假设检验与统计推断

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1、5-1Chapter5:HypothesisTestingandStatisticalInference一、假设检验的概念与思想什么是假设(hypothesis)?对总体参数的的数值所作的一种陈述总体参数包括总体均值、比例、方差等分析之前必需陈述其动机主要是企图利用人们掌握的反映现实的数据来找出假设与现实之间的矛盾，从而否定这个假设我认为该地区新生婴儿的平均体重为3190克!什么是假设检验(hypothesistesting)?事先对总体参数或分布形式作出某种假设，然后利用样本信息来判断原假设是

2、否成立有参数假设检验和非参数假设检验采用逻辑上的反证法，依据统计上的小概率原理假设检验的基本思想...因此我们拒绝假设=50...如果这是总体的真实均值样本均值m=50抽样分布H0这个值不像我们应该得到的样本均值...20总体假设检验的过程抽取随机样本均值X=20我认为人口的平均年龄是50岁提出假设拒绝假设!别无选择.作出决策5-7HypothesisTestingHypothesistestinginvolvesdrawinginferencesabouttwocont

3、rastingpropositions(hypotheses)relatingtothevalueofapopulationparameter,oneofwhichisassumedtobetrueintheabsenceofcontradictorydata.Weseekevidencetodetermineifthehypothesiscanberejected;ifnot,wecanonlyassumeittobetruebuthavenotstatisticallyprovenittrue

4、.5-8HypothesisTestingProcedureFormulatethehypothesisSelectalevelofsignificance,whichdefinestheriskofdrawinganincorrectconclusionthatatruehypothesisisfalseDetermineadecisionruleCollectdataandcalculateateststatisticApplythedecisionruleanddrawaconclusion

5、5-91.HypothesisFormulationNullhypothesis,H0–astatementthatisacceptedascorrectAlternativehypothesis,H1–apropositionthatmustbetrueifH0isfalseTestsinvolvingasinglepopulationparameterarecalledone-sampletests;testsinvolvingtwopopulationsarecalledtwo-sample

6、tests.5-10TypesofHypothesisTestsOneSampleTestsH0:populationparameterconstantvs.H1:populationparameterconstantH0:populationparameter=constantvs.H1:populationparameterconstantTwoSampleT

7、estsH0:populationparameter(1)-populationparameter(2)0vs.H1:populationparameter(1)-populationparameter(2)<0H0:populationparameter(1)-populationparameter(2)0vs.H1:populationparameter(1)-populationparameter(2)>0H0:populationparameter(1)-populationparam

8、eter(2)=0vs.H1:populationparameter(1)-populationparameter(2)05-11FormulatingHypothesesFormulatingthecorrectsetofhypothesesdependson“burdenofproof”–whatyouwishtoprovestatisticallyshouldbeH1Example:Toseekevidencethattechnicalsupportcallsaverage