《AP统计学讲义教案资料》由会员分享，可在线阅读，更多相关《AP统计学讲义教案资料（70页珍藏版）》请在金锄头文库上搜索。
1、AP统计学讲义2004 AP STATISTICS FREE-RESPONSE QUESTIONS(FORM B)STATISTICS SECTION Part A Questions 1-5 Spend about 65 minutes on this part of the exam. Percent of Section II grade75(b)Interpretthevalueofr 2.(c)Commentontheappropriatenessofthislinearregressionformodelingtherelationshipbetweenthetransformed
2、variables.2Atacertainuniversity,studentswholiveinthedormitorieseatatacommondininghall.Recently,somestudentshavebeencomplainingaboutthequalityofthefoodservedthere.Thedininghallmanagerdecidedtodoasurveytoestimatetheproportionofstudentslivinginthedormitorieswhothinkthatthequalityofthefoodshouldbeimprov
3、ed.Oneevening,themanageraskedthefirst100studentsenteringthedininghalltoanswerthefollowingquestion.(a)Inthissetting,explainhowbiasmayhavebeenintroducedbasedonthewaythisconveniencesamplewasselectedandsuggesthowthesamplecouldhavebeenselecteddifferentlytoavoidthatbias.(b)Inthissetting,explainhowbiasmayh
4、avebeenintroducedbasedonthewaythequestionwaswordedandsuggesthowitcouldhavebeenwordeddifferentlytoavoidthatbias.3TrainscarrybauxiteorefromamineinCanadatoanaluminumprocessingplantinnorthernNewYorkstateinhoppercars.Fillingequipmentisusedtoloadoreintothehoppercars.Whenfunctioningproperly,theactualweight
5、soforeloadedintoeachcarbythefillingequipmentatthemineareapproximatelynormallydistributedwithameanof70tonsandastandarddeviationof0.9ton.Ifthemeanisgreaterthan70tons,theloadingmechanismisoverfilling.(a)Ifthefillingequipmentisfunctioningproperly,whatistheprobabilitythattheweightoftheoreinarandomlyselec
6、tedcarwillbe70.7tonsormore?Showyourwork.(b)Supposethattheweightoforeinarandomlyselectedcaris70.7tons.Wouldthatfactmakeyoususpectthattheloadingmechanismisoverfillingthecars?Justifyyouranswer.(c)Ifthefillingequipmentisfunctioningproperly,whatistheprobabilitythatarandomsampleof10carswillhaveameanorewei
7、ghtof70.7tonsormore?Showyourwork.(d)Basedonyouranswerinpart(c),ifarandomsampleof10carshadameanoreweightof70.7tons,wouldyoususpectthattheloadingmechanismwasoverfillingthecars?Justifyyouranswer.4.TheprincipalatCrestMiddleSchool,whichenrollsonlysixth-gradestudentsandseventh-gradestudents,isinterestedin
8、determininghowmuchtimestudentsatthatschoolspendonhomeworkeachnight.Thetablebelowshowsthemeanandstandarddeviationoftheamountoftimespentonhomeworkeachnight(inminutes)forarandomsampleof20sixth-gradestudentsandaseparaterandomsampleof20seventh-gradestudentsatthisschool.Basedondotplotsofthesedata,itisnotu
9、nreasonabletoassumethatthedistributionoftimesforeachgradewereapproximatelynormallydistributed.(a)Estimatethedifferenceinmeantimesspentonhomeworkforallsixth-andseventh-gradestudentsinthisschoolusinganinterval.Besuretointerpretyourinterval.(b)Anassistantprincipalreasonedthatamuchnarrowerconfidenceinte
10、rvalcouldbeobtainedifthestudentswerepairedbasedontheirresponses;forexample,pairingthesixth-gradestudentandtheseventh-gradestudentwiththehighestnumberofminutesspentonhomework,thesixth-gradestudentandseventh-gradestudentwiththenexthighestnumberofminutesspentonhomework,andsoon.Istheassistantprincipalco
11、rrectinthinkingthatmatchingstudentsinthiswayandthencomputingamatched-pairsconfidenceintervalforthemeandifferenceintimespentonhomeworkisabetterprocedurethantheoneusedinpart(a)?Explainwhyorwhynot.5.AresearcherthinksthatmodernThaidogsmaybedescendantsofgoldenjackals.Arandomsampleof16animalswascollectedf
