APPENDIX
631
D. Thereisnosuchtestthatcanbeconducted.
Exercise14.2.34
(Solutiononp.670.)
Note: FDistributiontestofOne-WayANOVA;Notallclassescoverthistopic. . Whichofthe
followingstatementsistruewhenusingone-wayANOVA?
A. Thepopulationsfromwhichthesamplesareselectedhavedifferentdistributions.
B. Thesamplesizesarelarge.
C. Thetestistodetermineifthedifferentgroupshavethesamemeans.
D. Thereisacorrelationbetweenthefactorsoftheexperiment.
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632
APPENDIX
14.3DataSets
3
14.3.1LapTimes
ThefollowingtablesprovidelaptimesfromTerriVogel’sLogBook. Timesarerecordedinsecondsfor
2.5-milelapscompletedinaseriesofracesandpracticeruns.
RaceLapTimes(inSeconds)
Lap1
Lap2
Lap3
Lap4
Lap5
Lap6
Lap7
Race1
135
130
131
132
130
131
133
Race2
134
131
131
129
128
128
129
Race3
129
128
127
127
130
127
129
Race4
125
125
126
125
124
125
125
Race5
133
132
132
132
131
130
132
Race6
130
130
130
129
129
130
129
Race7
132
131
133
131
134
134
131
Race8
127
128
127
130
128
126
128
Race9
132
130
127
128
126
127
124
Race10
135
131
131
132
130
131
130
Race11
132
131
132
131
130
129
129
Race12
134
130
130
130
131
130
130
Race13
128
127
128
128
128
129
128
Race14
132
131
131
131
132
130
130
Race15
136
129
129
129
129
129
129
Race16
129
129
129
128
128
129
129
Race17
134
131
132
131
132
132
132
Race18
129
129
130
130
133
133
127
Race19
130
129
129
129
129
129
128
Race20
131
128
130
128
129
130
130
Table14.13
3
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APPENDIX
633
PracticeLapTimes(inSeconds)
Lap1
Lap2
Lap3
Lap4
Lap5
Lap6
Lap7
Practice1
142
143
180
137
134
134
172
Practice2
140
135
134
133
128
128
131
Practice3
130
133
130
128
135
133
133
Practice4
141
136
137
136
136
136
145
Practice5
140
138
136
137
135
134
134
Practice6
142
142
139
138
129
129
127
Practice7
139
137
135
135
137
134
135
Practice8
143
136
134
133
134
133
132
Practice9
135
134
133
133
132
132
133
Practice10
131
130
128
129
127
128
127
Practice11
143
139
139
138
138
137
138
Practice12
132
133
131
129
128
127
126
Practice13
149
144
144
139
138
138
137
Practice14
133
132
137
133
134
130
131
Practice15
138
136
133
133
132
131
131
Table14.14
14.3.2StockPrices
Thefollowingtablelistsinitialpublicoffering(IPO)stockpricesforall1999stocksthatatleastdoubledin
valueduringthefirstdayoftrading.Thisishistoricaldata.
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634
APPENDIX
IPOOfferPrices
$17.00
$23.00
$14.00
$16.00
$12.00
$26.00
$20.00
$22.00
$14.00
$15.00
$22.00
$18.00
$18.00
$21.00
$21.00
$19.00
$15.00
$21.00
$18.00
$17.00
$15.00
$25.00
$14.00
$30.00
$16.00
$10.00
$20.00
$12.00
$16.00
$17.44
$16.00
$14.00
$15.00
$20.00
$20.00
$16.00
$17.00
$16.00
$15.00
$15.00
$19.00
$48.00
$16.00
$18.00
$9.00
$18.00
$18.00
$20.00
$8.00
$20.00
$17.00
$14.00
$11.00
$16.00
$19.00
$15.00
$21.00
$12.00
$8.00
$16.00
$13.00
$14.00
$15.00
$14.00
$13.41
$28.00
$21.00
$17.00
$28.00
$17.00
$19.00
$16.00
$17.00
$19.00
$18.00
$17.00
$15.00
$14.00
$21.00
$12.00
$18.00
$24.00
$15.00
$23.00
$14.00
$16.00
$12.00
$24.00
$20.00
$14.00
$14.00
$15.00
$14.00
$19.00
$16.00
$38.00
$20.00
$24.00
$16.00
$8.00
$18.00
$17.00
$16.00
$15.00
$7.00
$19.00
$12.00
$8.00
$23.00
$12.00
$18.00
$20.00
$21.00
$34.00
$16.00
$26.00
$14.00
Table14.15
NOTE
:DatacompiledbyJayR.RitterofUniv.ofFloridausingdatafromSecuritiesDataCo.and
Bloomberg.
