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1、TestsofGoodnessofFitandIndependenceChapter12TestsofGoodnessofFitandIndependenceLearningObjectives1.Knowhowtoconductagoodnessoffittest.2.Knowhowtousesampledatatotestforindependenceoftwovariables.3.Understandtheroleofthechi-squaredistributioninconductingtestsofgood
2、nessoffitandindependence.4.Beabletoconductagoodnessoffittestforcaseswherethepopulationishypothesizedtohaveeitheramultinomial,aPoisson,oranormalprobabilitydistribution.5.Foratestofindependence,beabletosetupacontingencytable,determinetheobservedandexpectedfrequenci
3、es,anddetermineifthetwovariablesareindependent.12-17TestsofGoodnessofFitandIndependenceSolutions:1.Expectedfrequencies:e1=200(.40)=80,e2=200(.40)=80e3=200(.20)=40Actualfrequencies:f1=60,f2=120,f3=20=9.21034withk-1=3-1=2degreesoffreedomSince=35>9.21034rejectthenul
4、lhypothesis.Thepopulationproportionsarenotasstatedinthenullhypothesis.2.Expectedfrequencies:e1=300(.25)=75,e2=300(.25)=75e3=300(.25)=75,e4=300(.25)=75Actualfrequencies:f1=85,f2=95,f3=50,f4=70=7.81473withk-1=4-1=3degreesoffreedomSincec2=15.33>7.81473rejectH0Weconc
5、ludethattheproportionsarenotallequal.3.H0=pABC=.29,pCBS=.28,pNBC=.25,pIND=.18Ha=TheproportionsarenotpABC=.29,pCBS=.28,pNBC=.25,pIND=.1812-17TestsofGoodnessofFitandIndependenceExpectedfrequencies:300(.29)=87,300(.28)=84300(.25)=75,300(.18)=54e1=87,e2=84,e3=75,e4=5
6、4Actualfrequencies:f1=95,f2=70,f3=89,f4=46=7.81(3degreesoffreedom)DonotrejectH0;thereisnosignificantchangeintheviewingaudienceproportions.4.ObservedExpectedHypothesizedFrequencyFrequencyCategoryProportion(fi)(ei)(fi-ei)2/eiBrown0.30177151.84.18Yellow0.20135101.21
7、1.29Red0.2079101.24.87Orange0.104150.61.82Green0.103650.64.21Blue0.103850.63.14Totals:50629.51=11.07(5degreesoffreedom)Since29.51>11.07,weconcludethatthepercentagefiguresreportedbythecompanyhavechanged.5.ObservedExpectedHypothesizedFrequencyFrequencyCategoryPropo
8、rtion(fi)(ei)(fi-ei)2/eiFullService1/3264249.330.86Discount1/3255249.330.13Both1/3229249.331.66Totals:7482.65=4.61(2degreesoffreedom)Since2.65<4.61,thereisnosi
