lOMoARcPSD| 7651861
STA1502 inferential-stats-1b-the-course-notes-for-statistical
b
inference. i STA1502/1
CONTENTS
ORIENTATION iii
STUDYbUNITb1
1.1 Introduction 1
1.2 InferencebaboutbthebDifferencebBetweenbTwobPopulationbMeans: 1
IndependentbSamples
1.3 ObservationalbandbExperimentalbData 9
1.4 InferencebaboutbthebDifferencebBetweenbTwobPopulationbMeans: 9
MatchedbPairsbExperiment
1.5 InferencebaboutbthebRatiobofbTwobVariances 19
1.6 Self-correctingbExercisesbforbUnitb1 22
1.7 SolutionsbtobSelf-correctingbExercisesbforbUnitb1 23
1.8 LearningbOutcomes 27
STUDYbUNITb2
2.1 Introduction 28
2.2 InferencebaboutbthebDifferencebBetweenbTwobPopulationbProportions 28
2.3 One-WaybAnalysisbofbVariance 34
2.4 MultiplebComparisons 43
2.5 AnalysisbofbVariancebexperimentalbdesignsb(readbonly) 47
2.6 RandomizedbBlock(two-way)bAnalysisbofbVariance 47
2.7 Self-correctingbExercisesbforbUnitb2 51
2.8 SolutionsbtobSelf-correctingbExercisesbforbUnitb2 52
2.9 LearningbOutcomes 55
STUDYbUNITb3
3.1 Chi–squarebtest 57
3.2 Chi-squaredbgoodness-of-fitbtest 58
3.3 Chi-squaredbtestbofbabContingencybTable 62
3.4 Summarybofbtestbonbnominalbdata 64
STUDYbUNITb4
4.1 Simpleblinearbregressionbandbcorrelation 70
4.2 Estimatingbthebcoefficients 70
4.3 Errorbvariable:brequiredbconditions 75
4.4 Assessingbthebmodel 76
4.5 Usingbthebregressionbequation 77
4.6 Regressionbdiagnostics 77
ii
, lOMoARcPSD| 7651861
STUDYbUNITb5
5.1 Nonbparametricbstatistics 82
5.2 WilcoxonbRankbSumbTest 82
5.3 SignbtestbandbWilcoxonbsignedbrankbsumbtest 86
STUDYbUNITb6
6.1 Timebseriesbanalysisbandbtimebseriesbforecasting 96
6.2 Componentsbofbtimebseriesbandbsmoothingbpossibilities 96
6.3 Smoothingbtechniques 97
6.4 Trendbandbseasonalbeffects 100
6.5 Introductionbtobforecasting 102
6.6 Forcastingbmodels 102
, lOMoARcPSD| 7651861
iii STA1502/1
ORIENTATION
Welcome
WelcomebtobSTA1502.bThisbmodulebisbthebsecondbonebofbthebfirst-
yearbstatisticsbcourses.b STA1501bandbSTA1502bformbthebfirstb yearbStatisticsbcoursebforbstudentsbfromb
thebCollegebof EconomicbandbManagementb Sciences. Ifb youbarebabBScbstudent
inbthebCollegebof
Science,b EngineeringbandbTechnology,bthebthreebmodulesbSTA1501bandbS
TA1502bandbSTA1503bformbthebfirstbyearbinbStatistics.
InbthebprecedingbmodulebSTA1501,b webtreatedbprobabilitybandbprobabilitybdistributions,b andbunlessbon
ebhasbabproperbunderstandingbofbtheblawsbofbprobability,bthebmechanismsbunderlyingbstatisticalbdataban
alysisbwillbnotbbebunderstoodbproperly.bProbabilitybtheorybisbthebtoolbthatbmakesbstatisticalbinferencebpo
ssible.b InbSTA1502,b webconsiderbtobthebapplicationsbof thebprobabilitybdistributions.
YoubhaveblearnedbinbSTA1501bthatbthebsh
apebofbthebnormalbdistributionbisbdeterminedbbybthebvaluebofbthebmean
µbandbthebvariancebσ2,bwhilstbthebshapebofbthebbinomialbdistributionbisbdeterminedbbybthebsamplebsize
nbandbthebprobabilitybofbabsuccessb p.b Thesebcriticalb valuesbarebcalledbparameters.b Webmostboftenbdo
n’tbknowbwhatbthebvaluesbofbthebparametersbarebandbthusbwebcannotb"utilise"bthesebdistributionsb(i.e.
usebthebmathematicalbformulabtobdrawbabprobabilitybdensitybgraphborbcomputebspecificbprobabilities)bunl
essbwebsomehowbestimatebthesebunknownbparameters.
