41
1.11.5DiscussionQuestions
Discussthefollowingquestionsandthenanswerincompletesentences.
Exercise1.11.7
Listtworeasonswhythedatamaydiffer.
Exercise1.11.8
Canyoutellifoneresearcheriscorrectandtheotheroneisincorrect?Why?
Exercise1.11.9
Wouldyouexpectthedatatobeidentical?Whyorwhynot?
Exercise1.11.10
Howcouldtheresearchersgatherrandomdata?
Exercise1.11.11
Supposethatthe first researcherconductedhissurveybyrandomlychoosingonestate inthe
nationandthenrandomlypicking40patientsfromthatstate.Whatsamplingmethodwouldthat
researcherhaveused?
Exercise1.11.12
Supposethatthesecondresearcherconductedhissurveybychoosing40patientsheknew.What
samplingmethodwouldthatresearcherhaveused? Whatconcernswouldyouhaveaboutthis
dataset,baseduponthedatacollectionmethod?
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42
CHAPTER1. SAMPLINGANDDATA
1.12Homework
12
Exercise1.12.1
(Solutiononp.55.)
Foreachitembelow:
i. Identifythetypeofdata(quantitative-discrete,quantitative-continuous,orqualitative)that
wouldbeusedtodescribearesponse.
ii. Giveanexampleofthedata.
a. Numberofticketssoldtoaconcert
b. Amountofbodyfat
c. Favoritebaseballteam
d. Timeinlinetobuygroceries
e. NumberofstudentsenrolledatEvergreenValleyCollege
f. Most–watchedtelevisionshow
g. Brandoftoothpaste
h. Distancetotheclosestmovietheatre
i. AgeofexecutivesinFortune500companies
j. Numberofcompetingcomputerspreadsheetsoftwarepackages
Exercise1.12.2
Fiftypart-timestudentswereaskedhowmanycoursestheyweretakingthisterm. The(incom-
plete)resultsareshownbelow:
Part-timeStudentCourseLoads
#ofCourses
Frequency
RelativeFrequency
Cumulative
Relative
Frequency
1
30
0.6
2
15
3
Table1.22
a. Fillintheblanksinthetableabove.
b. Whatpercentofstudentstakeexactlytwocourses?
c. Whatpercentofstudentstakeoneortwocourses?
Exercise1.12.3
(Solutiononp.55.)
Sixtyadultswithgumdiseasewereaskedthenumberoftimesperweektheyusedtoflossbefore
theirdiagnoses.The(incomplete)resultsareshownbelow:
FlossingFrequencyforAdultswithGumDisease
#FlossingperWeek
Frequency
RelativeFrequency
CumulativeRelativeFreq.
0
27
0.4500
1
18
3
0.9333
6
3
0.0500
7
1
0.0167
12
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43
Table1.23
a. Fillintheblanksinthetableabove.
b. Whatpercentofadultsflossedsixtimesperweek?
c. Whatpercentflossedatmostthreetimesperweek?
Exercise1.12.4
Afitnesscenterisinterestedinthemeanamountoftimeaclientexercisesinthecentereachweek.
Definethefollowingintermsofthestudy.Giveexampleswhereappropriate.
a. Population
b. Sample
c. Parameter
d. Statistic
e. Variable
f. Data
Exercise1.12.5
(Solutiononp.55.)
Skiresortsareinterestedinthemeanagethatchildrentaketheirfirstskiandsnowboardlessons.
Theyneedthisinformationtooptimallyplantheirskiclasses.Definethefollowingintermsofthe
study.Giveexampleswhereappropriate.
a. Population
b. Sample
c. Parameter
d. Statistic
e. Variable
f. Data
Exercise1.12.6
Acardiologistisinterestedinthemeanrecoveryperiodfor herpatientswhohave hadheart
attacks.Definethefollowingintermsofthestudy.Giveexampleswhereappropriate.
a. Population
b. Sample
c. Parameter
d. Statistic
e. Variable
f. Data
Exercise1.12.7
(Solutiononp.56.)
Insurancecompaniesareinterestedinthemeanhealthcostseachyearfortheirclients,sothat
theycandeterminethecostsofhealthinsurance.Definethefollowingintermsofthestudy.Give
exampleswhereappropriate.
a. Population
b. Sample
c. Parameter
d. Statistic
e. Variable
f. Data
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44
CHAPTER1. SAMPLINGANDDATA
Exercise1.12.8
Apoliticianisinterestedintheproportionofvotersinhisdistrictthatthinkheisdoingagood
job.Definethefollowingintermsofthestudy.Giveexampleswhereappropriate.
a. Population
b. Sample
c. Parameter
d. Statistic
e. Variable
f. Data
Exercise1.12.9
(Solutiononp.56.)
Amarriagecounselorisinterestedintheproportiontheclientsshecounselsthatstaymarried.