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APPENDIX
635
14.4GroupProjects
14.4.1GroupProject:UnivariateData
4
14.4.1.1StudentLearningObjectives
 Thestudentwilldesignandcarryoutasurvey.
 Thestudentwillanalyzeandgraphicallydisplaytheresultsofthesurvey.
14.4.1.2Instructions
Asyoucompleteeachtaskbelow,checkitoff.Answerallquestionsinyoursummary.
____ Decidewhatdatayouaregoingtostudy.
E
XAMPLES
: Herearetwoexamples,butyoumayNOTusethem: numberofM&M’sper
smallbag,numberofpencilsstudentshaveintheirbackpacks.
____ Areyourdatadiscreteorcontinuous?Howdoyouknow?
____ Decidehowyouaregoingtocollectthedata(forinstance,buy30bagsofM&M’s;collectdatafrom
theWorldWideWeb).
____ Describeyoursamplingtechniqueindetail. Use e cluster, stratified, systematic, or simplerandom
(usingarandomnumbergenerator)sampling.Donotuseconveniencesampling.Whatmethoddid
youuse?Whydidyoupickthatmethod?
____ Conductyoursurvey.Yourdatasizemustbeatleast30.
____ Summarizeyourdatainachartwithcolumnsshowingdatavalue,frequency,relativefrequency
andcumulativerelativefrequency.
____ Answerthefollowing(roundedto2decimalplaces):
1.
x=
2. s=
3. Firstquartile=
4. Median=
5. 70thpercentile=
____ Whatvalueis2standarddeviationsabovethemean?
____ Whatvalueis1.5standarddeviationsbelowthemean?
____ Constructahistogramdisplayingyourdata.
____ Incompletesentences,describetheshapeofyourgraph.
____ Doyounoticeanypotentialoutliers?Ifso,whatvaluesarethey?Showyourworkinhowyouused
thepotentialoutlierformulainChapter2(sinceyouhaveunivariatedata)todeterminewhetheror
notthevaluesmightbeoutliers.
____ Constructaboxplotdisplayingyourdata.
____ Doesthemiddle50%ofthedataappeartobeconcentratedtogetherorspreadapart? Explainhow
youdeterminedthis.
____ Lookingatboththehistogramandtheboxplot,discussthedistributionofyourdata.
14.4.1.3AssignmentChecklist
Youneedtoturninthefollowingtypedandstapledpacket,withpagesinthefollowingorder:
____ Coversheet:name,classtime,andnameofyourstudy
4
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636
APPENDIX
____ Summarypage:Thisshouldcontainparagraphswrittenwithcompletesentences.Itshouldinclude
answerstoallthequestionsabove.Itshouldalsoincludestatementsdescribingthepopulationunder
study,thesample,aparameterorparametersbeingstudied,andthestatisticorstatisticsproduced.
____ URLfordata,ifyourdataarefromtheWorldWideWeb.
____ Chartofdata,frequency,relativefrequencyandcumulativerelativefrequency.
____ Page(s)ofgraphs:histogramandboxplot.
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APPENDIX
637
14.4.2GroupProject:ContinuousDistributionsandCentralLimitTheorem
5
14.4.2.1StudentLearningObjectives
 Thestudentwillcollectasampleofcontinuousdata.
 Thestudentwillattempttofitthedatasampletovariousdistributionmodels.
 ThestudentwillvalidatetheCentralLimitTheorem.
14.4.2.2Instructions
Asyoucompleteeachtaskbelow,checkitoff.Answerallquestionsinyoursummary.
14.4.2.3PartI:Sampling
____ Decidewhatcontinuousdatayouaregoingtostudy.(Herearetwoexamples,butyoumayNOTuse
them: theamountofmoneyastudentspendsoncollegesuppliesthistermorthelengthofalong
distancetelephonecall.)
____ Describeyoursamplingtechniqueindetail. Use e cluster, stratified, systematic, or simplerandom
(usingarandomnumbergenerator)sampling.Donotuseconveniencesampling.Whatmethoddid
youuse?Whydidyoupickthatmethod?
