,assumedequalσ1andσ2unknown,notassumedequalBusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap10-11Pooled-VariancetTestExampleYouareafinancialanalystforabrokeragefirm.IsthereadifferenceindividendyieldbetweenstockslistedontheNYSE&NASDAQ?Youcollectthefollowingdata:NYSENASDAQNumber2125Samplemean3.272.53Samplestddev1.301.16Assumingbothpopulationsareapproximatelynormalwithequalvariances,isthereadifferenceinmeanyield(a=0.05)?BusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap10-12Pooled-VariancetTestExample:CalculatingtheTestStatistic1.50211)25(1)-(211.161251.301211)n()1(nS1nS1nS22212222112p2.0402512115021.102.533.27n1n1SμμXXt212p2121Theteststatisticis:(continued)H0:μ1-μ2=0i.e.(μ1=μ2)H1:μ1-μ2≠0i.e.(μ1≠μ2)BusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap10-13Pooled-VariancetTestExample:HypothesisTestSolutionH0:μ1-μ2=0i.e.(μ1=μ2)H1:μ1-μ2≠0i.e.(μ1≠μ2)a=0.05df=21+25-2=44CriticalValues:t=±2.0154TestStatistic:Decision:Conclusion:RejectH0ata=0.05Thereisevidenceofadifferenceinmeans.t02.0154-2.0154.025RejectH0RejectH0.0252.0402.0402512115021.12.533.27tBusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap10-14Pooled-VariancetTestExample:ConfidenceIntervalforµ1-µ2SincewerejectedH0canwebe95%confidentthatµNYSEµNASDAQ?95%ConfidenceIntervalforµNYSE-µNASDAQSince0islessthantheentireinterval,wecanbe95%confidentthatµNYSEµNASDAQ)471.1,09.0(3628.00154.274.0n1n1StXX212p/221aBusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap10-15Populationmeans,independentsamplesHypothesistestsforµ1-µ2withσ1andσ2unknown,notassumedequalAssumptions:SamplesarerandomlyandindependentlydrawnPopulationsa