APStatisticsMultipleChoiceExam统计选择题.doc

APStatisticsMultipleChoiceExam统计选择题.doc

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Name_____________________________

2007APStatisticsMultipleChoiceExam

Directions:

Solveeachofthefollowingproblems,usingtheavailablespaceforscratchwork.Decidewhichisthebestofthechoicesgivenandfillinthecorrespondingovalontheanswersheet.Nocreditwillbegivenforanythingwritteninthetestbook.Donotspendtoomuchtimeonanyoneproblem.

1.Thestatisticsbelowprovideasummaryofthedistributionofheights,ininches,forasimplerandomsampleof200youngchildren.

Mean:

46inches

Median:

45inches

StandardDeviation:

3inches

FirstQuartile:

43inches

ThirdQuartile:

48inches

About100childreninthesamplehaveheightsthatare

（A） lessthan43inches

（B） lessthan48inches

（C） between43and48inches

（D） between40and52inches

（E） morethan46inches

2.Inwhichofthefollowingsituationswoulditbemostdifficulttouseacensus?

（A） Todeterminewhatproportionoflicensedbicyclesonauniversitycampushavelights

（B） Todeterminewhatproportionofstudentsinahighschoolsupportwearinguniforms

（C） Todeterminewhatproportionofregisteredstudentsenrolledinacollegeareemployedmorethan

20hourseachweek

（D） Todeterminewhatproportionofsingle-familydwellingsinasmalltownhavetwo-cargarages

（E） TodeterminewhatproportionoffishinLakeMichiganarebass

3.Thedistributionofthediametersofaparticularvarietyoforangesisapproximatelynormalwithastandarddeviationof0.3inch.Howdoesthediameterofanorangeatthe67thpercentilecomparewiththemeandiameter?

（A） 0.201inchbelowthemean

（B） 0.132inchbelowthemean

（C） 0.132inchabovethemean

（D） 0.201inchabovethemean

（E） 0.440inchabovethemean

4.Independentrandomsamplesof100luxurycarsand250non-luxurycarsinacertaincityareexaminedtoseeiftheyhavebumperstickers.Ofthe250non-luxurycars,125havebumperstickersandofthe100luxurycars,30havebumperstickers.Whichofthefollowingisa90percentconfidenceintervalforthedifferenceintheproportionofnon-luxurycarswithbumperstickersandtheproportionofluxurycarswithbumperstickersfromthepopulationofcarsrepresentedbythesesamples?

（A）

（B）

（C）

（D）

（E）

5.Asafetygroupclaimsthatthemeanspeedofdriversonahighwayexceedsthepostedspeedlimitof65milesperhour（mph）.Toinvestigatethesafetygroup'sclaim,whichofthefollowingstatementsisappropriate?

（A） Thenullhypothesisisthatthemeanspeedofdriversonthishighwayislessthan65mph.

（B） Thenullhypothesisisthatthemeanspeedofdriversonthishighwayisgreaterthan65mph.

（C） Thealternativehypothesisisthatthemeanspeedofdriversonthishighwayisgreaterthan65mph.

（D） Thealternativehypothesisisthatthemeanspeedofdriversonthishighwayislessthan65mph.

（E） Thealternativehypothesisisthatthemeanspeedofdriversonthishighwayisgreaterthanorequal

to65mph.

6.Afaircoinistobeflipped5times.Thefirst4flipsland"heads"up.Whatistheprobabilityof"heads"onthenext（5th）flipofthiscoin?

（A）

（B）

（C）

（D）

（E）

7.Thestemplotbelowshowstheyearlyearningspershareofstockfortwodifferentcompaniesoverasixteen-yearperiod.

CompanyA CompanyB

0 58,75,96,98

92,91,90,82,78,43,38,26 1 01,10,17,21,43,43,53,65,73

49,47,44,00 2 09,27,29

73,27,05,02 3

Whichofthefollowingstatementsistrue?

（A） ThemedianoftheearningsofCompanyAislessthanthemedianoftheearningsoftheCompanyB.

（B） TherangeoftheearningsofCompanyAislessthantherangeoftheearningsofCompanyB.

（C） ThethirdquartileofCompanyAissmallerthanthethirdquartileofCompanyB.

（D） ThemeanoftheearningsofCompanyAisgreaterthanthemeanoftheearningsofCompanyB.

（E） TheinterquartilerangeofCompanyAistwicetheinterquartilerangeofCompanyB.

8.LetXrepresentarandomvariablewhosedistributionisnormal,withameanof100andastandarddeviationof10.WhichofthefollowingisequivalenttoP（X>115）?

（A） P（X<115）

（B） P（X£115）

（C） P（X<85）

（D） P（85

（E） 1-P（X<85）

9.Atelevisionnewseditorwouldliketoknowhowlocalregisteredvoterswouldrespondtothequestion,"Areyouinfavoroftheschoolbondmeasurethatwillbevotedoninanupcomingspecialelection?

"Atelevisionsurveyisconductedduringabreakintheeveningnewsbylistingtwotelephonenumberssidebysideonthescreen,oneforviewerstocalliftheyapproveofthebondmeasure,andtheothertocalliftheydisapprove.Thissurveymethodcouldproducebiasedresultsforanumberofreasons.Whichoneofthefollowingisthemostobviousreason?

