Homework11Dueon2018-6-11.(TextbookSection8.3-1,Page322)SupposethatacertaindrugAwasadministeredtoeightpatientsselectedatrandom,andafterafixedtimeperiod,theconcentrationofthedrugincertainbodycellsofeachpatientwasmeasuredinappropriateunits.Supposethattheseconcentrationsfortheeightpatientswerefoundtobeasfollows:1.23,1.42,1.41,1.62,1.55,1.51,1.60,and1.76.SupposealsothataseconddrugBwasadministeredtosixdifferentpatientsselectedatrandom,andwhentheconcentrationofdrugBwasmeasuredinasimilarwayforthesesixpatients,theresultswereasfollows:1.76,1.41,1.87,1.49,1.67,and1.81.Assumingthatalltheobservationshaveanormaldistributionwithacommonunknownvariance,testthefollowinghypothesesatthelevelofsignificance0.10:Thenullhy-pothesesisthatthemeanconcentrationofdrugAamongallpatientsisatleastaslargeasthemeanconcentrationofdrugB.ThealternativehypothesesisthatthemeanconcentrationofdrugBislargerthanthatofdrugA.2.(TextbookSection8.4-7Page331)Considertwodifferentnormaldistributionsforwhichboththemeansµ1andµ2andthevariancesσ21andσ22areunknown,andsupposethatitisdesiredtotestthefollowinghypotheses:H0:σ21≤σ22,H1:σ21>σ22.Supposefurtherthatarandomsampleconsistingof16observationsforthefirstnormaldistributionyieldsthevalues�16i=1Xi=84and�16i=1X2i=563,andanindependentrandomsampleconsistingof10observationsfromthesecondnormaldistributionyieldsthevalue�10i=1Yi=18and�10i=1Y2i=72.(a)WhataretheM.L.E.’sofσ21andσ22?(b)IfanFtestiscarriedoutatthelevelofsignificance0.05,isthehypothesisH0acceptedorrejected?13.TextbookSection10.1-7(a),Page363–Supposethateightspecimensofacertaintypeofalloywereproducedatdifferenttem-peratures,andthedurabilityofeachspecimenwasthenobserved.Theobservedvaluesaregivenintable10.3,wherexidenotesthetemperature(incodedunits)atwhichspec-imeniwasproducedandyidenotesthedurability(incodedunits)ofthatspecimen.ixiyi10.54021.04131.54342.04252.54463.04273.54384.042Fitastraightlineofformy=β0+β1xtothosevaluesbythemethodofleastsquares.2
