Group Samplesize Samplemean Samplestandarddeviation Beef 20 15685 2264 Poultry 17 12247 2548 Sowehavex1x215685122473438Thestandarddeviationsareapproximatelyequalsowecancalculatethepoole ID: 207029
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Example:(DatatakenfromMooreandMcCabe{IntroductiontothePracticeofStatistics)AU.S.magazine,ConsumerReports,carriedoutasurveyofthecalorieandsodiumcon-tentofanumberofdi erentbrandsofhotdog.Therewerethreetypesofhotdog:beef,'meat`(mainlyporkandbeefbutcancontainupto15%poultry)andpoultry.Theresultsbelowarethecaloriecontentofthedi erentbrandsofbeefandpoultryhotdogs.Beefhotdogs:186;181;176;149;184;190;158;139;175;148;152;111;141;153;190;157;131;149;135;132Poultryhotdogs:129;132;102;106;94;102;87;99;170;113;135;142;86;143;152;146;144Beforecarryingoutat-testyoushouldcheckwhetherthetwosamplesareroughlynor-mallydistributed.Thiscanbedonebylookingathistogramsofthedata.Inthiscasetherearenooutliersandthedatalookreasonablyclosetoanormaldistribution;thet-testisthereforeappropriate.So,rstweneedtocalculatethesamplemeanandstandarddeviationineachgroup: Group Samplesize Samplemean Samplestandarddeviation Beef 20 156.85 22.64 Poultry 17 122.47 25.48 So,wehavex1�x2=156:85�122:47=34:38Thestandarddeviationsareapproximatelyequal,sowecancalculatethepooledstandarddeviation:sp=s (n1�1)s21+(n2�1)s22 n1+n2�2=s (19)22:642+(16)25:482 35=23:98WecannowcalculateSE(x1�x2):sps 1 n1+1 n2=23:98s 1 20+1 17=7:91AndnowthevalueforT:t=x1�x2 SE(x1�x2)=34:38 7:91Ifwelookthisupintablesofthet-distributionwith35degreesoffreedom,wendp0:001.Therefore,thereisstrongevidencethatthecaloriecontentofpoultryhotdogsislowerthanthecaloriecontentofbeefhotdogs.2