____ Conductyoursurvey.Gatheratleast150piecesofcontinuousquantitativedata.
____ Define(inwords)therandomvariableforyourdata.X=_______
____ Create2listsofyourdata:(1)unordereddata,(2)inorderofsmallesttolargest.
____ Findthesamplemeanandthesamplestandarddeviation(roundedto2decimalplaces).
1.
x=
2. s=
____ Constructahistogramofyourdatacontaining5-10intervalsofequalwidth.Thehistogramshould
bearepresentativedisplayofyourdata.Labelandscaleit.
14.4.2.4PartII:PossibleDistributions
____ SupposethatXfollowedthetheoreticaldistributionsbelow. Setupeachdistributionusingtheap-
propriateinformationfromyourdata.
____ Uniform:X~U____________Usethelowestandhighestvaluesasaandb.
____ Exponential:X~Exp____________Use
xtoestimatem.
____ Normal:X~N____________Use
xtoestimateformandstoestimatefors.
____ Mustyourdatafitoneoftheabovedistributions?Explainwhyorwhynot.
____ Couldthedatafit2or3oftheabovedistributions(atthesametime)?Explain.
____ Calculate the value k(anvalue)that is s 1.75 standard deviations above e the sample mean. =
_________(roundedto2decimalplaces)Note:k=
x+(1.75)s
____ Determinetherelativefrequencies(RF)roundedto4decimalplaces.
1. RF=
frequency
totalnumbersurveyed
2. RF(X<k)=
3. RF(X>k)=
4. RF(X=k)=
UseaseparatepieceofpaperforEACHdistribution(uniform,exponential,normal)torespondtothe
followingquestions.
5
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638
APPENDIX
NOTE
:Youshouldhaveonepagefortheuniform,onepagefortheexponential,andonepagefor
thenormal
____ Statethedistribution:X _________
____ Drawagraphforeachofthethreetheoreticaldistributions.Labeltheaxesandmarkthemappropri-
ately.
____ Findthefollowingtheoreticalprobabilities(roundedto4decimalplaces).
1. P(X<k)=
2. P(X>k)=
3. P(X=k)=
____ Comparetherelativefrequenciestothecorrespondingprobabilities.Arethevaluesclose?
____ Doesitappearthatthedatafitthedistributionwell?Justifyyouranswerbycomparingtheprobabil-
itiestotherelativefrequencies,andthehistogramstothetheoreticalgraphs.
14.4.2.5PartIII:CLTExperiments
______ Fromyouroriginaldata(beforeordering),usearandomnumbergeneratortopick40samplesof
size5.Foreachsample,calculatetheaverage.
______ Onaseparatepage,attachedtothesummary,includethe40samplesofsize5,alongwiththe40
sampleaverages.
______ Listthe40averagesinorderfromsmallesttolargest.
______ Definetherandomvariable,
X,inwords.
X=
______ Statetheapproximatetheoreticaldistributionof
X.
X
______ Basethisonthemeanandstandarddeviationfromyouroriginaldata.
______ Constructahistogramdisplayingyourdata.Use5to6intervalsofequalwidth.Labelandscaleit.
Calculate thevalue
k(an
value)that is1.75standarddeviationsabovethe samplemean.
k=_____
(roundedto2decimalplaces)
Determinetherelativefrequencies(RF)roundedto4decimalplaces.
1. RF(
X<
k)=
2. RF(
X>
k)=
3. RF(
X=
k)=
Findthefollowingtheoreticalprobabilities(roundedto4decimalplaces).
•. P(
X<
k)=
•. P(
X>
k)=
•. P(
X=
k)=
______ DrawthegraphofthetheoreticaldistributionofX.
______ Answerthequestionsbelow.
______ Comparetherelativefrequenciestotheprobabilities.Arethevaluesclose?
______ Doesitappearthat thedataofaveragesfitthe distributionof
X
well? Justifyyouranswerby
comparingtheprobabilitiestotherelativefrequencies,andthehistogramtothetheoreticalgraph.
______ In3-5completesentencesforeach,answerthefollowingquestions.Givethoughtfulexplanations.
______ Insummary,doyouroriginaldataseemtofittheuniform,exponential,ornormaldistributions?
Answerwhyorwhynotforeachdistribution.Ifthedatadonotfitanyofthosedistributions,explain
why.
______ What happened tothe shapeanddistributionwhenyouaveragedyourdata? Intheory, what
shouldhavehappened?Intheory,would“it”alwayshappen?Whyorwhynot?
