APPENDIX
641
____ Graphicrepresentationofyourdata,createdfollowingtheguidelinesdiscussedabove.Includeonly
graphswhichareappropriateanduseful.
____ RawdatacollectedANDatablesummarizingthesampledata(n,xbarands; orx,n,andp’,as
appropriateforyourhypotheses). Therawdatadoesnotneedtobetyped,butthesummarydoes.
Handinthedataasyoucollectedit. (Eitherattachyourtallysheetoranenvelopecontainingyour
questionnaires.)
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642
APPENDIX
14.4.4PartnerProject:HypothesisTesting-WordProblem
7
14.4.4.1StudentLearningObjectives
 Thestudentwillwrite,edit,andsolveahypothesistestingwordproblem.
14.4.4.2Instructions
WriteanoriginalhypothesistestingproblemforeitherONEpopulationmeanorONEpopulationpropor-
tion.Asyoucompleteeachtask,checkitoff.Answerallquestionsinyoursummary.Lookatthehomework
fortheHypothesisTesting:SingleMeanandSingleProportionchapterforexamples(poems,twoactsofa
play,aworkrelatedproblem).Theproblemswithnamesattachedtothemareproblemswrittenbystudents
inpastquarters. Someotherexamplesthatarenotinthehomeworkinclude: : asoccerhypothesistesting
poster,acartoon,anewsreports,achildren’sstory,asong.
____ Yourproblemmustbeoriginalandcreative. ItalsomustbeinproperEnglish. IfEnglishisdifficult
foryou,havesomeoneedityourproblem.
____ Yourproblemmustbeatleast½page,typedandsingledspaced.ThisDOESNOTincludethedata.
Datawillmaketheproblemlongerandthatisfine.Forthisproblem,thedataandstorymaybereal
orfictional.
____ Inthenarrativeoftheproblem,makeitveryclearwhatthenullandalternativehypothesesare.
____ YoursamplesizemustbeLARGERTHAN50(evenifitisfictional).
____ Stateinyourproblemhowyouwillcollectyourdata.
____ Includeyourdatawithyourwordproblem.
____ Statethestatisticsthatarearesultofyourdatacollection: samplesize,samplemean, , andsample
standarddeviation,ORsamplesizeandnumberofsuccesses.
____ Createagraphthatillustratesyourproblem. Thismaybeapieorbarchartormaybeahistogram
orboxplot,dependingonthenatureofyourdata. Produceagraphthatmakessenseforyourdata
andgivesusefulvisualinformationaboutyourdata.Youmayneedtolookatseveraltypesofgraphs
beforeyoudecidewhichisthemostappropriateforyourproblem.
____ Make2copiesoftheappropriatesolutionsheet.
____ Recordthehypothesistestonthesolutionsheet,basedonyourproblem.DoaDRAFTsolutionfirst
ononeofthesolutionsheetsandcheckitovercarefully. Makeyourdecisionusinga5%levelof
significance.Includethe95%confidenceintervalonthesolution
14.4.4.3AssignmentChecklist
Youneedtoturninthefollowingtyped(12point)andstapledpacketforyourfinalproject:
____ Coversheetcontainingyourname,thenameofyourproblem,andthedate
____ Theproblem
____ Datafortheproblem
____ Solutionsheetneatlyandcompletelyfilledout.Thesolutionsheetdoesnotneedtobetyped.
____ Graphicrepresentationofthedata,createdfollowingtheguidelinesdiscussedabove. Includeonly
graphsthatareappropriateanduseful.
____ Sentencesinterpretingtheresultsofthehypothesistestandtheconfidenceintervalinthecontext
ofthesituationintheproject.
7
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APPENDIX
643
14.4.5GroupProject:BivariateData,LinearRegression,andUnivariateData
8
14.4.5.1StudentLearningObjectives
 Thestudentswillcollectabivariatedatasamplethroughtheuseofappropriatesamplingtechniques.
 Thestudentwillattempttofitthedatatoalinearmodel.
 Thestudentwilldeterminetheappropriatenessoflinearfitofthemodel.
 Thestudentwillanalyzeandgraphunivariatedata.
14.4.5.2Instructions
1. Asyoucompleteeachtaskbelow,checkitoff.Answerallquestionsinyourintroductionorsummary.
2. Checkyourcoursecalendarforintermediateandfinalduedates.
3. Graphsmaybeconstructedbyhandorbycomputer,unlessyourinstructorinformsyouotherwise.
Allgraphsmustbeneatandaccurate.
4. Allotherresponsesmustbedoneonthecomputer.
5. Neatnessandqualityofexplanationsareusedtodetermineyourfinalgrade.
14.4.5.3PartI:BivariateData
Introduction
____ Statethebivariatedatayourgroupisgoingtostudy.
E
XAMPLES
:Herearetwoexamples,butyoumayNOTusethem:heightvs.weightandage
vs.runningdistance.
