Collaborative Statistics for MT230

2011·4.6 MB·English

by  Robert Gallagher

Collaborative Statistics for MT230
Collection Editor:
Robert Gallagher

Collaborative Statistics for MT230
Collection Editor:
Robert Gallagher
Authors:
Susan Dean
Barbara Illowsky, Ph.D.
Online:
< http://cnx.org/content/col11345/1.2/ >
C O N N E X I O N S
Rice University, Houston, Texas
ThisselectionandarrangementofcontentasacollectioniscopyrightedbyRobertGallagher. Itislicensedunderthe
CreativeCommonsAttribution3.0license(http://creativecommons.org/licenses/by/3.0/).
Collectionstructurerevised:August18,2011
PDFgenerated:June20,2012
Forcopyrightandattributioninformationforthemodulescontainedinthiscollection,seep.593.
Table of Contents
Preface ................................................................................................1
AdditionalResources .............................................................. ...................5
AuthorAcknowledgements ....................................................... ...................9
StudentWelcomeLetter ..............................................................................11
1 SamplingandData
1.1 SamplingandData ..........................................................................13
1.2 Statistics ....................................................................................13
1.3 Probability ..................................................................................15
1.4 KeyTerms ..................................................................................15
1.5 Data ........................................................................................17
1.6 Variation ....................................................................................18
1.7 AnswersandRoundingOff .................................................................20
1.8 Frequency ..................................................................... .............21
1.9 Summary ...................................................................................25
1.10 Practice: SamplingandData ...............................................................26
1.11 Homework ................................................................................29
1.12 Lab1: DataCollection ......................................................................37
1.13 Lab2: SamplingExperiment ...............................................................39
Solutions ........................................................................................42
2 DescriptiveStatistics
2.1 DescriptiveStatistics ........................................................................45
2.2 DisplayingData .............................................................................45
2.3 StemandLeafGraphs(Stemplots),LineGraphsandBarGraphs .............................46
2.4 Histograms .................................................................................49
2.5 MeasuresoftheCenteroftheData ..........................................................53
2.6 SkewnessandtheMean,Median,andMode .................................................56
2.7 MeasuresoftheSpreadoftheData ..........................................................58
2.8 SummaryofFormulas ......................................................... .............67
2.9 Practice1: CenteroftheData ................................................................68
2.10 Practice2: SpreadoftheData ..............................................................71
2.11 Homework ................................................................................72
2.12 Lab: DescriptiveStatistics ..................................................................89
Solutions ........................................................................................91
3 LinearRegressionandCorrelation
3.1 LinearRegressionandCorrelation ...........................................................97
3.2 LinearEquations ............................................................................97
3.3 SlopeandY-InterceptofaLinearEquation ..................................... .............99
3.4 ScatterPlots ................................................................................100
3.5 TheRegressionEquation ...................................................................102
3.6 CorrelationCoefficientandCoefficientofDetermination ...................................108
3.7 TestingtheSignificanceoftheCorrelationCoefficient .......................................110
3.8 Prediction ..................................................................................115
3.9 Outliers ....................................................................................115
3.10 95%CriticalValuesoftheSampleCorrelationCoefficientTable ............................122
3.11 Summary .................................................................................125
3.12 Practice: LinearRegression ................................................................126
iv
3.13 Homework ...............................................................................129
3.14 Lab1: Regression(DistancefromSchool) ..................................................144
3.15 Lab2: Regression(TextbookCost) .........................................................147
3.16 Lab3: Regression(FuelEfficiency) ........................................................149
Solutions .......................................................................................152
4 ProbabilityTopics
4.1 ProbabilityTopics ..........................................................................157
4.2 Terminology ...............................................................................158
4.3 IndependentandMutuallyExclusiveEvents ...............................................160
4.4 TwoBasicRulesofProbability ..............................................................163
4.5 ContingencyTables ........................................................................167
4.6 VennDiagrams(optional) ..................................................................170
4.7 TreeDiagrams(optional) ...................................................................171
4.8 SummaryofFormulas .....................................................................176