______ Weretherelativefrequenciescomparedtothetheoreticalprobabilitiescloserwhencomparingthe
Xor
X
distributions?Explainyouranswer.
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APPENDIX
639
14.4.2.6AssignmentChecklist
Youneedtoturninthefollowingtypedandstapledpacket,withpagesinthefollowingorder:
____ Coversheet:name,classtime,andnameofyourstudy
____ Summarypages:Theseshouldcontainseveralparagraphswrittenwithcompletesentencesthatde-
scribetheexperiment,includingwhatyoustudiedandyoursamplingtechnique,aswellasanswers
toallofthequestionsabove.
____ URLfordata,ifyourdataarefromtheWorldWideWeb.
____ Pages,oneforeachtheoreticaldistribution,withthedistributionstated,thegraph,andtheproba-
bilityquestionsanswered
____ Pagesofthedatarequested
____ Allgraphsrequired
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640
APPENDIX
14.4.3PartnerProject:HypothesisTesting-Article
6
14.4.3.1StudentLearningObjectives
 Thestudentwillidentifyahypothesistestingprobleminprint.
 Thestudentwillconductasurveytoverifyordisputetheresultsofthehypothesistest.
 Thestudentwillsummarizethearticle,analysis,andconclusionsinareport.
14.4.3.2Instructions
Asyoucompleteeachtaskbelow,checkitoff.Answerallquestionsinyoursummary.
____ Findanarticleinanewspaper,magazineorontheinternetwhichmakesaclaimaboutONEpopula-
tionmeanorONEpopulationproportion.Theclaimmaybebaseduponasurveythatthearticlewas
reportingon.Decidewhetherthisclaimisthenulloralternatehypothesis.
____ Copyorprintoutthearticleandincludeacopyinyourproject,alongwiththesource.
____ Statehowyouwillcollectyourdata.(Conveniencesamplingisnotacceptable.)
____ Conductyoursurvey. Youmusthavemorethan50responsesinyoursample. Whenyouhandin
yourfinalproject,attachthetallysheetorthepacketofquestionnairesthatyouusedtocollectdata.
Yourdatamustbereal.
____ Statethestatisticsthatarearesultofyourdatacollection: samplesize,samplemean,andsample
standarddeviation,ORsamplesizeandnumberofsuccesses.
____ Make2copiesoftheappropriatesolutionsheet.
____ Recordthehypothesistestonthesolutionsheet,basedonyourexperiment. DoaDRAFTsolution
firstononeofthesolutionsheetsandcheckitovercarefully. Haveaclassmatecheckyoursolution
toseeifitisdonecorrectly. Makeyourdecisionusinga5%levelofsignificance. Includethe95%
confidenceintervalonthesolutionsheet.
____ Createagraphthatillustratesyourdata.Thismaybeapieorbarchartormaybeahistogramorbox
plot,dependingonthenatureofyourdata.Produceagraphthatmakessenseforyourdataandgives
usefulvisualinformationaboutyourdata. Youmayneedtolookatseveraltypesofgraphsbefore
youdecidewhichisthemostappropriateforthetypeofdatainyourproject.
____ Writeyour r summary(incomplete sentences s and paragraphs, with proper r grammar and correct
spelling)thatdescribestheproject.ThesummaryMUSTinclude:
1. Briefdiscussionofthearticle,includingthesource.
2. Statementoftheclaimmadeinthearticle(oneofthehypotheses).
3. Detaileddescriptionofhow,where,andwhenyoucollectedthedata,includingthesamplingtech-
nique. Didyouusecluster,stratified,systematic,orsimplerandomsampling(usingarandom
numbergenerator)?Asstatedabove,conveniencesamplingisnotacceptable.
4. Conclusionaboutthearticleclaiminlightofyourhypothesistest. Thisistheconclusionofyour
hypothesistest,statedinwords,inthecontextofthesituationinyourprojectinsentenceform,
asifyouwerewritingthisconclusionforanon-statistician.
5. Sentenceinterpretingyourconfidenceintervalinthecontextofthesituationinyourproject.
14.4.3.3AssignmentChecklist
Turninthefollowingtyped(12point)andstapledpacketforyourfinalproject:
____ Coversheetcontainingyourname(s),classtime,andthenameofyourstudy.
____ Summary,whichincludesallitemslistedonsummarychecklist.
____ Solutionsheetneatlyandcompletelyfilledout.Thesolutionsheetdoesnotneedtobetyped.
6
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