____ Describehowyourgroupisgoingtocollectthedata(forinstance,collectdatafromtheweb,survey
studentsoncampus).
____ Describeyoursamplingtechniqueindetail. Use e cluster, stratified, systematic, or simplerandom
sampling(usingarandomnumbergenerator)sampling.ConveniencesamplingisNOTacceptable.
____ Conductyoursurvey.Yournumberofpairsmustbeatleast30.
____ Printoutacopyofyourdata.
Analysis
____ Onaseparatesheetofpaperconstructascatterplotofthedata.Labelandscalebothaxes.
____ Statetheleastsquareslineandthecorrelationcoefficient.
____ Onyourscatterplot,inadifferentcolor,constructtheleastsquaresline.
____ Isthecorrelationcoefficientsignificant?Explainandshowhowyoudeterminedthis.
____ Interprettheslopeofthelinearregressionlineinthecontextofthedatainyourproject. Relatethe
explanationtoyourdata,andquantifywhattheslopetellsyou.
____ Doestheregressionlineseemtofitthedata?Whyorwhynot?Ifthedatadoesnotseemtobelinear,
explainifanyothermodelseemstofitthedatabetter.
____ Arethereanyoutliers? Ifso,whatarethey? Showyourworkinhowyouusedthepotentialoutlier
formulaintheLinearRegressionandCorrelationchapter(sinceyouhavebivariatedata)todetermine
whetherornotanypairsmightbeoutliers.
8
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644
APPENDIX
14.4.5.4PartII:UnivariateData
Inthissection,youwillusethedataforONEvariableonly. Pickthevariablethatismoreinterestingto
analyze. Forexample:ifyourindependentvariableissequentialdatasuchasyearwith30yearsandone
pieceofdataperyear,yourx-valuesmightbe1971,1972,1973,1974,...,2000.Thiswouldnotbeinteresting
toanalyze.Inthatcase,choosetousethedependentvariabletoanalyzeforthispartoftheproject.
_____ Summarizeyourdatainachartwithcolumnsshowingdatavalue,frequency,relativefrequency,
andcumulativerelativefrequency.
_____ Answerthefollowing,roundedto2decimalplaces:
1. Samplemean=
2. Samplestandarddeviation=
3. Firstquartile=
4. Thirdquartile=
5. Median=
6. 70thpercentile=
7. Valuethatis2standarddeviationsabovethemean=
8. Valuethatis1.5standarddeviationsbelowthemean=
_____ Constructahistogramdisplayingyourdata. Groupyourdatainto6–10intervalsofequalwidth.
Pickregularlyspacedintervalsthatmakesenseinrelationtoyourdata.Forexample,doNOTgroup
databyageas20-26,27-33,34-40,41-47,48-54,55-61. ..Instead,maybeuseagegroups19.5-24.5,24.5-
29.5,...or19.5-29.5,29.5-39.5,39.5-49.5,...
_____ Incompletesentences,describetheshapeofyourhistogram.
_____ Arethereanypotentialoutliers? Whichvaluesarethey? ? Showyourworkandcalculationsasto
howyouusedthepotentialoutlierformulainchapter2(sinceyouarenowusingunivariatedata)to
determinewhichvaluesmightbeoutliers.
_____ Constructaboxplotofyourdata.
_____ Doesthemiddle50%ofyourdataappeartobeconcentratedtogetherorspreadout? Explainhow
youdeterminedthis.
_____ LookingatboththehistogramANDtheboxplot,discussthedistributionofyourdata.Forexample:
howdoesthespreadofthemiddle50%ofyourdatacomparetothespreadoftherestofthedatarep-
resentedintheboxplot;howdoesthiscorrespondtoyourdescriptionoftheshapeofthehistogram;
howdoesthegraphicaldisplayshowanyoutliersyoumayhavefound;doesthehistogramshowany
gapsinthedatathatarenotvisibleintheboxplot;arethereanyinterestingfeaturesofyourdatathat
youshouldpointout.
14.4.5.5DueDates
• PartI,Intro:__________(keepacopyforyourrecords)
• PartI,Analysis:__________(keepacopyforyourrecords)
• EntireProject,typedandstapled:__________
____ Coversheet:names,classtime,andnameofyourstudy.
____ PartI:labelthesections“Intro”and“Analysis.”
____ PartII:
____ Summarypagecontainingseveralparagraphswrittenincompletesentencesdescribingtheex-
periment,includingwhatyoustudiedandhowyoucollectedyourdata. Thesummarypage
shouldalsoincludeanswerstoALLthequestionsaskedabove.
____ Allgraphsrequestedintheproject.
____ Allcalculationsrequestedtosupportquestionsindata.
____ Description:whatyoulearnedbydoingthisproject,whatchallengesyouhad,howyouover-
camethechallenges.
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APPENDIX
645
NOTE
IncludeanswerstoALLquestionsasked,evenifnotexplicitlyrepeatedintheitems
above.
