Statistical Methods Second Edition This Page Intentionally Left Blank Statistical Methods Second Edition Rudolf J. Freund TexasA&MUniversity William J. Wilson UniversityofNorthFlorida Amsterdam Boston London NewYork Oxford Paris SanDiego SanFrancisco Singapore Sydney Tokyo SeniorEditor,Mathematics BarbaraHolland SeniorProjectManager AngelaDooley EditorialCoordinator TomSinger ProductManager AnneO’Mara CoverDesign DickHannus Copyeditor CharlesLauder Composition ITC Printer EdwardsBros. Thisbookisprintedonacid-freepaper.(cid:2)∞ Copyright2003,1996,1993,ElsevierScience(USA) Allrightsreserved. Nopartofthispublicationmaybereproducedortransmittedinanyformorbyany means,electronicormechanical,includingphotocopy,recording,oranyinformation storageandretrievalsystem,withoutpermissioninwritingfromthepublisher. Requestsforpermissiontomakecopiesofanypartoftheworkshouldbemailedto: PermissionsDepartment,Harcourt,Inc.,6277SeaHarborDrive,Orlando, Florida32887-6777. AcademicPress AnimprintofElsevierScience 525BStreet,Suite1900,SanDiego,California92101-4495,USA http://www.academicpress.com AcademicPress AnimprintofElsevierScience 84Theobald’sRoad,LondonWC1X8RR,UK http://www.academicpressbooks.com AcademicPress AnimprintofElsevierScience 200WheelerRoad,Burlington,Massachusetts01803,USA http://www.academicpressbooks.com LibraryofCongressControlNumber:2002111023 InternationalStandardBookNumber:0-12-267651-3 PRINTEDINTHEUNITEDSTATESOFAMERICA 02 03 04 05 06 9 8 7 6 5 4 3 2 1 Contents Preface xvii 1 DATAANDSTATISTICS 1 1.1 Introduction 1 DataSources 4 UsingtheComputer 5 1.2 ObservationsandVariables 6 1.3 TypesofMeasurementsforVariables 10 1.4 Distributions 12 GraphicalRepresentationofDistributions 14 1.5 NumericalDescriptiveStatistics 19 Location 20 Dispersion 23 OtherMeasures 28 ComputingtheMeanandStandardDeviation fromaFrequencyDistribution 30 ChangeofScale 30 1.6 ExploratoryDataAnalysis 32 TheStemandLeafPlot 32 TheBoxPlot 35 Comments 36 v vi Contents 1.7 BivariateData 38 CategoricalVariables 39 CategoricalandIntervalVariables 40 IntervalVariables 42 1.8 Populations,Samples,andStatisticalInference— APreview 42 1.9 ChapterSummary 44 Summary 48 1.10 ChapterExercises 49 ConceptQuestions 49 PracticeExercises 51 Exercises 52 2 PROBABILITYANDSAMPLINGDISTRIBUTIONS 62 2.1 Introduction 63 ChapterPreview 65 2.2 Probability 66 DefinitionsandConcepts 66 SystemReliability 70 RandomVariables 71 2.3 DiscreteProbabilityDistributions 73 PropertiesofDiscreteProbabilityDistributions 74 DescriptiveMeasuresforProbabilityDistributions 74 TheDiscreteUniformDistribution 76 TheBinomialDistribution 77 ThePoissonDistribution 79 2.4 ContinuousProbabilityDistributions 81 CharacteristicsofaContinuousProbabilityDistribution 81 TheContinuousUniformDistribution 82 TheNormalDistribution 83 CalculatingProbabilitiesUsingtheTable oftheNormalDistribution 86 2.5 SamplingDistributions 91 SamplingDistributionoftheMean 92 UsefulnessoftheSamplingDistribution 96 SamplingDistributionofaProportion 99 Contents vii 2.6 OtherSamplingDistributions 101 Theχ2 Distribution 102 DistributionoftheSampleVariance 103 Thet Distribution 104 Usingthet Distribution 105 The F Distribution 106 Usingofthe F Distribution 106 RelationshipsamongtheDistributions 108 2.7 ChapterSummary 108 2.8 ChapterExercises 109 ConceptQuestions 109 PracticeExercises 109 Exercises 110 3 PRINCIPLESOFINFERENCE 117 3.1 Introduction 117 3.2 HypothesisTesting 118 GeneralConsiderations 119 TheHypotheses 120 RulesforMakingDecisions 121 PossibleErrorsinHypothesisTesting 122 ProbabilitiesofMakingErrors 123 Choosingbetweenα andβ 125 Five-StepProcedureforHypothesisTesting 125 WhyDoWeFocusontheTypeIError? 126 Choosingα 127 TheFiveStepsforExample3.3 131 P Values 132 TypeIIErrorandPower 134 Power 136 UniformlyMostPowerfulTests 137 One-TailedHypothesisTests 138 3.3 Estimation 139 InterpretingtheConfidenceCoefficient 141 RelationshipbetweenHypothesisTesting andConfidenceIntervals 143 viii Contents 3.4 SampleSize 144 3.5 Assumptions 147 StatisticalSignificanceversusPracticalSignificance 148 3.6 ChapterSummary 150 3.7 ChapterExercises 152 ConceptQuestions 152 PracticeExercises 153 MultipleChoiceQuestions 154 Exercises 155 4 INFERENCESONASINGLEPOPULATION 159 4.1 Introduction 159 4.2 InferencesonthePopulationMean 161 HypothesisTestonμ 161 Estimationofμ 164 SampleSize 165 DegreesofFreedom 166 4.3 InferencesonaProportion 166 HypothesisTeston p 167 Estimationof p 168 SampleSize 169 4.4 InferencesontheVarianceofOnePopulation 169 HypothesisTestonσ2 170 Estimationofσ2 171 4.5 Assumptions 172 RequiredAssumptionsandSourcesofViolations 173 PreventionofViolations 173 DetectionofViolations 173 TestsforNormality 175 IfAssumptionsFail 176 AlternateMethodology 177 4.6 ChapterSummary 179 4.7 ChapterExercises 180 ConceptQuestions 180 PracticeExercises 180 Exercises 181 Contents ix 5 INFERENCESFORTWOPOPULATIONS 185 5.1 Introduction 185 5.2 InferencesontheDifferencebetweenMeans UsingIndependentSamples 188 SamplingDistributionofaLinearFunction ofRandomVariables 188 TheSamplingDistributionoftheDifference betweenTwoMeans 188 VariancesKnown 189 VariancesUnknownbutAssumedEqual 191 ThePooledVarianceEstimate 191 The“Pooled”t Test 192 VariancesUnknownbutNotEqual 194 5.3 InferencesonVariances 197 5.4 InferencesonMeansforDependentSamples 200 5.5 InferencesonProportions 205 ComparingProportionsUsingIndependentSamples 205 ComparingProportionsUsingPairedSamples 207 5.6 AssumptionsandRemedialMethods 208 5.7 ChapterSummary 211 5.8 ChapterExercises 213 ConceptQuestions 213 PracticeExercises 214 Exercises 215 6 INFERENCESFORTWOORMOREMEANS 219 6.1 Introduction 219 UsingtheComputer 220 6.2 TheAnalysisofVariance 221 NotationandDefinitions 222 HeuristicJustificationfortheAnalysisofVariance 225 ComputationalFormulasandthePartitioning ofSumsofSquares 228 TheSumofSquaresamongMeans 228 TheSumofSquareswithinGroups 229 TheRatioofVariances 229 PartitioningoftheSumsofSquares 229