CollaborativeStatistics
By:
BarbaraIllowsky,Ph.D.
SusanDean
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CollaborativeStatistics
By:
BarbaraIllowsky,Ph.D.
SusanDean
Online:
<http://cnx.org/content/col10522/1.40/>
CONNEXIONS
RiceUniversity,Houston,Texas
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ThisselectionandarrangementofcontentasacollectioniscopyrightedbyMaxfieldFoundation.Itislicensedunder
theCreativeCommonsAttributionLicense3.0(http://creativecommons.org/licenses/by/3.0/).
Collectionstructurerevised:July3,2012
PDFgenerated:October10,2013
Forcopyrightandattributioninformationforthemodulescontainedinthiscollection,seep.685.
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Preface ................................................................................................1
AdditionalResources .................................................................................5
AuthorAcknowledgements ..........................................................................9
StudentWelcomeLetter ..............................................................................11
1 SamplingandData
1.1 SamplingandData..........................................................................13
1.2 Statistics ....................................................................................13
1.3 Probability..................................................................................16
1.4 KeyTerms ..................................................................................16
1.5 Data ........................................................................................18
1.6 Sampling ...................................................................................24
1.7 Variation....................................................................................31
1.8 AnswersandRoundingOff .................................................................33
1.9 Frequency ..................................................................................33
1.10 Summary..................................................................................38
1.11 Practice:SamplingandData ...............................................................39
1.12 Homework ................................................................................42
1.13 Lab1:DataCollection......................................................................50
1.14 Lab2:SamplingExperiment ...............................................................52
Solutions ........................................................................................55
2 DescriptiveStatistics
2.1 DescriptiveStatistics ........................................................................59
2.2 DisplayingData.............................................................................59
2.3 StemandLeafGraphs(Stemplots),LineGraphsandBarGraphs.............................60
2.4 Histograms .................................................................................63
2.5 BoxPlots....................................................................................68
2.6 MeasuresoftheLocationoftheData ........................................................71
2.7 MeasuresoftheCenteroftheData ..........................................................76
2.8 SkewnessandtheMean,Median,andMode.................................................79
2.9 MeasuresoftheSpreadoftheData ..........................................................81
2.10 SummaryofFormulas .....................................................................89
2.11 Practice1:CenteroftheData...............................................................90
2.12 Practice2:SpreadoftheData ..............................................................93
2.13 Homework ................................................................................95
2.14 Lab:DescriptiveStatistics .................................................................112
Solutions .......................................................................................114
3 ProbabilityTopics
3.1 ProbabilityTopics..........................................................................121
3.2 Terminology ...............................................................................122
3.3 IndependentandMutuallyExclusiveEvents ...............................................124
3.4 TwoBasicRulesofProbability..............................................................127
3.5 ContingencyTables ........................................................................131
3.6 VennDiagrams(optional) ..................................................................134
3.7 TreeDiagrams(optional)...................................................................135
3.8 SummaryofFormulas .....................................................................140
3.9 Practice1:ContingencyTables .............................................................141
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3.10 Practice2:CalculatingProbabilities .......................................................143
3.11 Homework ...............................................................................144
3.12 Review ...................................................................................155
3.13 Lab:ProbabilityTopics....................................................................157
Solutions .......................................................................................160
4 DiscreteRandomVariables
4.1 DiscreteRandomVariables.................................................................167
4.2 ProbabilityDistributionFunction(PDF)foraDiscreteRandomVariable ....................168
4.3 MeanorExpectedValueandStandardDeviation...........................................169
4.4 CommonDiscreteProbabilityDistributionFunctions.......................................172
4.5 Binomial ...................................................................................172
4.6 Geometric(optional).......................................................................175
4.7 Hypergeometric(optional).................................................................178
4.8 Poisson ....................................................................................180
4.9 SummaryofFunctions .....................................................................183
4.10 Practice1:DiscreteDistribution ...........................................................185
4.11 Practice2:BinomialDistribution ..........................................................186
4.12 Practice3:PoissonDistribution ...........................................................188
4.13 Practice4:GeometricDistribution.........................................................189
4.14 Practice5:HypergeometricDistribution...................................................191
4.15 Homework ...............................................................................192
4.16 Review ...................................................................................202
4.17 Lab1:DiscreteDistribution(PlayingCardExperiment) ...................................205
4.18 Lab2:DiscreteDistribution(LuckyDiceExperiment) .....................................209
