ISBN: 9781394336623
Section1.1Solutions
1.1 (a)Thecasesarethepeoplewhoareaskedthequestion.
(b)Thevariableiswhethereachpersonsupportsthelawornot.Itiscategorical.
1.2 (a)Thecasesarethe100stocks.
(b)Thevariableisthepercentagechange,whichisanumericalquantity,foreachofthestocks.Itis quantitative.
1.3 (a)Thecasesaretheteenagersinthesample.
(b)Thevariableistheresult(yesorno)indicatingwhethereachteenagereatsatleastfiveservingsaday offruitsandvegetables.Itiscategorical.
1.4 (a)Thecasesarethebunchesofbananasinthesample.
(b)Thevariableisthenumberofdaysuntilthebananasgobad.Itisquantitative.
1.5 (a)The10beamsthatweretested.
(b)Theforceatwhicheachbeambroke.Itisquantitative.
1.6 (a)Thecasesarecountriesoftheworld.
(b)Thevariableiswhetherornottheliteracyrateisover75%.Itiscategorical.
1.7 Sinceweexpectthenumberofyearssmokingcigarettestoimpactlungcapacity,wethinkofthenumber ofyearssmokingastheexplanatoryvariableandthelungcapacityastheresponsevariable.
1.8 Sinceweexpecttheamountoffertilizerusedtoimpacttheyield(andnottheotherwayaround),we thinkoftheamountoffertilizerastheexplanatoryvariableandtheyieldofthecropastheresponsevariable.
1.9 Ingestingmorealcoholicdrinkswillcausethelevelofalcoholinthebloodtoincrease,sothenumberof drinksistheexplanatoryvariableandbloodalcoholcontentistheresponse.
1.10 Theworldrecordtimewillcontinuetodecreaseastheyearsgobysoweexpecttheyeartoimpact marathonrecordtime.Wethinkoftheyearastheexplanatoryvariableandtherecordtimeastheresponse variable.
1.11 (a) Year and HigherSAT arecategorical.Theothersixvariablesareallquantitative,although Siblings mightbeclassifiedaseithercategoricalorquantitative.
(b)Therearemanypossibleanswers,suchas“Whatproportionofthestudentsarefirstyearstudents?” or“Whatistheaverageweightofthesestudents?”
(c)Therearemanypossibleanswers,suchas“Doseniorsseemtoweighmorethanfirstyearstudents?” or“DostudentswithhighVerbalSATscoresseemtoalsohavehighMathSATscores?”
1.12 (a)Inadditiontotheidentificationcolumn, Country,thereare24variables.Weseethat Developed isacategoricalvariable,whiletheother23variablesareallquantitative.
(b)Therearemanypossibleanswers,suchas“Whatistheaveragelifeexpectancyforallcountriesofthe world?”or“Whatproportionofcountriesaredeveloped?”
(c)Therearemanypossibleanswers,suchas“Docountrieswithagreaterlandareahavealargerpercent rural?”or“Docountriesthatspendarelativelylargeamountonthemilitaryspendarelativelysmall amountonhealthcare?”or“Dodevelopedcountrieshavealongerlifeexpectancythandeveloping countries?”
1.13 (a)Theexplanatoryvariableisthetypeofformatinwhichthestoryispresented.Itiscategorical, withthreecategories(audio,illustrated,andanimated).
(b)Theresponsevariableisthemeasureofbrainconnectivity.Itisquantitative.
(c)Thecasesarethefour-year-oldsinthestudy,sothereare27cases.
1.14 (a)ThecasesarefemalegamersinGreatBritain.
(b)Therearethreevariablesmentioned:Whetherthegamershadreceivedobscenemessages(categorical), howmanyhoursaweektheyplayed(quantitative),andwhethertheyfelttherewereenoughstrong femalecharactersingames(categorical).
(c)Thereare1151casesand3variables,sothedatasetwillhave1151rowsand3columns.
1.15 (a)Thecasesarethestudentsinthecollegephysicsclass.
(b)Thereare3variables:Whetherthestudentwasassignedtoanactiveorpassivelearningclass,the measureofhowmuchthestudentthoughttheylearned,andthescoreofactuallearningonthetest. Theclassassignmentiscategorical,whiletheothertwoarequantitative.
(c)Theclassassignment(activeorpassive)istheexplanatoryvariable,whilethetwomeasuresoflearning areresponsevariables.
(d)Thestudentsinthephysicsclassarethecases,sothereare154+142=296cases.Therearethree variables,sothedatasetwillhave296rowsand3columns.
1.16 Thereareatleasttwovariables.Onevariableiswhetherornotthespiderengagedinmock-sex.This variableiscategoricalandtheexplanatoryvariable.Anothervariableislengthoftimetoreachthepointof realmatingoncethespiderisfullymature.Thisvariableisquantitativeandtheresponsevariable.
1.17 Theindividualcasesarethelakesfromwhichwatersamplesweretaken.Foreachlakeinthesample, werecordtheconcentrationofestrogeninthewaterandthefertilityleveloffish.Botharequantitative variables.