Itbmakesbperfectblogicalbsensebthatb tobest
imatebthebvaluebofbanbunknownbpopulationbparameter,bwebcomputebabcorrespondingborbcomparablebcha
racteristicbofbthebsample.
Thebobjectivebofbthisbmodulebisbtobfocusbonbthebissuesbrelatedbtobpredictionbandbinferencebinbstatisticsb
andbthereforebitbisbcalledbStatisticalb Inferencebandbtheb"I"binbthebtitlebindicatesbthatbitbisbabmodulebatbthe
firstblevel.b Webdrawbinferencebaboutbabpopulationb(abcompletebsetbofbdata)bbasedbonbtheblimitedbinfor
b
mationbcontainedbinbabsample.b Inbdictionarybterms,binferencebisbthebactborbprocessbofbinferring;b tobinfe
rb meansb tobconcludeborbjudgebfrombpremisesborbevidence;b meaningbtobderivebbybreasoning.bInbgene
ral,bthebtermbimpliesbabconclusionbbasedbonbexperienceborbknowledge.
Morebspecificallybinb
statistics,bwebhavebasbevidencebtheblimitedbinformationbcontainedbinbtheboutcomebof
absamplebandbwebw
antbtobconcludebsomethingbaboutbthebunknownbpopulationbfrombwhichbthebsamplebwasbdrawn.bThebse
tbofbprinciples,bproceduresbandbmethodsbthatbwebusebtobstudybpopulationsbbybmakingbusebofbinformati
onbobtainedbfrombsamplesbisbcalledbstatisticalbinference.
Learning outcomesb
, lOMoARcPSD| 7651861
Therebarebverybspecificboutcomesbforbthisbmodule,blistedbbelow.bThroughoutbyourbstudybofbthisbmoduleb
youbmustbcomebbackbtobthisbpage,bsitbbackbandbreflectbuponbthem,bthinkbthembthrough,bdigestbthembinto
yourbsystembandbfeelbconfidentbinbthebendbthatbyoubhavebmasteredbthebfollowingboutcomes:
b
STA1502 inferential-stats-1b-the-course-notes-for-statistical
b
inference. i STA1502/1
CONTENTS
ORIENTATION iii
STUDYbUNITb1
1.1 Introduction 1
1.2 InferencebaboutbthebDifferencebBetweenbTwobPopulationbMeans: 1
IndependentbSamples
1.3 ObservationalbandbExperimentalbData 9
1.4 InferencebaboutbthebDifferencebBetweenbTwobPopulationbMeans: 9
MatchedbPairsbExperiment
1.5 InferencebaboutbthebRatiobofbTwobVariances 19
1.6 Self-correctingbExercisesbforbUnitb1 22
1.7 SolutionsbtobSelf-correctingbExercisesbforbUnitb1 23
1.8 LearningbOutcomes 27
STUDYbUNITb2
2.1 Introduction 28
2.2 InferencebaboutbthebDifferencebBetweenbTwobPopulationbProportions 28
2.3 One-WaybAnalysisbofbVariance 34
2.4 MultiplebComparisons 43
2.5 AnalysisbofbVariancebexperimentalbdesignsb(readbonly) 47
2.6 RandomizedbBlock(two-way)bAnalysisbofbVariance 47
2.7 Self-correctingbExercisesbforbUnitb2 51
2.8 SolutionsbtobSelf-correctingbExercisesbforbUnitb2 52
2.9 LearningbOutcomes 55
STUDYbUNITb3
3.1 Chi–squarebtest 57
3.2 Chi-squaredbgoodness-of-fitbtest 58
3.3 Chi-squaredbtestbofbabContingencybTable 62
3.4 Summarybofbtestbonbnominalbdata 64
STUDYbUNITb4
4.1 Simpleblinearbregressionbandbcorrelation 70
4.2 Estimatingbthebcoefficients 70
4.3 Errorbvariable:brequiredbconditions 75
4.4 Assessingbthebmodel 76
4.5 Usingbthebregressionbequation 77
4.6 Regressionbdiagnostics 77
ii
, lOMoARcPSD| 7651861
STUDYbUNITb5
5.1 Nonbparametricbstatistics 82
5.2 WilcoxonbRankbSumbTest 82
5.3 SignbtestbandbWilcoxonbsignedbrankbsumbtest 86
STUDYbUNITb6
6.1 Timebseriesbanalysisbandbtimebseriesbforecasting 96
6.2 Componentsbofbtimebseriesbandbsmoothingbpossibilities 96
6.3 Smoothingbtechniques 97
6.4 Trendbandbseasonalbeffects 100
6.5 Introductionbtobforecasting 102
6.6 Forcastingbmodels 102
, lOMoARcPSD| 7651861
iii STA1502/1
ORIENTATION
Welcome
WelcomebtobSTA1502.bThisbmodulebisbthebsecondbonebofbthebfirst-
yearbstatisticsbcourses.b STA1501bandbSTA1502bformbthebfirstb yearbStatisticsbcoursebforbstudentsbfromb
thebCollegebof EconomicbandbManagementb Sciences. Ifb youbarebabBScbstudent
inbthebCollegebof
Science,b EngineeringbandbTechnology,bthebthreebmodulesbSTA1501bandbS
TA1502bandbSTA1503bformbthebfirstbyearbinbStatistics.
