统计学课件-ch03-总体均数的估计与假设检验

统计学课件-ch03-总体均数的估计与假设检验统计学课件-ch03isanengagingandinformativepresentationthatcoverstheestimationandhypothesistestingofpopulationmeans.总体均数的定义PopulationMeanTheaverageofallvaluesinapopulation.ImportanceUnderstandingthepopulationmeanhelpsusmakeinferencesabouttheentirepopulation.SymbolThepopulationmeanisrepresentedbytheGreekletterμ.总体均数的点估计PointEstimationUsingsampledatatoestimatethepopulationmean.SampleMeanTheaverageofasamplefromthepopulation.MethodsVariousmethodslikethemethodofmomentsandmaximumlikelihoodestimationcanbeused.总体均数的区间估计1ConfidenceIntervalArangeofvalueswithinwhichthepopulationmeanislikelytofall.2MarginofErrorAmeasureoftheuncertaintyassociatedwiththeestimate.3LevelofConfidenceTheprobabilitythattheintervalcontainsthetruepopulationmean.总体均数的假设检验1HypothesisTestingAstatisticalproceduretotestaclaimaboutthepopulationmean.2NullHypothesisAssumesthatthereisnosignificantdifferencebetweenthesamplemeanandthepopulationmean.3AlternativeHypothesisStatesthatthereisasignificantdifferencebetweenthesamplemeanandthepopulationmean.小样本均数的T分布检验T-DistributionUsedwhenthesamplesizeissmallorwhenthepopulationstandarddeviationisunknown.CriticalValuesComparestheteststatisticwiththecriticalvalue/stodetermineifthenullhypothesisisrejected.P-ValueTheprobabilityofobtainingateststatisticasextremeastheobserved,assumingthenullhypothesisistrue.大样本均数的Z分布检验Z-DistributionUsedwhenthesamplesizeislargeandthepopulationstandarddeviationisknown.StandardizedTestStatisticTheteststatisticiscalculatedbysubtractingthehypothesizedmeanfromthesamplemeananddividingbythestandarddeviation.LevelofSignificanceTheprobabilityofrejectingthenullhypothesiswhenitisactuallytrue.Commonvaluesare0.05and0.01.均数差的假设检验IndependentSamplesUsedtocomparetwomeansfromdifferentpopulations,suchasexperimentalandcontrolgroups.PairedSamplesUsedtocomparetwomeansfromthesamepopulationbeforeandafteratreatmen