1.18 Therearetwovariables.Onevariableindicatesthepresenceorabsenceofthegenevariantandthe secondvariableindicateswhichofthethreeethnicgroupstheindividualbelongsto.Bothvariablesare categorical.
1.19 (a)Thereare10cases,correspondingtothe10cities.Thetwovariablesarepopulation,whichis quantitative,andthehemispherethecityisin,whichiscategorical.
(b)Weneedtwocolumns,oneforeachvariable.Thecolumnscanbeineitherorder.Seethetable.
1.20 (a)Thereare7cases,representingthesevenpigeons.Therearetwovariables.Oneisthesexofthe pigeon,whichiscategorical,andtheotheristhespeedofthepigeon,whichisquantitative.
(b)Thedatasetwillhave7rowsand2columns.Seethetable.(Thesevencasescanbelistedinany order.)
Sex Speed
Hen 1676
Hen 1452
Hen 1449
Cock 1458
Cock 1435
Cock 1418
Cock 1413
1.21 (a)Thecasesarethehomingpigeons,sothereare1412ofthem.
(b)Thereare4variables.Twoarecategorical(loft,sex)andtwoarequantitative(distance,speed).
(c)Thedatasetwillhave1412rows(oneforeachpigeon)and4columns(oneforeachvariable).
1.22 Onevariableiswhethereachmalewasfedahigh-fatdietoranormaldiet.Thisistheexplanatory variableanditiscategorical.Theresponsevariableiswhetherornotthedaughtersdevelopedmetabolic syndrome,whichisalsocategorical.
1.23 Onevariableiswhethertheyoungfemalemicelivedinanenrichedenvironmentornot.Thisisthe explanatoryvariableanditiscategorical.Theresponsevariableishowfasttheoffspringlearnedtonavigate mazesandisquantitative.
1.24 (a)Themodeoftransportation(e.g.,bus,car,walk)givesacategoricalvalueforeachstudent.
(b)Theansweraboutallergies(yesorno)givesacategoricalvalueforeachstudent.
(c)Theproportionofstudentsinthesamplewhoarevegetariansisasinglenumber,basedonallofthe students,anddoesnotgiveavalueforeachindividualstudent.Itisnotavariableforthedataset.
(d)Thenumberofhoursworkedatapaidjobgivesaquantitativevalueforeachstudent.
(e)Thedifferenceinhoursofsleeponschoolnightsandnon-schoolnightsgivesaquantitativevaluefor eachstudent.
(f)Themaximumtimetogettoschoolisasinglenumber,basedonallofthestudents,anddoesnotgive avalueforeachindividualstudent.Itisnotavariableforthedataset.
(g)Thedesiredsuperpowerchosenfromalistgivesacategoricalvalueforeachstudent.
1.25 (a)Thetotaltuitionandfeesisaquantitativevalueforeachschool.
(b)ThenumberofschoolsintheNortheastisasinglevalue,basedonalloftheschools,anddoesnotgive avalueforeachindividualschool.Itisnotavariableforthedataset.
(c)Thetypeofschool(public,private,forprofit)isacategoricalvalueforeachschool.
(d)Thenumberofundergraduatesisaquantitativevalueforeachschool.
(e)Thepercentageofpart-timestudentsisaquantitativevalueforeachschool.
(f)Theschoolwiththehighestaveragefacultysalaryisasinglevalue,basedonalloftheschools,and doesnotgiveavalueforeachindividualschool.Itisnotavariableforthedataset.
1.26 Inthefirststudy,thecasesarethestudents.Theonlyvariableiswhetherornotthestudenthas smokedahookah.Thisisacategoricalvariable.
Inthesecondstudy,thecasesarethepeopleinahookahbar.Thevariablesarethelengthofthesession, thefrequencyofpuffing,andthedepthofinhalation.Allarequantitative.
Inthethirdstudy,thecasesarethesmokesamples,andthevariablesaretheamountoftar,nicotine,and heavymetals.Allthreevariablesarequantitative.
1.27 (a)Thisdescriptionofthestudymentionssixvariables:age,nosevolume,nosesurfacearea,nose height,nosewidth,andgender.
(b)Oneofthevariables(gender)iscategorical,andtheotherfivearequantitative.
(c)Therearesixvariablessothedatasetwillhavesixcolumns.The859participantsarethecases,sothe datasetwillhave859rows.
1.28 (a)Thecasesarethe47participants.
(b)Thedescriptionofthestudyincludesthreedifferentvariables:thescoreontheno-distractionstest, thescoreonthetestwhiletexting,andwhetherornotthestudentconsideredhimorherselftobe goodatmultitasking.Thetwotestscorevariablesarequantitativeandthemultitaskingvariableis categorical.
(c)Thedatasetwouldhave47rows(oneforeachparticipant)andthreecolumns(oneforeachofthethree variables).
1.29 (a)Thecasesarethe40peoplewithinsomniawhowereincludedinthestudy.
(b)Therearetwovariables.Oneiswhichgroupthepersonisassignedto,eithertherapyornot,andthe otheriswhetherornotthepersonreportedsleepimprovements.Botharecategorical.
(c)Thedatasetwouldhavetwocolumns,oneforeachofthetwovariables,and40rows,oneforeachof thepeopleinthestudy.