InbthebprecedingbmodulebSTA1501,b webtreatedbprobabilitybandbprobabilitybdistributions,b andbunlessbon
ebhasbabproperbunderstandingbofbtheblawsbofbprobability,bthebmechanismsbunderlyingbstatisticalbdataban
alysisbwillbnotbbebunderstoodbproperly.bProbabilitybtheorybisbthebtoolbthatbmakesbstatisticalbinferencebpo
ssible.b InbSTA1502,b webconsiderbtobthebapplicationsbof thebprobabilitybdistributions.
YoubhaveblearnedbinbSTA1501bthatbthebsh
apebofbthebnormalbdistributionbisbdeterminedbbybthebvaluebofbthebmean
µbandbthebvariancebσ2,bwhilstbthebshapebofbthebbinomialbdistributionbisbdeterminedbbybthebsamplebsize
nbandbthebprobabilitybofbabsuccessb p.b Thesebcriticalb valuesbarebcalledbparameters.b Webmostboftenbdo
n’tbknowbwhatbthebvaluesbofbthebparametersbarebandbthusbwebcannotb"utilise"bthesebdistributionsb(i.e.
usebthebmathematicalbformulabtobdrawbabprobabilitybdensitybgraphborbcomputebspecificbprobabilities)bunl
essbwebsomehowbestimatebthesebunknownbparameters.
Itbmakesbperfectblogicalbsensebthatb tobest
imatebthebvaluebofbanbunknownbpopulationbparameter,bwebcomputebabcorrespondingborbcomparablebcha
racteristicbofbthebsample.
Thebobjectivebofbthisbmodulebisbtobfocusbonbthebissuesbrelatedbtobpredictionbandbinferencebinbstatisticsb
andbthereforebitbisbcalledbStatisticalb Inferencebandbtheb"I"binbthebtitlebindicatesbthatbitbisbabmodulebatbthe
firstblevel.b Webdrawbinferencebaboutbabpopulationb(abcompletebsetbofbdata)bbasedbonbtheblimitedbinfor
b
mationbcontainedbinbabsample.b Inbdictionarybterms,binferencebisbthebactborbprocessbofbinferring;b tobinfe
rb meansb tobconcludeborbjudgebfrombpremisesborbevidence;b meaningbtobderivebbybreasoning.bInbgene
ral,bthebtermbimpliesbabconclusionbbasedbonbexperienceborbknowledge.
Morebspecificallybinb
statistics,bwebhavebasbevidencebtheblimitedbinformationbcontainedbinbtheboutcomebof
absamplebandbwebw
antbtobconcludebsomethingbaboutbthebunknownbpopulationbfrombwhichbthebsamplebwasbdrawn.bThebse
tbofbprinciples,bproceduresbandbmethodsbthatbwebusebtobstudybpopulationsbbybmakingbusebofbinformati
onbobtainedbfrombsamplesbisbcalledbstatisticalbinference.
Learning outcomesb
, lOMoARcPSD| 7651861
Therebarebverybspecificboutcomesbforbthisbmodule,blistedbbelow.bThroughoutbyourbstudybofbthisbmoduleb
youbmustbcomebbackbtobthisbpage,bsitbbackbandbreflectbuponbthem,bthinkbthembthrough,bdigestbthembinto
yourbsystembandbfeelbconfidentbinbthebendbthatbyoubhavebmasteredbthebfollowingboutcomes:
b