Definethefollowingintermsofthestudy.Giveexampleswhereappropriate.
a. Population
b. Sample
c. Parameter
d. Statistic
e. Variable
f. Data
Exercise1.12.10
Politicalpollstersmaybeinterestedintheproportionofpeople that willvoteforaparticular
cause.Definethefollowingintermsofthestudy.Giveexampleswhereappropriate.
a. Population
b. Sample
c. Parameter
d. Statistic
e. Variable
f. Data
Exercise1.12.11
(Solutiononp.56.)
Amarketingcompanyisinterestedintheproportionofpeoplethatwillbuyaparticularproduct.
Definethefollowingintermsofthestudy.Giveexampleswhereappropriate.
a. Population
b. Sample
c. Parameter
d. Statistic
e. Variable
f. Data
Exercise1.12.12
Airlinecompaniesareinterestedintheconsistencyofthenumberofbabiesoneachflight,sothat
theyhaveadequatesafetyequipment.Supposeanairlineconductsasurvey.OverThanksgiving
weekend,itsurveys6flightsfromBostontoSaltLakeCitytodeterminethenumberofbabieson
theflights.Itdeterminestheamountofsafetyequipmentneededbytheresultofthatstudy.
a. Usingcompletesentences,listthreethingswrongwiththewaythesurveywasconducted.
b. Usingcompletesentences,listthreewaysthatyouwouldimprovethesurveyifitweretobe
repeated.
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45
Exercise1.12.13
Supposeyouwanttodeterminethemeannumberofstudentsperstatisticsclassinyourstate.
Describeapossiblesamplingmethodin3–5completesentences.Makethedescriptiondetailed.
Exercise1.12.14
Supposeyouwanttodeterminethemeannumberofcansofsodadrunkeachmonthbypersons
intheirtwenties. Describeapossible e samplingmethodin3-5completesentences. . Makethe
descriptiondetailed.
Exercise1.12.15
(Solutiononp.56.)
771distancelearningstudentsat LongBeachCityCollege responded tosurveysinthe2010-
11 academic year. . Highlights s ofthe e summary y report t are listed inthe e table e below. . (Source:
http://de.lbcc.edu/reports/2010-11/future/highlights.html#focus).
LBCCDistanceLearningSurveyResults
Havecomputerathome
96%
Unabletocometocampusforclasses
65%
Age41orover
24%
WouldlikeLBCCtooffermoreDLcourses
95%
TookDLclassesduetoadisability
17%
Liveatleast16milesfromcampus
13%
TookDLcoursestofulfilltransferrequirements
71%
Table1.24
a. Whatpercentofthestudentssurveyeddonothaveacomputerathome?
b. Abouthowmanystudentsinthesurveyliveatleast16milesfromcampus?
c. IfthesamesurveywasdoneatGreatBasinCollegeinElko,Nevada,doyouthinkthepercent-
ageswouldbethesame?Why?
Exercise1.12.16
NineteenimmigrantstotheU.Swereaskedhowmanyyears,tothenearestyear,theyhavelived
intheU.S.Thedataareasfollows:
2;5;7;2;2;10;20;15;0;7;0;20;5;12;15;12;4;5;10
Thefollowingtablewasproduced:
AvailableforfreeatConnexions<http://cnx.org/content/col10522/1.40>
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46
CHAPTER1. SAMPLINGANDDATA
FrequencyofImmigrantSurveyResponses
Data
Frequency
RelativeFrequency
CumulativeRelativeFrequency
0
2
2
19
0.1053
2
3
3
19
0.2632
4
1
1
19
0.3158
5
3
3
19
0.1579
7
2
2
19
0.5789
10
2
2
19
0.6842
12
2
2
19
0.7895
15
1
1
19
0.8421
20
1
1
19
1.0000
Table1.25
a. Fixthe errorsonthetable. . Also, , explainhowsomeone mighthave arrivedattheincorrect
number(s).
b. Explainwhatiswrongwiththisstatement: “47percentofthepeoplesurveyedhavelivedin
theU.S.for5years.”
c. Fixthestatementabovetomakeitcorrect.
d. WhatfractionofthepeoplesurveyedhavelivedintheU.S.5or7years?
e. WhatfractionofthepeoplesurveyedhavelivedintheU.S.atmost12years?
f. WhatfractionofthepeoplesurveyedhavelivedintheU.S.fewerthan12years?
g. WhatfractionofthepeoplesurveyedhavelivedintheU.S.from5to20years,inclusive?
Exercise1.12.17
A“randomsurvey”wasconductedof3274peopleofthe“microprocessorgeneration”(people
bornsince1971,theyearthemicroprocessorwasinvented). Itwasreportedthat t 48%ofthose
individualssurveyed stated that iftheyhad$2000to spend, , theywould d use it for computer
equipment. Also,66%ofthosesurveyedconsideredthemselvesrelativelysavvycomputerusers.