1.30 Ifwesimplyrecordageinyearsandincomeindollars,thevariablesarequantitative.Often,however, inasurvey,wedon’taskfortheexactagebutratherwhatagecategorytheparticipantfallsin(20 29, 30 39,etc.).Similarly,weoftendon’taskforexactincomebutforanincomecategory(lessthan$10,000, between$10,000and$25,000,etc.).Ifweaskparticipantswhatcategorytheyareinforeachvariable,then thevariablesarecategorical.
1.31 Wecouldsamplepeopleeligibletovoteandaskthemeachtheirpoliticalpartyandwhethertheyvoted inthelastelection.Thecaseswouldbepeopleeligibletovotethatwecollectdatafrom.Thevariables wouldbepoliticalpartyandwhetherornotthepersonvotedinthelastelection.Alternatively,wecould askwhethereachpersonplanstovoteinanupcomingelection.
1.32 Wecouldsurveyasampleofpeopleandasktheirhouseholdincomeandmeasurehappinessinsome way,suchasaskinghowhappytheyareonascaleof1–10.Thecaseswouldbethepeoplewecollectdata from.Thevariablesinthiscasewouldbehouseholdincomeandhappinessrating,althoughanytwovariables measuringwealthandhappinessarepossible.
1.33 Answerswillvary.
Section1.2Solutions
1.34 Thisisasample,becauseonlyasubsetoffisharemeasured.
1.35 Thisisapopulation,becauseallcustomersareaccountedfor.
1.36 Thisisapopulation,becauseallregisteredvehiclesareaccountedfor.
1.37 Thisisasample,becauseonlyasubsetofcollegestudentsweresentthequestionnaire.
1.38 Thesampleisthe120peopleinterviewed.Thepopulationmightbeallpeopleinthattownorall peoplethatgotothemallinthattownoravarietyofothergroupslargerthanandcontainingthe120 peopleinthesample.
1.39 ThesampleisthefivehundredCanadianadultsthatwereaskedthequestion;thepopulationisall Canadianadults.
1.40 Thesampleisthe100customerssurveyed;thepopulationisallcustomersofthecellphonecarrier.
1.41 Thesampleisthe1000householdswhichhavedataboxesattachedtothetelevisions.Thepopulation isallUShouseholdswithtelevisions.
1.42 (a)Thesampleisthe100collegestudentswhowereaskedthequestion.
(b)ThepopulationweareinterestedinisallAmericans.
(c)Apopulationwecangeneralizeto,givenoursample,iscollegestudents.
1.43 (a)Thesampleisthe10selectedtwitteraccounts.
(b)Thetargetpopulationisalltwitteraccounts.
(c)Thepopulationwecangeneralizeto,giventhesample,isonlytwitteraccountsofthisauthor’sfollowers, sincethisisthepopulationfromwhichthesamplewasdrawn.
1.44 (a)Thesampleisthe1500peoplewhowerecontacted.
(b)ThepopulationweareinterestedinisallresidentsoftheUS.
(c)Apopulationwecangeneralizeto,givenoursample,isresidentsofMinnesota.
1.45 (a)Thesampleisthegirlswhoareontheselectedbasketballteams.
(b)Thepopulationweareinterestedinisallfemalehighschoolstudents.
(c)Apopulationwecangeneralizeto,givenoursample,isfemalehighschoolstudentswhoareona basketballteam.
1.46 Yes,thisisarandomsamplefromthepopulation.
1.47 Yes,thisisrandomsamplefromthepopulation.
1.48 No,thisisnotarandomsample,becausesomeemployeesmaybemorelikelythanotherstoactually completethesurvey.
1.49 No,thisisnotarandomsample,becausecertainsegmentsofthepopulation(e.g.,thosenotattending college)cannotbeselected.
1.50 No,thisisnotarandomsample.Wemightthinkwecanpickouta“representativesample”,butwe probablycan’t.Weneedtoletarandomnumbergeneratordoitforus.
1.51 No,thisisnotarandomsample,thisisavolunteersample,sincetheonlypeopleinthesampleare thosethatself-selecttorespondtotheonlinepoll.
1.52 ThissampleisdefinitelybiasedbecauseonlystudentswhoareatthelibraryonaFridaynightcanbe selected.Therandomsampleshouldbefromallstudents.
1.53 Thisisbiasedbecausethewaythequestioniswordedisnotatallobjective.Althoughthesampleis arandomsample,thewordingbiasmaydistorttheresults.
1.54 Thissampleisbiasedbecausetaking10applesoffthetopisnotarandomsample.Theapplesonthe bottomofthetruckloadareprobablymorelikelytobebruised.
1.55 Fromthedescription,itappearsthatthismethodofdatacollectionisnotbiased.
1.56 Thissampleisbiasedbecauseitisavolunteersurveyinwhichpeoplechoosetoparticipateornot. Mostlikely,thepeopletakingthetimetorespondtotheemailwillhavestrongeropinionsthantherestof thestudentbody.