4.9 Practice1: ContingencyTables .............................................................177
4.10 Practice2: CalculatingProbabilities .......................................................179
4.11 Homework ...............................................................................180
4.12 Review ...................................................................................191
4.13 Lab: ProbabilityTopics ....................................................................193
Solutions .......................................................................................196
5 DiscreteRandomVariables
5.1 DiscreteRandomVariables .................................................................203
5.2 ProbabilityDistributionFunction(PDF)foraDiscreteRandomVariable ....................204
5.3 MeanorExpectedValueandStandardDeviation ...........................................205
5.4 CommonDiscreteProbabilityDistributionFunctions .......................................208
5.5 Binomial ...................................................................................208
5.6 SummaryofFunctions .....................................................................212
5.7 Practice1: DiscreteDistribution ............................................................214
5.8 Practice2: BinomialDistribution ...........................................................215
5.9 Homework ................................................................................217
5.10 Review ...................................................................................227
5.11 Lab1: DiscreteDistribution(PlayingCardExperiment) ...................................230
5.12 Lab2: DiscreteDistribution(LuckyDiceExperiment) .....................................234
Solutions .......................................................................................238
6 TheNormalDistribution
6.1 TheNormalDistribution ...................................................................245
6.2 TheStandardNormalDistribution .........................................................246
6.3 Z-scores ....................................................................................247
6.4 AreastotheLeftandRightofx .............................................................249
6.5 CalculationsofProbabilities ................................................................249
6.6 SummaryofFormulas .....................................................................253
6.7 Practice: TheNormalDistribution ..........................................................254
6.8 Homework ................................................................................256
6.9 Review ....................................................................................262
6.10 Lab1: NormalDistribution(LapTimes) ...................................................264
6.11 Lab2: NormalDistribution(PinkieLength) ...............................................267
Solutions .......................................................................................269
7 TheCentralLimitTheorem
7.1 TheCentralLimitTheorem .................................................................273
7.2 TheCentralLimitTheoremforSampleMeans(Averages) ...................................274
v
7.3 TheCentralLimitTheoremforSums .......................................................277
7.4 UsingtheCentralLimitTheorem ...........................................................278
7.5 SummaryofFormulas .....................................................................286
7.6 Practice: TheCentralLimitTheorem .......................................................287
7.7 Homework ................................................................................290
7.8 Review ....................................................................................297
7.9 Lab1: CentralLimitTheorem(PocketChange) .............................................299
7.10 Lab2: CentralLimitTheorem(CookieRecipes) ............................................303
Solutions .......................................................................................308
8 ConfidenceIntervals
8.1 ConfidenceIntervals .......................................................................311
8.2 Confidence Interval, Single Population Mean, Population Standard Deviation
Known,Normal ...........................................................................313
8.3 Confidence Interval, Single Population Mean, Standard Deviation Unknown,
Student-T ..................................................................................320
8.4 ConfidenceIntervalforaPopulationProportion ............................................323
8.5 SummaryofFormulas .....................................................................328
8.6 Practice1: ConfidenceIntervalsforAverages,KnownPopulationStandardDevi-
ation ......................................................................................329
8.7 Practice2:ConfidenceIntervalsforAverages,UnknownPopulationStandardDe-
viation .....................................................................................331
8.8 Practice3: ConfidenceIntervalsforProportions ............................................333
8.9 Homework ................................................................................335
8.10 Review ...................................................................................345
8.11 Lab1: ConfidenceInterval(HomeCosts) ..................................................348
8.12 Lab2: ConfidenceInterval(PlaceofBirth) .................................................351
8.13 Lab3: ConfidenceInterval(Womens’Heights) ............................................353
Solutions .......................................................................................355
9 HypothesisTesting: SingleMeanandSingleProportion
9.1 HypothesisTesting: SingleMeanandSingleProportion ....................................361
9.2 NullandAlternateHypotheses .............................................................362
9.3 OutcomesandtheTypeIandTypeIIErrors ................................................363
9.4 DistributionNeededforHypothesisTesting ................................................364
9.5 Assumption ................................................................................365