(Source:SanJoseMercuryNews)
a. Doyouconsiderthesamplesizelargeenoughforastudyofthistype?Whyorwhynot?
b. Basedonyour“gutfeeling,”doyoubelievethepercentsaccuratelyreflecttheU.S.population
forthoseindividualsbornsince1971?Ifnot,doyouthinkthepercentsofthepopulationare
actuallyhigherorlowerthanthesamplestatistics?Why?
Additionalinformation:ThesurveywasreportedbyIntelCorporationofindividualswhovisited
theLosAngelesConventionCentertoseetheSmithsonianInstiture’sroadshowcalled“America’s
Smithsonian.”
c. Withthisadditionalinformation, doyoufeelthatalldemographicandethnicgroupswere
equallyrepresentedattheevent?Whyorwhynot?
d. Withtheadditionalinformation,commentonhowaccuratelyyouthinkthesamplestatistics
reflectthepopulationparameters.
Exercise1.12.18
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47
a. Listsomepracticaldifficultiesinvolvedingettingaccurateresultsfromatelephonesurvey.
b. Listsomepracticaldifficultiesinvolvedingettingaccurateresultsfromamailedsurvey.
c. Withyourclassmates, brainstormsomewaysto overcometheseproblemsifyouneededto
conductaphoneormailsurvey.
1.12.1Trythesemultiplechoicequestions
Thenextfourquestionsrefertothefollowing:ALakeTahoeCommunityCollegeinstructorisinterested
inthemeannumberofdaysLakeTahoeCommunityCollegemathstudentsareabsentfromclassduringa
quarter.
Exercise1.12.19
(Solutiononp.56.)
Whatisthepopulationsheisinterestedin?
A. AllLakeTahoeCommunityCollegestudents
B. AllLakeTahoeCommunityCollegeEnglishstudents
C. AllLakeTahoeCommunityCollegestudentsinherclasses
D. AllLakeTahoeCommunityCollegemathstudents
Exercise1.12.20
(Solutiononp.56.)
Considerthefollowing:
X=numberofdaysaLakeTahoeCommunityCollegemathstudentisabsent
Inthiscase,Xisanexampleofa:
A. Variable
B. Population
C. Statistic
D. Data
Exercise1.12.21
(Solutiononp.56.)
Theinstructortakeshersamplebygatheringdataon5randomlyselectedstudentsfromeach
LakeTahoeCommunityCollegemathclass.Thetypeofsamplingsheusedis
A. Clustersampling
B. Stratifiedsampling
C. Simplerandomsampling
D. Conveniencesampling
Exercise1.12.22
(Solutiononp.56.)
Theinstructor’ssampleproducesanmeannumberofdaysabsentof3.5days. Thisvalueisan
exampleofa
A. Parameter
B. Data
C. Statistic
D. Variable
Thenexttwoquestionsrefertothefollowingrelativefrequencytableonhurricanesthathavemadedirect
hitsonthe U.Sbetween1851and2004. . Hurricanesare e givenastrengthcategoryratingbasedonthe
minimumwindspeedgeneratedbythestorm.(http://www.nhc.noaa.gov/gifs/table5.gif13)
13
http://www.nhc.noaa.gov/gifs/table5.gif
AvailableforfreeatConnexions<http://cnx.org/content/col10522/1.40>
48
CHAPTER1. SAMPLINGANDDATA
FrequencyofHurricaneDirectHits
Category
NumberofDirectHits
RelativeFrequency
CumulativeFrequency
1
109
0.3993
0.3993
2
72
0.2637
0.6630
3
71
0.2601
4
18
0.9890
5
3
0.0110
1.0000
Total=273
Table1.26
Exercise1.12.23
(Solutiononp.56.)
Whatistherelativefrequencyofdirecthitsthatwerecategory4hurricanes?
A. 0.0768
B. 0.0659
C. 0.2601
D. Notenoughinformationtocalculate
Exercise1.12.24
(Solutiononp.56.)
WhatistherelativefrequencyofdirecthitsthatwereATMOSTacategory3storm?
A. 0.3480
B. 0.9231
C. 0.2601
D. 0.3370
Thenextthreequestionsrefertothefollowing:Astudywasdonetodeterminetheage,numberoftimes
perweekandtheduration(amountoftime)ofresidentuseofalocalparkinSanJose. Thefirsthousein
theneighborhoodaroundtheparkwasselectedrandomlyandthenevery8thhouseintheneighborhood
aroundtheparkwasinterviewed.
Exercise1.12.25
(Solutiononp.56.)
“‘Numberoftimesperweek”’iswhattypeofdata?
A. qualitative
B. quantitative-discrete
C. quantitative-continuous
Exercise1.12.26
(Solutiononp.56.)