Solutions .......................................................................................213
5 ContinuousRandomVariables
5.1 ContinuousRandomVariables .............................................................221
5.2 ContinuousProbabilityFunctions ..........................................................223
5.3 TheUniformDistribution ..................................................................226
5.4 TheExponentialDistribution...............................................................233
5.5 SummaryoftheUniformandExponentialProbabilityDistributions ........................239
5.6 Practice1:UniformDistribution............................................................240
5.7 Practice2:ExponentialDistribution ........................................................243
5.8 Homework ................................................................................245
5.9 Review ....................................................................................251
5.10 Lab:ContinuousDistribution .............................................................254
Solutions .......................................................................................257
6 TheNormalDistribution
6.1 TheNormalDistribution ...................................................................261
6.2 TheStandardNormalDistribution .........................................................262
6.3 Z-scores....................................................................................263
6.4 AreastotheLeftandRightofx.............................................................265
6.5 CalculationsofProbabilities................................................................265
6.6 SummaryofFormulas .....................................................................269
6.7 Practice:TheNormalDistribution..........................................................270
6.8 Homework ................................................................................272
6.9 Review ....................................................................................278
6.10 Lab1:NormalDistribution(LapTimes)...................................................280
6.11 Lab2:NormalDistribution(PinkieLength) ...............................................283
Solutions .......................................................................................285
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v
7 TheCentralLimitTheorem
7.1 TheCentralLimitTheorem.................................................................289
7.2 TheCentralLimitTheoremforSampleMeans(Averages)...................................290
7.3 TheCentralLimitTheoremforSums .......................................................293
7.4 UsingtheCentralLimitTheorem...........................................................294
7.5 SummaryofFormulas .....................................................................301
7.6 Practice:TheCentralLimitTheorem .......................................................302
7.7 Homework ................................................................................305
7.8 Review ....................................................................................312
7.9 Lab1:CentralLimitTheorem(PocketChange).............................................314
7.10 Lab2:CentralLimitTheorem(CookieRecipes)............................................318
Solutions .......................................................................................323
8 ConfidenceIntervals
8.1 ConfidenceIntervals .......................................................................327
8.2 Confidence Interval, Single e Population n Mean, PopulationStandard Deviation
Known,Normal ...........................................................................329
8.3 Confidence Interval, , Single e Population Mean, Standard d Deviation Unknown,
Student’s-t.................................................................................336
8.4 ConfidenceIntervalforaPopulationProportion............................................339
8.5 SummaryofFormulas .....................................................................344
8.6 Practice1: ConfidenceIntervalsforMeans,KnownPopulationStandardDevia-
tion........................................................................................345
8.7 Practice2:ConfidenceIntervalsforMeans,UnknownPopulationStandardDevi-
ation ......................................................................................347
8.8 Practice3:ConfidenceIntervalsforProportions ............................................349
8.9 Homework ................................................................................351
8.10 Review ...................................................................................361
8.11 Lab1:ConfidenceInterval(HomeCosts)..................................................364
8.12 Lab2:ConfidenceInterval(PlaceofBirth).................................................367
8.13 Lab3:ConfidenceInterval(Womens’Heights) ............................................369
Solutions .......................................................................................371
9 HypothesisTesting:SingleMeanandSingleProportion
9.1 HypothesisTesting:SingleMeanandSingleProportion ....................................377
9.2 NullandAlternateHypotheses.............................................................378
9.3 OutcomesandtheTypeIandTypeIIErrors ................................................379
9.4 DistributionNeededforHypothesisTesting................................................380
9.5 Assumption................................................................................381
9.6 RareEvents ................................................................................381
9.7 UsingtheSampletoTesttheNullHypothesis ..............................................382
9.8 DecisionandConclusion...................................................................383
9.9 AdditionalInformation ....................................................................383
9.10 SummaryoftheHypothesisTest ..........................................................385
9.11 Examples .................................................................................385
9.12 SummaryofFormulas ....................................................................396
9.13 Practice1:SingleMean,KnownPopulationStandardDeviation ...........................397
9.14 Practice2:SingleMean,UnknownPopulationStandardDeviation ........................399
9.15 Practice3:SingleProportion ..............................................................401
9.16 Homework ...............................................................................403
9.17 Review ...................................................................................416
9.18 Lab:HypothesisTestingofaSingleMeanandSingleProportion...........................419
Solutions .......................................................................................423
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vi
10 HypothesisTesting:TwoMeans,PairedData,TwoProportions
10.1 HypothesisTesting:TwoPopulationMeansandTwoPopulationProportions..............429