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646
APPENDIX
14.5SolutionSheets
14.5.1SolutionSheet:HypothesisTestingforSingleMeanandSingleProportion
9
ClassTime:
Name:
a. H
o
:
b. H
a
:
c. Inwords,CLEARLYstatewhatyourrandomvariable
XorP’represents.
d. Statethedistributiontouseforthetest.
e. Whatistheteststatistic?
f. Whatisthep-value?In1–2completesentences,explainwhatthep-valuemeansforthisproblem.
g. Usethepreviousinformationtosketchapictureofthissituation.CLEARLY,labelandscalethehorizon-
talaxisandshadetheregion(s)correspondingtothep-value.
Figure14.1
h. Indicatethecorrectdecision(“reject”or“donotreject”thenullhypothesis),thereasonforit,andwrite
anappropriateconclusion,usingcompletesentences.
i. Alpha:
ii. Decision:
iii. Reasonfordecision:
iv. Conclusion:
i. Constructa95%ConfidenceIntervalforthetruemeanorproportion. Includeasketchofthegraphof
thesituation.LabelthepointestimateandthelowerandupperboundsoftheConfidenceInterval.
Figure14.2
9
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APPENDIX
647
14.5.2 Solution n Sheet: : Hypothesis s Testing for Two Means, , Paired d Data, , and d Two
Proportions
10
ClassTime:
Name:
a. H
o
:_______
b. H
a
:_______
c. Inwords,clearlystatewhatyourrandomvariable
X
1
X
2
,P
1
’ P
2
’-or
X
d
represents.
d. Statethedistributiontouseforthetest.
e. Whatistheteststatistic?
f. Whatisthep-value?In1–2completesentences,explainwhatthep-valuemeansforthisproblem.
g. Usethepreviousinformationtosketchapictureofthissituation.CLEARLYlabelandscalethehorizon-
talaxisandshadetheregion(s)correspondingtothep-value.
Figure14.3
h. Indicatethecorrectdecision(“reject”or“donotreject”thenullhypothesis),thereasonforit,andwrite
anappropriateconclusion,usingcompletesentences.
i. Alpha:
ii. Decision:
iii. Reasonfordecision:
iv. Conclusion:
i. Incompletesentences,explainhowyoudeterminedwhichdistributiontouse.
10
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648
APPENDIX
14.5.3SolutionSheet:TheChi-SquareDistribution
11
ClassTime:
Name:
a. H
o
:_______
b. H
a
:_______
c. Whatarethedegreesoffreedom?
d. Statethedistributiontouseforthetest.
e. Whatistheteststatistic?
f. Whatisthep-value?In1–2completesentences,explainwhatthep-valuemeansforthisproblem.
g. Usethepreviousinformationtosketchapictureofthissituation.Clearlylabelandscalethehorizontal
axisandshadetheregion(s)correspondingtothep-value.
Figure14.4
h. Indicatethecorrectdecision(“reject”or“donotreject”thenullhypothesis)andwriteappropriatecon-
clusions,usingcompletesentences.
i. Alpha:
ii. Decision:
iii. Reasonfordecision:
iv. Conclusion:
11
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APPENDIX
649
14.5.4SolutionSheet:FDistributionandOne-WayANOVA
12
ClassTime:
Name:
a. H
o
:
b. H
a
:
c. df(n)=______df(d)=_______
d. Statethedistributiontouseforthetest.
e. Whatistheteststatistic?
f. Whatisthep-value?
g. Usethepreviousinformationtosketchapictureofthissituation.Clearlylabelandscalethehorizontal
axisandshadetheregion(s)correspondingtothep-value.
Figure14.5
h. Indicatethecorrectdecision(“reject”or“donotreject”thenullhypothesis)andwriteappropriatecon-
clusions,usingcompletesentences.
i. Alpha:
ii. Decision:
iii. Reasonfordecision:
iv. Conclusion:
12
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650
APPENDIX
14.6EnglishPhrasesWrittenMathematically
13
14.6.1EnglishPhrasesWrittenMathematically
WhentheEnglishsays:
Interpretthisas:
Xisatleast4.
X4
TheminimumofXis4.
X4
Xisnolessthan4.
X4
Xisgreaterthanorequalto4.
X4
Xisatmost4.
X4
ThemaximumofXis4.
X4
Xisnomorethan4.
X4
Xislessthanorequalto4.
X4
Xdoesnotexceed4.
X4
Xisgreaterthan4.
X>4
Xismorethan4.
X>4
Xexceeds4.
X>4
Xislessthan4.
X<4
TherearefewerXthan4.
X<4
Xis4.
X=4
Xisequalto4.
X=4
Xisthesameas4.
X=4
Xisnot4.
X6=4
Xisnotequalto4.
X6=4
Xisnotthesameas4.
X6=4
Xisdifferentthan4.
X6=4
Table14.16
13
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