9.6 RareEvents ................................................................................365
9.7 UsingtheSampletoSupportOneoftheHypotheses .......................................366
9.8 DecisionandConclusion ...................................................................367
9.9 AdditionalInformation ....................................................................367
9.10 SummaryoftheHypothesisTest ..........................................................369
9.11 Examples .................................................................................369
9.12 SummaryofFormulas ....................................................................380
9.13 Practice1: SingleMean,KnownPopulationStandardDeviation ...........................381
9.14 Practice2: SingleMean,UnknownPopulationStandardDeviation ........................383
9.15 Practice3: SingleProportion ..............................................................385
9.16 Homework ...............................................................................387
9.17 Review ...................................................................................400
9.18 Lab: HypothesisTestingofaSingleMeanandSingleProportion ...........................403
Solutions .......................................................................................407
10 HypothesisTesting: TwoMeans,PairedData,TwoProportions
10.1 HypothesisTesting: TwoPopulationMeansandTwoPopulationProportions ..............413
vi
10.2 Comparing Two Independent Population Means with Unknown Population
StandardDeviations .......................................................................414
10.3 ComparingTwoIndependentPopulationMeanswithKnownPopulationStan-
dardDeviations ...........................................................................417
10.4 ComparingTwoIndependentPopulationProportions .....................................419
10.5 MatchedorPairedSamples ...............................................................421
10.6 SummaryofTypesofHypothesisTests ....................................................426
10.7 Practice1: HypothesisTestingforTwoProportions ........................................427
10.8 Practice2: HypothesisTestingforTwoAverages ..........................................429
10.9 Homework ...............................................................................431
10.10 Review ..................................................................................443
10.11 Lab: HypothesisTestingforTwoMeansandTwoProportions ............................445
Solutions .......................................................................................450
11 TheChi-SquareDistribution
11.1 TheChi-SquareDistribution ..............................................................455
11.2 Notation ..................................................................................456
11.3 FactsAbouttheChi-SquareDistribution ..................................................456
11.4 Goodness-of-FitTest ......................................................................458
11.5 TestofIndependence ......................................................................465
11.6 SummaryofFormulas ....................................................................470
11.7 Practice1: Goodness-of-FitTest ...........................................................471
11.8 Practice2: ContingencyTables ............................................................473
11.9 Homework ...............................................................................475
11.10 Review ..................................................................................484
11.11 Lab1: Chi-SquareGoodness-of-Fit .......................................................488
11.12 Lab2: Chi-SquareTestforIndependence .................................................493
Solutions .......................................................................................495
12 FDistributionandANOVA
12.1 FDistributionandANOVA ...............................................................501
12.2 ANOVA ..................................................................................502
12.3 TheFDistributionandtheFRatio .........................................................502
12.4 FactsAbouttheFDistribution ............................................................504
12.5 Summary .................................................................................509
12.6 Practice: ANOVA .........................................................................510
12.7 Homework ...............................................................................512
12.8 Review ...................................................................................514
12.9 Lab: ANOVA .............................................................................518
Solutions .......................................................................................520
13 Appendix
13.1 PracticeFinalExam1 .....................................................................523
13.2 PracticeFinalExam2 .....................................................................532
13.3 DataSets ..................................................................................541
13.4 GroupProjects ............................................................................544
13.5 SolutionSheets ...........................................................................555
13.6 EnglishPhrasesWrittenMathematically ...................................................559
13.7 SymbolsandtheirMeanings ..............................................................560
13.8 Formulas .................................................................................565
13.9 NotesfortheTI-83,83+,84Calculator .....................................................567
Solutions .......................................................................................577
14 Tables ............................................................................................581
vii
Glossary .............................................................................................582
Index ................................................................................................589
Attributions .........................................................................................593
viii