10.2 Comparing Two Independent t Population n Means s with Unknown Population
StandardDeviations .......................................................................430
10.3 ComparingTwoIndependentPopulationMeanswithKnownPopulationStan-
dardDeviations ...........................................................................433
10.4 ComparingTwoIndependentPopulationProportions .....................................435
10.5 MatchedorPairedSamples ...............................................................437
10.6 SummaryofTypesofHypothesisTests....................................................442
10.7 Practice1:HypothesisTestingforTwoProportions........................................443
10.8 Practice2:HypothesisTestingforTwoAverages ..........................................445
10.9 Homework ...............................................................................447
10.10 Review ..................................................................................459
10.11 Lab:HypothesisTestingforTwoMeansandTwoProportions ............................461
Solutions .......................................................................................466
11 TheChi-SquareDistribution
11.1 TheChi-SquareDistribution ..............................................................471
11.2 Notation ..................................................................................472
11.3 FactsAbouttheChi-SquareDistribution ..................................................472
11.4 Goodness-of-FitTest ......................................................................474
11.5 TestofIndependence......................................................................481
11.6 TheChi-SquareDistribution:TestforHomogeneity .......................................485
11.7 The Chi-Square Distribution: : ComparisonSummaryofthe e Chi-Square Tests
Goodness-of-Fit,IndependenceandHomogeneity .........................................488
11.8 TestofaSingleVariance...................................................................488
11.9 SummaryofFormulas ....................................................................491
11.10 Practice1:Goodness-of-FitTest ..........................................................492
11.11 Practice2:ContingencyTables ...........................................................494
11.12 Practice3:TestofaSingleVariance.......................................................496
11.13 Homework ..............................................................................498
11.14 Review ..................................................................................507
11.15 Lab1:Chi-SquareGoodness-of-Fit .......................................................511
11.16 Lab2:Chi-SquareTestforIndependence .................................................516
Solutions .......................................................................................518
12 LinearRegressionandCorrelation
12.1 LinearRegressionandCorrelation ........................................................523
12.2 LinearEquations..........................................................................523
12.3 SlopeandY-InterceptofaLinearEquation ................................................525
12.4 ScatterPlots...............................................................................526
12.5 TheRegressionEquation..................................................................528
12.6 CorrelationCoefficientandCoefficientofDetermination ..................................534
12.7 TestingtheSignificanceoftheCorrelationCoefficient......................................536
12.8 Prediction.................................................................................541
12.9 Outliers...................................................................................541
12.10 95%CriticalValuesoftheSampleCorrelationCoefficientTable ...........................548
12.11 Summary................................................................................551
12.12 Practice:LinearRegression...............................................................552
12.13 Homework ..............................................................................555
12.14 Lab1:Regression(DistancefromSchool).................................................571
12.15 Lab2:Regression(TextbookCost)........................................................574
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vii
12.16 Lab3:Regression(FuelEfficiency) .......................................................576
Solutions .......................................................................................579
13 FDistributionandOne-WayANOVA
13.1 FDistributionandOne-WayANOVA .....................................................583
13.2 One-WayANOVA ........................................................................584
13.3 TheFDistributionandtheFRatio.........................................................585
13.4 FactsAbouttheFDistribution ............................................................589
13.5 TestofTwoVariances .....................................................................593
13.6 Summary.................................................................................596
13.7 Practice:One-WayANOVA ...............................................................597
13.8 Homework ...............................................................................599
13.9 Review ...................................................................................604
13.10 Lab:One-WayANOVA ..................................................................608
Solutions .......................................................................................610
14 Appendix
14.1 PracticeFinalExam1 .....................................................................613
14.2 PracticeFinalExam2 .....................................................................622
14.3 DataSets..................................................................................632
14.4 GroupProjects ............................................................................635
14.5 SolutionSheets ...........................................................................646
14.6 EnglishPhrasesWrittenMathematically...................................................650
14.7 SymbolsandtheirMeanings ..............................................................651
14.8 Formulas .................................................................................656
14.9 NotesfortheTI-83,83+,84Calculator.....................................................658
Solutions .......................................................................................668
15 Tables ............................................................................................671
Glossary .............................................................................................672
Index ................................................................................................680
Attributions .........................................................................................685
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