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1、Chapter8.StatisticalIntervalsforaSingleSampleWewillcoverChapter8uptopage258.Themainideahereisthereportingofparameterestimates'likely*uncertainties*,alongwiththeirvalues.Uncertaintiesarerepresentedas"confidenceintervals",asin"95%confidenceinterval".Knowthethreetypesofintervalsonpg.253.A95%co
2、nfidenceintervalmeansthatifsamplingwasrepeatedmanytimes,95%ofallsampleswouldproduceavalueandassociated95%confidenceintervalthatcontainedthetruepopulationvalue.A99%confidenceintervalwouldbewider,anda90%CIwouldbenarrower.Inmanycases,estimatinganX%confidenceintervalcorrespondstoidentifyingthev
3、alueswhichmarktheupperandlowerlimitsofasymmetricareaofX%inthecenterofthenormaldistribution.CI'sareoftendefinedintermsofalpha,wherealphaisdefinedbythefactthattheconfidenceis100%*(1-alpha).NotethatoftentherearetwowaystobeoutsidetheCI(a"two-sidedconfidenceinterval"),sofora95%confidenceinterval
4、alphais0.05,andthealpha/2usedbelowinthecalculationofthewidthoftheCIis0.025.Onpg256,thereisadiscussionofthetradoffbetweenhighconfidence,andnarrowCI's(seeEq8-6).Thesecalculationsaredoneafterstandardizingthedistribution(asinmanyotherplaces).Thewidthsoftheconfidenceintervalsextendawayfromthemea
5、nbyadistanceZ-sub-alpha-over-two,timessigmaoverrootn.HereZ-sub-alpha-over-twoistheZvalueoftheupper100alpha-over-twoofthestandardnormaldistribution(seeEqns8-4and8-5).ThestuffonPg254isthekeyhere.Alsolookhardatsection8-1.2,andExamples8-2and8-3.Chapter9.TestsofHypothesesforaSingleSampleTopage29
6、7.Chapters9and10,onhypothesistestingforsinglesamples,andstatisticalinferencefortwosamples,aretheessenceofwhatmanypeoplethinkofas"Statistics".Theyalsoaretheconceptuallyhardestpartsofthiswholeclass,formanypeople,inpartbecauseoftheseveralvocabularytermsintroduced,andthestiffformalismoftheNullH
7、ypothesis.ThemaingoalofthemethodsinChapter9istoallowyoutodecidewhetherquantitativeclaimsaretrue.KnowTypeIandTypeIIerrors,andalphaandbeta.Thepropellantexampleonpp.287-288isthecoreofthematerialhere.Besureyouunderstandallthestepsoftheprocedurein9-1.6.Chapte