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1、http://www.paper.edu.cnSamplesizedeterminedmethodusingfeaturesofCVofthesampledpopulationYefengWu*ZifangDuSouthChinaSeaInstituteofOceanologyofSchoolofStatisticsofRenminUniversityofChina,ChineseAcademyofSciences,Beijing,P.R.China,100872164WestXingangRoad,Guangzhou,duzifang@sohu.comP.
2、R.China,510301yefengwu@126.comAbstractInsamplingdesign,thenecessarysamplesizeoftenneedstobedeterminedbeforetheexecutionofthesurvey.Usingtheuplimitofcoefficientofvariation(CV)ofthesampledpopulationtocomputetheneededapproximatesamplesizeisoneofthemosteffectiveandconvenientmethods.Inf
3、act,tocommonpopulations,itdoesexistsomeuplimitsfortheirCVs.So,thispaperaimstofindtheseuplimitsofCVforthemtofacilitatethedeterminationoftheappropriatesamplesizeinadvance.Keywords:Coefficientofvariation;Samplesize;Samplesurveys;Statistics1IntroductionAtthephaseofsamplingdesigninsampl
4、esurveys,itisoftenrequiredtodecidetheappropriatesamplesizebeforetheexecutionofthesurvey.Takethesimplerandomsamplingwithoutreplacementforinstance,n1weusuallyusethesamplemean(x=∑xi)toinferthepopulationmean(notatedasX),andusetheni=1Nn−2varianceofxtoevaluatetheeffectofthatinference,whi
5、chappearsasVar()x=S(here,NandnN2Sdenotethesizeandvarianceofthepopulationrespectively,andndenotesthesamplesize).Thedeterminationoftheappropriatesamplesizedependsonthespecifictypeofaccuracyrequirementsandthevariationofthetargetpopulation,a)Astheaccuracyrequirementofthatinferenceisexp
6、ressedastheuplimitofvarianceofx,whichisNn−2Nn−2notatedasV,namely,Var()x=S≤V,wecanuseS＝VtocomputethemaximumnNnN2SV2/Snsamplesizeneededandget.Letn=,then0Nn=0n=.Andwhenis2V1/+SNV1+n/N0largeenough,itexistsn≈n;0b)Astheaccuracyrequirementisexpressedastheuplimitofabsoluteerror(notatedasd)
7、ofx,thatis22⎛⎞d⎛⎞dtosayVar()x≤⎜⎟.Accordingtotheconclusionsincasea),wecanletV＝⎜⎟andgetuu⎝⎠α⎝⎠α1http://www.paper.edu.cn2⎛uS⎞⎜α⎟n=.0⎜d⎟⎝⎠c)Whentheaccuracyrequirementisexpressedastheuplimitofrelativeerror(notatedasr)ofx,it22⎛⎞rX⎛uαS⎞Sexistsd=rX.Similarly,wecanletV＝⎜⎟andgetn0=⎜⎟.Asisthe
8、coefficient⎝⎠uα⎝rX⎠Xofvari