Thesamplingmethodwas:
A. simplerandom
B. systematic
C. stratified
D. cluster
Exercise1.12.27
(Solutiononp.56.)
“‘Duration(amountoftime)”’iswhattypeofdata?
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49
A. qualitative
B. quantitative-discrete
C. quantitative-continuous
Exercises28and29arenotmultiplechoiceexercises.
Exercise1.12.28
(Solutiononp.56.)
Namethesamplingmethodusedineachofthefollowingsituations:
A. Awomanintheairportishandingoutquestionnairestotravelersaskingthemtoevaluatethe
airport’sservice.Shedoesnotasktravelerswhoarehurryingthroughtheairportwiththeir
handsfullofluggage,butinsteadasksalltravelerssittingneargatesandwhoarenottaking
napswhiletheywait.
B. Ateacherwantstoknowifherstudentsaredoinghomeworksosherandomlyselectsrows2
and5,andthencallsonallstudentsinrow2andallstudentsinrow5topresentthesolution
tohomeworkproblemstotheclass.
C. Themarketingmanagerforanelectronicschainstorewantsinformationabouttheagesofits
customers.Overthenexttwoweeks,ateachstorelocation,100randomlyselectedcustomers
aregivenquestionnairestofilloutwhichasksforinformationaboutage,aswellasabout
othervariablesofinterest.
D. Thelibrarianatapubliclibrarywantstodeterminewhatproportionofthelibraryusersare
children.Thelibrarianhasatallysheetonwhichshemarkswhetherthebooksarechecked
outbyanadultorachild.Sherecordsthisdataforevery4thpatronwhochecksoutbooks.
E. Apoliticalpartywantstoknowthereactionofvoterstoadebatebetweenthecandidates.The
dayafterthedebate,theparty’spollingstaffcalls1200randomlyselectedphonenumbers.
Ifaregisteredvoteranswersthephoneorisavailabletocometothephone,thatregistered
voter isaskedwhohe/she intendsto votefor andwhetherthedebate changed his/her
opinionofthecandidates.
**ContributedbyRobertaBloom
Exercise1.12.29
(Solutiononp.57.)
Severalonline textbookretailersadvertise thattheyhave lower pricesthanon-campusbook-
stores.However,animportantfactoriswhethertheinternetretailersactuallyhavethetextbooks
thatstudentsneedinstock.Studentsneedtobeabletogettextbookspromptlyatthebeginningof
thecollegeterm.Ifthebookisnotavailable,thenastudentwouldnotbeabletogetthetextbook
atall,ormightgetadelayeddeliveryifthebookisbackordered.
A college newspaper r reporter is investigating textbook k availability at t online retailers. . He
decides to o investigate one textbook for each h of f the following 7 subjects: : calculus, , biology,
chemistry, physics, statistics,geology,andgeneralengineering. . Heconsultstextbookindustry
salesdataandselectsthe mostpopularnationallyusedtextbookineachofthesesubjects. . He
visitswebsitesforarandomsampleofmajoronlinetextbooksellersandlooksupeachofthese7
textbookstoseeiftheyareavailableinstockforquickdeliverythroughtheseretailers. Basedon
hisinvestigation,hewritesanarticleinwhichhedrawsconclusionsabouttheoverallavailability
ofallcollegetextbooksthroughonlinetextbookretailers.
Write an analysis ofhis studythat t addressesthe followingissues: : Ishis s sample representa-
tiveofthepopulationofallcollegetextbooks? Explainwhyorwhynot. Describesomepossible
sourcesofbiasinthisstudy,andhowitmightaffecttheresultsofthestudy. Givesomesugges-
tionsaboutwhatcouldbedonetoimprovethestudy.
**ContributedbyRobertaBloom
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50
CHAPTER1. SAMPLINGANDDATA
1.13Lab1:DataCollection
14
ClassTime:
Names:
1.13.1StudentLearningOutcomes
 Thestudentwilldemonstratethesystematicsamplingtechnique.
 ThestudentwillconstructRelativeFrequencyTables.
 Thestudentwillinterpretresultsandtheirdifferencesfromdifferentdatagroupings.
1.13.2MovieSurvey
Askfiveclassmatesfromadifferentclasshowmanymoviestheysawlastmonthatthetheater. Donot
includerentedmovies.
1. Recordthedata
2. Inclass,randomlypickoneperson. . Ontheclasslist,markthatperson’sname. . Movedownfour
people’snamesontheclasslist.Markthatperson’sname.Continuedoingthisuntilyouhavemarked
12people’snames. Youmayneedtogobacktothestartofthelist. Foreachmarkednamerecord
belowthefivedatavalues.Younowhaveatotalof60datavalues.
3. Foreachnamemarked,recordthedata:
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
Table1.27
1.13.3OrdertheData
Completethetworelativefrequencytablesbelowusingyourclassdata.
14
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