1.57 BecausethiswasarandomsampleofparentsinKansasCity,theresultcanbegeneralizedtoallparents inKansasCity.
1.58 (a)No,thesampleisalmostcertainlynotrepresentative,sinceitisavolunteersampleandonly includespeoplewhovisitthatwebsiteandwhochosetoparticipateinthepoll.
(b)No,itisnotappropriatetogeneralizesincethesampleisnotrepresentative.
1.59 (a)Yes,thesampleislikelytoberepresentativesinceitisarandomsample.
(b)Yes,sincethesampleisarandomsample,wecangeneralizetothepopulationofallCanadianconsumers.
1.60 (a)Thesampleisthe1, 000USadultsthatwerecontacted.TheintendedpopulationisallUSadults.
(b)Yes,itisreasonabletogeneralizesincethesamplewasselectedrandomly.
1.61 (a)Thesampleisthe800peoplewhoparticipatedinthesurvey.TheintendedpopulationisallUS smartphoneusers.
(b)Thecasesarethepeoplewhoparticipatedinthesurvey.Therearetwovariables:Whetherornota fooddeliveryappwasusedinthelastmonth,andwhichapp(ifany)wasused.Botharecategorical.
1.62 (a)The457studentsinthesampleisnotalargerpopulation.Wewouldknowtheexactanswersfor thisgroupsononeedtogeneralize.
(b)ThesamplewasrandomlyselectedfromamongallPennsylvaniahighschoolseniorswhoparticipated intheCensusatSchoolproject,sothatwouldbeareasonablepopulationtogeneralizeresultsto.
(c)Theremightbesomethingspecialaboutschools(orstudents)whoparticipateintheCensusatSchool project,soitmightnotbereasonabletogeneralizetheresultsfromthatsampletoallPennsylvania highschoolseniors.
(d)ItwouldnotbereasonabletogeneralizefromasampleofonlyPennsylvaniastudentstostudentsfrom allstates.
1.63 (a)Thereisnosamplingbiashere,sincewearetoldthatarandomsamplewasused.Theresults arebeingmanipulatedbasedonlyontheorderoftheoptions(thewordingofthequestion)sothisis anexampleofwordingbias.
(b)Weseethatpeoplearemorelikelytoselectthefirstoptiongiven,soyoushouldaskyourfriendto choosebetween“Option W andOption Q,“withOption W presentedfirst.
1.64 (a)Yes,thereisprobablysamplingbiassincethegrouphasnotsharedthemethod.No,wecannot knowifitisappropriatetogeneralize,anditisprobablynotappropriatetodoso.Thesurveymight havebeenaskedofchildren,forexample.Thiswouldcertainlycreatesamplingbias.
(b)Yes,thewaythequestionwaswordedalmostcertainlybiasedtheresults.Abetterwaymightbeto askanopen-endedquestionsuchasdescribehowchocolatemilkismade,
1.65 (a)Theindividualcasesaretheover6000restroompatronswhowereobserved.Thedescription makesitclearthatatleastthreevariablesarerecorded.Oneiswhetherornotthepersonwashed theirhands,anotheristhegenderoftheindividual,andathirdisthelocationoftheobservation.All threearecategorical.
(b)Inaphonesurvey,peoplearelikelytorepresentthemselvesinthebestlightandnotalwaysgive completelyhonestanswers.Thatiswhyitisimportanttoalsofindotherwaysofcollectingdata,such asthismethodofobservingpeople’sactualhabitsintherestroom.
1.66 (a)Thesampleisthesurveyparticipants,thepopulationisallprofessorsattheUniversityofNebraska.
(b)No,wecannotconcludethatthesampleofsurveyrespondersisnotrepresentativeofprofessorsatthe UniversityofNebraskasincewearenotgivenenoughinformationtodecideonewayortheother.
(c)No,the94%isbasedonselfdescriptions,whichcanbe(andinthiscase,probablyare)biased.
1.67 No.Thisisavolunteersample,andthereisreasontobelievetheparticipantsarenotrepresentativeof thepopulation.Forexample,somemaychoosetoparticipatebecausetheyLIKEalcoholand/ormarijuana, andthoseinthesamplemaytendtohavemoreexperiencewiththesesubstancesthantheoverallpopulation. Inaddition,theadvertisementsforthestudywereairedonrockradiostationsinSydney,soonlythosepeople wholistentorockradiostationsinSydneywouldhearabouttheoptiontoparticipate.
1.68 Yes!Thesampleisarandomsamplesowecanbequiteconfidentthatitisprobablyarepresentative sample.
1.69 (a)Thisisnotasimplerandomsamplefromthepopulation,sinceonlythosewhosawandwanted toclickandcompletethesurveywereincluded.
(b)Theseresultscouldalsohavebeenbiasedbyhowthesurveywasconstructed.Thewordingofthe questionsmightalsointroducebias.
1.70 Thestudygivenfoundarelationshipinasampleofrats.Thisrelationshipmaynotgeneralizetothe humanpopulation.
1.71 Thesampleofplanesthatreturnfrombombingmissionswasbiased.Morebulletholeswerefoundin thewingsandtailbecauseplanesthatwereshotinotherregionsweremorelikelytocrashandnotreturn.