（A） Itusesastratifiedsampleratherthanasimplerandomsample.

（B） Peoplewhofeelstronglyabouttheissuearemorelikelytorespond.

（C） Viewersshouldbetoldabouttheissuesbeforethesurveyisconducted.

（D） Someregisteredvoterswhocallmightnotvoteintheelection.

（E） Thewordingofthequestionisbiased.

10.Ahighschoolphysicsteacherwasconductinganexperimentwithhisclassonthelengthoftimeitwilltakeamarbletorolldownaslopedchute.Theclassranrepeatedtrialsinordertodeterminetherelationshipbetweenthelength,incentimeters,oftheslopedchuteandthetime,inseconds,forthemarbletorolldownthechute.Alinearrelationshipwasobservedandthecorrelationcoefficientwas0.964.Afterdiscussingtheirresults,theteacherinstructedthestudentstoconvertallofthelengthmeasurementstometersbutleavethetimeinseconds.Whateffectwillthishaveonthecorrelationofthetwovariables?

（A） Becausethestandarddeviationofthelengthsinmeterswillbeonehundredthofthestandard

deviationofthelengthsincentimeters,thecorrelationwilldecreasebyonehundredthto0.954.

（B） Becausethestandarddeviationofthelengthsinmeterswillbeonehundredthofthestandard

deviationofthelengthsincentimeters,thecorrelationwilldecreaseproportionallyto0.00964.

（C） Becausechangingfromcentimeterstometersdoesnotaffectthevalueofthecorrelation,the

correlationwillremain0.964.

（D） Becauseonlythelengthmeasurementshavebeenchanged,thecorrelationwilldecrease

substantially.

（E） Becausemetersareamuchmorecommonmeasurementforlengthindeterminingspeed,thelinear

relationshipofthedatawillbestrongerandthusthecorrelationwillincreasesubstantially.

11.Juliegeneratesasampleof20randomintegersbetween0and9inclusive.Sherecordsthenumberof6'sinthesample.Sherepeatsthisprocess99moretimes,recordingthenumberof6'sineachsample.Whatkindofdistributionhasshesimulated?

（A） Thesamplingdistributionofthesampleproportionwithn=20andp=0.6

（B） Thesamplingdistributionofthesampleproportionwithn=100andp=0.1

（C） Thebinomialdistributionwithn=20andp=0.1

（D） Thebinomialdistributionwithn=100andp=0.1

（E） Thebinomialdistributionwithn=20andp=0.6

n

Mean

Median

SampleI

21

42.6

45.0

SampleII

26

49.2

48.5

12.Thetableaboveshowsthesamplesize,themean,andthemedianfortwosamplesofmeasurements.Whatisthemedianforthecombinedsampleof47measurements?

（A）

（B）

（C）

（D）

（E） Itcannotbedeterminedfromtheinformationgiven.

13.Dan,atraineratthePopularGym,wasinterestedincomparinglevelsofphysicalfitnessofstudentsattendinganearbycommunitycollegeandthoseattendinga4-yearcollegeintown.Heselectedarandomsampleof320studentsfromthecommunitycollege.Themeanandstandarddeviationoftheirfitnessscoreswere95and10,respectively.Danalsoselectedarandomsampleof320studentsfroma4-yearcollege.Themeanandstandarddeviationoftheirfitnessscoreswere

92and13,respectively.Hethenconductedatwo-sidedt-testthatresultedinat-valueof3.27.Whichofthefollowingisanappropriateconclusionfromthisstudy?

（A） Becausethesamplemeansonlydifferedby3,thepopulationmeansarenotsignificantlydifferent.

（B） Becausethesecondgrouphadalargerstandarddeviation,theirmeanfitnessscoreissignificantly

higher.

（C） Becausethesecondgrouphadalargerstandarddeviation,themeanfitnessscoreofthefirstgroup

issignificantlyhigher.

（D） Becausethep-valueislessthana=0.05,themeanfitnessscoresforthetwogroupsofstudents

aresignificantlydifferent.

（E） Becausethep-valueisgreaterthana=0.05,themeanfitnessscoresforthetwogroupsofstudents

aresignificantlydifferent.

14.Aresearcherwishestotestanewdrugdevelopedtotreathypertension（highbloodpressure）.Agroupof40hypertensivemenand60hypertensivewomenistobeused.Theexperimenterrandomlyassigns20ofthemenand30ofthewomentotheplaceboandassignstheresttothetreatment.Themajorreasonforseparateassignmentformenandwomenisthat

（A） itisalargestudywith100subjects

（B） thenewdrugmayaffectmenandwomendifferently

（C） thenewdrugmayaffecthypertensiveandnonhypertensivepeopledifferently

（D） thisdesignusesmatchedpairstodetectthenew-drugeffect

（E） theremustbeanequalnumberofsubjectsinboththeplacebogroupandthetreatmentgroup.

15.Thehistogramsbelowrepresentthedistributionoffivedifferentdatasets,eachcontaining28integers,from1through7,inclusive.Thehorizontalandverticalscalesarethesameforallgraphs.Whichgraphrepresentsthedatasetwiththelargeststandarddevia