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1、8.TestingHypothesesOften,theproblemconfrontingscientistsorengineersisnotsomuchtheestimationofapopulationparameterasdiscussedinChapter7,butrathertheformationofdata-baseddecisionprocedurethatcanproduceaconclusionaboutsomescientificsystem.Weshallnowconsideroneofthemostimport
2、antproblemsthatoftestingstatisticalhypotheses.8.1StatisticalHypotheses:GeneralconceptsFirst,letusdefinewhatwemeanbyastatisticalhypothesis.Definition8.1.1Astatisticalhypothesisisanassertionorconjectureconcerningoneormorepopulation.一个统计假设是关于总体某些参数所作的假设。Forexample,supposewew
3、ishtotestthe“honesty”ofacoin.Thisisastatisticalhypothesis,sincetheassumptionof“honesty”isequivalenttotheassumptionthatforthepopulationofaverylargenumberoftossesofthiscoin,theprobabilityofobtainingheadsis.Thetruthorfalsityofastatisticalhypothesisisneverknownwithabsolutecer
4、tainlyunlessweexaminetheentirepopulation.This,ofcourse,wouldbeimpracticalinmostsituations.Instead,weareforcetotakeasamplefromthepopulationandusethedatacontainedinthissampleindecidingwhetherthehypothesisistrueorfalse.Inaboveexample,supposenowintossingthecoin100timesweobtai
5、n60heads,andfromthisinformationweareforcedtoreachadecisionregardingthehonestyofthecoin.Definition8.1.2Astatisticalprocedureordecisionrulethatleadstoestablishingthetruthorfalsityofahypothesisiscalledastatisticaltest.统计检验是统计推测假设是否正确nullhypothesis.零假设alternativehypothesis备择假
6、设Anullhypothesisconcerningapopulationparameterwillalwaysbestatedsoastospecifyanexactvalueoftheparameter,thealternativehypothesisallowsforthepossibilityofseveralvalues.一般做法：Assumingthatthenullhypothesisistrue,Usesthesampledatatodecide:whethertheevidencefavorsratherthanandd
7、rawsoneofthesetwoconclusions:(1)Rejectandaccept(2)AcceptastrueExample8.1.1Youwishtoshowthattheaveragehourlywageofconstructionworkersinthesampleofonecityisdifferentfrom$14,whichisthenationalaverage,thenullhypothesisis:andthealternativehypothesisis:(two-tailedtest)Youwouldl
8、iketorejectthenullhypothesis,thusconcludingthatthecitymeanisnotequalto$14.Example8.1.2Amillingpr