1.72 (a)ThepopulationintheCPSisallUSresidents.(Alsoacceptable:UScitizens,UShouseholds...) (b)ThepopulationintheCESsurveyisallnon-farmbusinessesandgovernmentagenciesintheUS.
(c)i.TheCESsurveywouldbemorerelevant,becausethequestionpertainstocompanies.
ii.TheCPSwouldbemorerelevant,becausethequestionpertainstoAmericanpeople.
iii.TheCPSwouldbemorerelevant,becausethequestionpertainstopeople,notbusinesses.
1.73 (a)SincetheNHANESsampleisdrawnfromallpeopleintheUS,thatisthepopulationwecan generalizeto.
(b)SincetheNHAMCSsampleisdrawnfrompatientsinemergencyroomsintheUS,wecangeneralize theresultstoallemergencyroompatientsintheUS.
(c)i.NHANES:Thequestionaboutanassociationbetweenbeingoverweightanddevelopingdiabetes appliestoallpeopleintheUS,notjustthosewhovisitanemergencyroom.
ii.NHAMCS:Thisquestionasksspecificallyaboutthetypeofinjuryforpeoplewhogotoan emergencyroom.
iii.NHAMCS:Thisquestionofaveragewaitingtimeonlyappliestoemergencyroompatients.
iv.NHANES:ThisquestionisaskingaboutallUSresidents.Notethattheproportionwouldbe equaltooneforthepeoplesampledinNAMCSsincetheyonlygetintothesampleiftheyvisit anemergencyroom!
1.74 Answerswillvary.Seethetechnologynotestoseehowtousespecifictechnologytoselectarandom sample.
1.75 Answerswillvary.Seethetechnologynotestoseehowtousespecifictechnologytoselectarandom sample.
Section1.3Solutions
1.76 Theuseof“improves”impliesthisisacausalassociation.
1.77 Since“nolinkisfound”thereisneitherassociationnorcausation.
1.78 Thephrase“leadstodeaths”indicatesacausalassociation.
1.79 Thephrase“morelikely”indicatesanassociation,butthereisnoclaimthatwealth causes peopleto lie,cheatorsteal.
1.80 Thephrase“tendtobemoreeducated”indicatesanassociation,butthereisnoclaimthatowninga catcausesmoreeducation(orthatbettereducationcausespeopletoprefercats).
1.81 Thestatementsimplythateatingmorefiberwillcausepeopletoloseweight,sothisisacausal association.
1.82 Onepossibleconfoundingvariableistemperature(orseason).Morepeopleeaticecream,andgo swimming,inwarmweather.Otheranswersarepossible.Rememberthataconfoundingvariableshouldbe associatedwithbothofthevariablesofinterest.
1.83 Onepossibleconfoundingvariableispopulation.Increasingpopulationintheworldovertimemay meanmorebeefandmoreporkisconsumed.Otheranswersarepossible.Rememberthataconfounding variableshouldbeassociatedwithbothofthevariablesofinterest.
1.84 Onepossibleconfoundingvariableiswealth.Peoplewhoownayachtarelikelywealthyandcanafford asportscar.Otheranswersarepossible.Rememberthataconfoundingvariableshouldbeassociatedwith bothofthevariablesofinterest.
1.85 Onepossibleconfoundingvariableissnowinthewinter.Whenthereismoresnow,salesofboth toboggansandmittenswillbehigher.Rememberthataconfoundingvariableshouldbeassociatedwith bothofthevariablesofinterest.
1.86 Onepossibleconfoundingvariableisnumberofcars(andalsonumberofpeople).Iftherearelotsof cars,therewillbemorepavementandmoreairpollution.Rememberthataconfoundingvariableshouldbe associatedwithbothofthevariablesofinterest.
1.87 Onepossibleconfoundingvariableisgender.Malesusuallyhaveshorterhairandaretaller.Other answersarepossible.Rememberthataconfoundingvariableshouldbeassociatedwithbothofthevariables ofinterest.
1.88 Wearenotmanipulatinganyvariablesinthisstudy,weareonlycollectinginformation(ricepreference andmetabolism)astheyexist.Thisisanobservationalstudy.
1.89 Weareactivelymanipulatingtheexplanatoryvariable(playingmusicornot),sothisisanexperiment.
1.90 Weareactivelymanipulatingtheexplanatoryvariable(plantingtreesornot),sothisisanexperiment.
1.91 Wearenotmanipulatinganyvariablesinthisstudy,weareonlymeasuringthings(omega-3oilsand wateracidity)astheyexist.Thisisanobservationalstudy.
1.92 Datawerecollectedafterthefactfromsprinters,marathonrunners,andnon-athletes.Nogeneswere manipulated.Thesedatacamefromanobservationalstudy.
1.93 Thepenguinsinthisstudywererandomlyassignedtogeteitherametaloranelectronictagsothisis anexperiment.
1.94 Allthreestudiesareexperimentssincethescientistsactivelycontrolthetreatment(tearsorsalt solution).
1.95 Apossibleconfoundingvariableisamountofsnowandiceontheroads.Whenmoresnowandicehas fallen,moresaltwillbeneeded and morepeoplewillhaveaccidents.Noticethattheconfoundingvariable hasanassociationwith both thevariablesofinterest.
