a confidence-interval estimate of a parameter consists of an interval 一个参数的置信区间估计的区间

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1、Chapter6--ConfidenceIntervals6.1ConfidenceIntervalfortheMeanParameter:Anumericalmeasurementdescribingsomecharacteristicofapopulation.Statistic:Anumericalmeasurementdescribingsomecharacteristicofasample.Acommonprobleminstatisticsistoobtaininformationaboutthepopulationmean,m,ofapopulation

2、.Ifthepopulationissmall,wecandeterminemfromthepopulationdata.Butifthepopulationislarge,asitoftenisinpractice,collectingdataabouttheentirepopulationisextremelyexpensiveandtimeconsuming.Insuchcases,weobtainanestimateofmbyfindingbytakingasamplefromthepopulation.SamplingError:Whenasamplemea

3、n()isusedtoestimatethepopulationmean(m),anaturalquestiontoaskis:howgoodistheestimate?WedefinethesamplingerrorasSamplingError=

4、-m

5、Notethesamplingerrorcannotbecomputedasmisunknown.However,wecanusethedistributionoftomakeprobabilitystatementsaboutthesamplingerror.PointEstimate:Apointestimat

6、eofaparameteristhevalueofastatisticthatisusedtoestimatetheparameter.Example1:Example1onpage270(SeeNotes)Aconfidence-intervalestimateofaparameterconsistsofanintervalofnumbersobtainedfromapointestimateoftheparametertogetherwithaprobabilitythatspecifieshowconfidentwearethattheparameterlies

7、intheinterval.Theconfidenceprobabilityiscalledtheconfidencelevel.Notethat~N(m,s/)providednisatleast30orXisnormallydistributed.ProbabilityStatementabouttheSamplingError:Thereis1-aprobabilitythatthevalueofasamplemeanwillprovideasamplingerrorofZ(s)orless.IntervalEstimationofaPopulationmean

8、Wehavetheabilitytomakeprobabilitystatementsaboutthesamplingerror.Wecannowcombinethepointestimatewiththeprobabilityinformationaboutthesamplingerrortoobtainanintervalestimateofthepopulationmean.Wewillassumethatnisatleast30orXisnormallydistributed.ConfidenceInterval:Aconfidenceintervalfore

9、stimatingmis[-Z(s/)+Z(s/)]where1-isthecalledtheconfidencecoefficientandZisthez-valueprovidinganareaofintheuppertailofthestandardnormalprobabilitydistribution.Inshort,wedenoteaconfidenceinterval(CI)as±Z(s/)3-SpecialConfidenceIntervals:90%CI:+1.65(s/)95%CI:+1.96(s/)99%CI:+2.58(s/