1.96 Ageorgradelevel!Certainly,studentsinsixthgradecanreadsubstantiallybetterthanstudentsin firstgradeandtheyarealsosubstantiallytaller.Gradelevelisinfluencingbothofthevariablesanditisa confoundingvariable.Ifwelookatindividualgradesoneatatime,theassociationcouldeasilydisappear.
1.97 (a)Thecasesarepeople.Thetwovariablesarewhetherornotthepersonisagolferandhowlong thepersonlives.
(b)Novariablesweremanipulated,sothisresultcomesfromanobservationalstudy.
(c)Aconfoundingvariableisavariablethatisassociatedwiththeothervariablesandmayhelpexplain theassociation.Wealthorincomeisoneobviousconfoundingvariable,sincegolfingisarelatively expensivesportandthereforeassociatedwithwealthandwealthisalsoassociatedwithlivinglonger. Otherconfoundingvariablesarealsopossible.
1.98 (a)Thecasesarethe1, 773participants.
(b)Theexplanatoryvariableisthegrouptowhichtheparticipantisassigned.Itiscategorical.
(c)Thisisanexperimentsincethegroupisrandomlyassignedbytheresearchers.
(d)Thereare1, 773casesandfourvariables(groupassignmentandallthreeattitudemeasures),sothe datasetwillhave1773rowsand4columns.
1.99 Yes,thisstudyprovidesevidencethatloudermusiccausespeopletodrinkmorebeer,becausethe explanatoryvariable(volumeofmusic)wasrandomlydeterminedbytheresearchersandanassociationwas found.
1.100 Study1isarandomized,controlledexperiment,whileStudy2isobservational.Therefore,Study1 providesbetterevidenceofcausation,whileStudy2ismorepronetoconfoundingvariables(e.g.,people whoeatmorenutsmayalsobemorehealthyinotherways).
1.101 (a)Yes.Becausethestudyinmicewasarandomizedexperiment,wecanconcludecausation.
(b)No.Sinceitappearsthatthestudyinhumanswasanobservationalstudy,itisnotappropriate toconcludecausation.Althoughtheheadlinemaystillbetrueforhumans,wecannotmakethis conclusionbasedonthestudydescribed.
1.102 (a)Sincethestudentsweren’tassignedtoonetypeofdietoranother,thisisanobservationalstudy.
(b)No,wecannotconcludeacause-and-effectrelationshipsincetheresultdoesnotcomefromarandomized experiment.
(c)Aconfoundingvariableisavariablethatisassociatedwiththeothervariablesandmayhelpexplain theassociation.Inthiscase,therearemanypossibleconfoundingvariables.Oneisexercise,since studentswhoexercisemayalsotendtoeatwellandmayalsohavelowerratesofdepression.
1.103 (a)Thetwovariablesareamountofironinthesoilandamountofpotassiuminspinachgrownin thatsoil.Bothvariablesarequantitative.
(b)Amountofironinthesoilistheexplanatoryvariablesinceitappearstoaffecttheamountofpotassium inthespinach.
(c)Sincethereisnoindicationthattheamountofironinthesoilwascontrolledbytheresearchers,the dataappeartocomefromanobservationalstudy.
(d)No.Sincethedatadonotcomefromanexperiment,wecannotassumecausation.
(e)Aconfoundingvariableisavariablethatmightaffectboththeamountofironinthesoilandtheamount ofpotassiuminthespinachleaves.Examplesmightbetheamountofrainfallorthetemperatureof thesoilorotherchemicalsinthesoil.
1.104 (a)Thecasesarethechildrenbeingstudiedandthereare19ofthem.Therearethreevariables: Hoursspentreading,Hoursofscreentime,andConnectivityinthebrain.
(b)Allthreevariablesarequantitative.Itappearsthathoursspentreadingandhoursofscreentimeare theexplanatoryvariablesandconnectivityinthebrainistheresponsevariable.
(c)Thisisanobservationalstudy,sincenovariableswerecontrolled.
(d)No,wecannotconcludecausationsincethiswasnotanexperiment.
(e)Aconfoundingvariableaffectsbothvariablesinanassociationandmighthelpexplaintheapparent association.Inthiscase,onepossibleconfoundingvariablemightbetheconnectivityintheparents’ brains,sinceparentswithhigherbrainconnectivitymightbemorelikelytoreadtotheirkidsandless likelytohavethemspendtimeonscreens,andchildrenofparentswithhighbrainconnectivitymight bemorelikelytoinherithighbrainconnectivity.Otheranswersarepossible.
1.105 (a)Thisisanobservationalstudysincenoneofthevariableswascontrolled.
(b)Thereareseveralpossibleanswers.Wealthisone,sincewealthhasbeenshowntobeassociatedwith betterhealthandwealthypeoplemightfinditeasiertotakevacations.Jobstressmightbeanother sincejobstressmightharmhealthandjobstressmightalsomakeitdifficulttotakevacations.
(c)Theresultsofthisstudyindicateanassociationbutnotacausationassociation.Thusthefirsttwo statementsareappropriateandthesecondtwoarenot.(i)Yes(ii)Yes(iii)No(iv)No.
(d)No.“WanttobeHealthier?TakeaVacation!”impliescause-and-effect,whichisnotanappropriate conclusionfromthisobservationalstudy.
1.106 No,thiswasanobservationalstudyandallowedformanyconfoundingvariables.
1.107 (a)Thecasesarethe2,623schoolchildren.
(b)Theexplanatoryvariableistheamountofgreeneryaroundtheschools.
(c)Theresponsevariableisthescoreonthememoryandattentiontests.
(d)Yes,theheadlineimpliesthatmoregreenspacecauseskidstobesmarter.
(e)Novariablesweremanipulatedsothisisanobservationalstudy.
(f)No!Sincethisisnotanexperiment,wecannotconcludecausation.
(g)Thesocioeconomicstatusofthechildrenisapossibleconfoundingvariable,sinceitislikelytoeffect boththeamountofgreenspaceandalsothetestscores.Thereareotherpossibleanswers.
1.108 (a)ThecasesaretheDanishmenwhowereincludedinthestudy.
(b)Theexplanatoryvariableiswhetherornotthepersonhasbeeninthehospitalforaninfection.Since theansweriseitheryesorno,thisisacategoricalvariable.
(c)TheresponsevariableistheIQscorefortheperson.Wecanfindanaveragesothisisaquantitative variable.
(d)Yes,theheadlineimpliesthatinfectionslowerIQ,whichiscausation.
(e)Theexplanatoryvariablewasnotmanipulated,sothisisanobservationalstudy.
(f)No,sincethiswasnotanexperiment,itisnotappropriatetoconcludecausation.Therearemany possiblelurkingvariablesthatmightimpactbothIQandthelikelihoodofhavinganinfection.
1.109 (a)Theexplanatoryvariableisamountofleisuretimespentsittingandtheresponsevariableis whetherornotthepersongetscancer.
(b)Thisisanobservationalstudybecausetheexplanatoryvariablewasnotrandomlyassigned.
(c)No,wecannotconcludespendingmoreleisuretimesittingcausescancerinwomenbecausethisisan observationalstudy.
(d)No,wealsocannotconcludethatspendingmoreleisuretimesittingdoesnotcausecancerinwomen; becausethiswasanobservationalstudywecanmakenoconclusionsaboutcausality.Sittingmayor maynotcausecancer.
1.110 (a)Theexplanatoryvariableiswhetherornottheparticipantsweregivenaccesstofoodanddrink after10pm,orjustwater.Theresponsevariablesarereactiontimeandnumberofattentionlapses.
(b)Thisisarandomizedexperimentbecausetheexplanatoryvariablewasrandomlyassigned.
(c)Yes,wecanconcludethateatinglateatnightworsensreactiontimeandincreasesattentionlapsesfor sleepdeprivedpeople.
(d)No,therearenotlikelytobeconfoundingvariables,becausethiswasarandomizedexperiment.
1.111 (a)Thisisanobservationalstudybecausewecannotrandomlydeterminewhenachildlearnsto talk.
(b)No,wecannotconcludethatearlylanguageskillsreducepreschooltantrumsbecausethisisanobservationalstudy.
(c)Therearemanypossibleconfoundingvariables,suchastheintelligenceofthechildorparentalinvolvement.
1.112 (a)No,becauseitisanobservationalstudy,notarandomizedexperiment.Peoplewerenotrandomlyassignedtobuyorganicfoodornot,butratherchoseforthemselves,sothegroupsalmost certainlydifferedtobeginwith.
(b)Answerswillvary,butpossibleanswersmayincludeincome(organicfoodcostsmoremoneyand wealthierpeoplearegenerallyhealthier)orotherhealth-consciousbehaviors(peoplewhocareabout eatingorganicmayeathealthieringeneral).
(c)No,becausewedonothaveevidenceagainstalternativeexplanation(ii);wecannotdeterminewhether explanation(i)or(ii)(orboth)aredrivingtheobserveddifference.
1.113 (a)Yes,becausethiswasarandomizedexperiment;itwasrandomlydeterminedwhichfliesate organicandwhichateconventionalfood.
(b)Answertopart(a)wasnotno.
(c)Yes,becausewehaveevidenceagainstbothofthecompetingalternativeexplanations,wehaveconvincingevidencethateatingorganicfoodreallydoesmakefruitflieslivelonger.
1.114 (a)Sinceallthechildrenarepresentedwithallthreeformats,thisisamatchedpairsexperiment (althoughitmightmoreaccuratelybecalledamatchedtriplesexperiment!)
(b)Yes,wecanconcludecausationsincetheresultscomefromanexperiment.
(c)Theformats(andthestoriesused)shouldbepresentedtothechildreninrandomorder.(Thisishow theexperimentwasconducted.)
1.115 (a)Theexplanatoryvariableiswhetherthepersonjusthadafullnightofsleepor24hoursofbeing awake.Theresponsevariableisabilitytorecognizefacialexpressions.
(b)Thisisarandomizedexperiment,amatchedpairsexperimentbecauseeachpersonreceivedboth treatments.
(c)Yes,wecanconcludethatmissinganightofsleephinderstheabilitytorecognizefacialexpressions, becausetheexplanatoryvariablewasrandomlyassigned.
(d)No,wecannotconcludethatbetterqualityofREMsleepimprovesabilitytorecognizefacialexpressions,becausetheexplanatoryvariableinthiscase(qualityofREMsleep)wasnotrandomlyassigned.
1.116 (a)No,wecannotconcludethatdrinkingdietsodacausesweightgainbecausethestudywas observationalandpronetoconfoundingvariables.Forexample,itispossiblethatseniorswhodrink moredietsodadosobecausetheyknowtheyarepronetogainingweight.
(b)Neitherstudyisperfect.Thestudyonseniorcitizensisobservationalandthestudyonratsmaynot generalizetohumans.However,togetherthesestudiesprovideamoreconvincingcasethatdietsoda cancauseweightgain.Opinionscanvaryonhowstrongthisevidenceforcausationis.
1.117 (a)Itisanobservationalstudysincenooneassignedsomepeopletoliveinacityandsometolive inthecountry.
(b)No,sincewecanneverconcludefromanobservationalstudythatthereisacausalassociation.
(c)The2011studyisalsoanobservationalstudy,since,again,nooneassignedsomepeopletoliveina cityandsometoliveinthecountry.
(d)Theexplanatoryvariableiswhetherornottheparticipantlivesinthecityorthecountry,whichisa categoricalvariable.Theresponsevariableislevelofactivityinstresscentersofthebrain,whichis quantitative.
(e)No!Theresultscomefromanobservationalstudy,sowecannotconcludeacausalrelationship.
1.118 Theexplanatoryvariablesarethetypeof payment and sex.Onlythetypeofpaymentcanberandomly assigned.Thenumberof items orderedand cost areresponsevariables.
1.119 (a)Theexplanatoryvariableiswhetherornotthepersonhadagoodnight’ssleeporissleepdeprived.Theresponsevariableisattractivenessrating.
(b)Sincetheexplanatoryvariablewasactivelymanipulated,thisisanexperiment.Thetwotreatments arewell-restedandsleep-deprived.Sinceall23subjectswerephotographedwithbothtreatments,this isamatchedpairsexperiment.
(c)Yes,wecanconcludethatsleep-deprivationcausespeopletolooklessattractive,becausethisisan experiment.
1.120 (a)Werandomlydividetheparticipantsintotwogroupsof25each.Halfwillbegivenfluoxetine andhalfwillgetaplacebo.
(b)Theplacebopillswilllookexactlylikethefluoxetinepillsandwillbetakenthesameway,butthey willnothaveanyactiveingredients.
(c)Thepatientswon’tknowwhoisgettingwhichtypeofpill(thefluoxetineortheplacebo)andthe peopletreatingthepatientsandadministeringthequestionnairewon’tknowwhoisinwhichgroup.
1.121 (a)Theexplanatoryvariableisamountofsleepandtheresponsevariableisgrowthinheight.
(b)Wewouldtakeasampleofchildrenandrandomlydividethemintotwogroups.Onegroupwouldget lotsofsleepandtheotherwouldbedeprivedofsleep.Thenaftersometimepassed,wewouldcompare theamountofheightincreaseforthechildreninthetwogroups.
(c)Anexperimentisnecessaryinordertoverifyacauseandeffectrelationship,butitwoulddefinitely notbeappropriatetorandomlyassignsomeofthekidstobesleep-deprivedforlongperiodsoftime justforthepurposesoftheexperiment!
1.122 (a)Randomlyassign25peopletocarbo-loadand25peopletonotcarbo-loadandthenmeasure eachperson’sathleticperformancethefollowingday.
(b)Wewouldhaveeachpersoncarbo-loadandnotcarbo-load,ondifferentdays(preferablydifferent weeks).Theorderwouldberandomlydetermined,sosomepeoplewouldcarbo-loadfirstandother peoplewouldcarbo-loadsecond.Inbothcasesathleticperformancewouldbemeasuredthefollowing dayandwewouldlookatthedifferenceinperformanceforeachpersonbetweenthetwotreatments.
(c)Thematchedpairsexperimentisprobablybetterbecauseweareabletocomparethedifferenteffects forthesameperson.Itismoreprecisecomparingoneperson’sathleticperformanceundertwodifferent treatments,ratherthandifferentpeople’sathleticperformanceundertwodifferenttreatments.
1.123 (a)Randomlydividethestudentsintotwogroupsof20studentseach.Onegroupgetsalcoholand theothergetswater.Measurereactiontimeforstudentsinbothgroups.
(b)Measurereactiontimeforall40studentsbothways:afterdrinkingalcoholandafterdrinkingwater. Dothetestsonseparatedaysandrandomizetheorderinwhichthestudentsaregiventhedifferent treatments.Measurethedifferenceinreactiontimeforeachstudent.
1.124 Answerswillvary.Example:Thetotalamountofpizzaconsumedandthetotalamountofcheese consumed,peryear,overthelastcentury.Eatingmorepizzacausespeopletoeatmorecheese,butthe overallriseinpopulationisalsoaconfoundingvariable.