12、romeachofthetwopopulations.Thelength(inmillimeters)ofthemandible(jawbone)wasmeasuredforeachanimal.Thelowerquartile,median,andupperquartileforeachsampleareshowninthetablebelow,alongwithallvaluesbelowthelowerquartileandallvaluesabovetheupperquartile.(a)Displayparallelboxplotsofmandiblelengths(showingo
13、utliers,ifany)forthemodernThaidogsandthegoldenjackalsonthegridbelow.Basedontheboxplots,writeafewsentencescomparingthedistributionsofmandiblelengthsforthetwotypesofdogs.(b)IsitreasonabletousethesampleofmandiblelengthsofmodernThaidogstoconstructanintervalestimateofthemeanmandiblelengthforthepopulation
14、ofmodernThaidogs?Justifyyouranswer.(Note:Youdonothavetocomputetheinterval.)(c)IsitreasonabletousethesampledataofmandiblelengthsofmodernThaidogsandthesampledataofmandiblelengthsofgoldenjackalstoperformatwo-samplef-testforthedifferenceinmeanmandiblelengthsforthetwotypesofdogs?Justifyyouranswer.(Note:Y
15、oudonothavetoconductthetest.)2004 AP STATISTICS FREE-RESPONSE QUESTIONS(FORM B)STATISTICS SECTION Part B Questions 6 Spend about 25 minutes on this part of the exam. Percent of Section II grade256.Inordertomonitorthepopulationsofbirdsofaparticularspeciesontwoislands,thefollowingprocedurewasimplement
16、ed.Researcherscapturedaninitialsampleof200birdsofthespeciesonIslandA;theyattachedlegbandstoeachofthebirds,andthenreleasedthebirds.Similarly,asampleof250birdsofthesamespeciesonIslandBwascaptured,banded,andreleased.Sufficienttimewasallowedforthebirdstoreturntotheirnormalroutineandlocation.Subsequentsa
17、mplesofbirdsofthespeciesofinterestwerethentakenfromeachisland.Thenumberofbirdscapturedandthenumberofbirdswithlegbandswererecorded.Theresultsaresummarizedinthefollowingtable.Assumethatboththeinitialsampleandthesubsequentsamplesthatweretakenoneachislandcanberegardedasrandomsamplesfromthepopulationofbi
18、rdsofthisspecies.(a)Dothedatafromthesubsequentsamplesindicatethatthereisadifferenceinproportionsofthebandedbirdsonthesetwoislands?Givestatisticalevidencetosupportyouranswer.(b)Researcherscanestimatethetotalnumberofbirdsofthisspeciesonanislandbyusinginformationonthenumberofbirdsintheinitialsampleandt
19、heproportionofbandedbirdsinthesubsequentsample.UsethisinformationtoestimatethetotalnumberofbirdsofthisspeciesonIslandA.Showyourwork.(c)Theanalysesinparts(a)and(b)assumethatthesamplesofbirdscapturedinboththeinitialandsubsequentsamplescanberegardedasrandomsamplesofthepopulationofbirdsofthisspeciesthat
20、liveontherespectiveislands.Thisisacommonassumptionmadebywildliferesearchers.Describetwoconcernsthatshouldbeaddressedbeforemakingthisassumption.2006 AP STATISQUESTIONS2006 AP STATISQUESTIONSSTATISTICS STATISTICS SECTION SECTION Part A Part A Questions 1-5 Questions 1-5 Spend about 65 minutes on this
21、part Spend about 65 minutes on this part of the exam. of the exam. Percent of Section II grade75Percent of Section II grade75TICS FREE-RESPONSETICS FREE-RESPONSE1.Twoparentshaveeachbuiltatoycatapultforuseinagameatanelementaryschoolfair.Toplaythegame,studentswillattempttolaunchPing-Pongballsfromtheca
22、tapultssothattheballslandwithina5-centimeterband.Atargetlinewillbedrawnthroughthemiddleoftheband,asshowninthefigurebelow.Allpointsonthetargetlineareequidistantfromthelaunchinglocation.Ifaballlandswithintheshadedband,thestudentwillwinaprize.Theparentshaveconstructedthetwocatapultsaccordingtoslightlyd
23、ifferentplans.Theywanttotestthesecatapultsbeforebuildingadditionalones.Underidenticalconditions,theparentslaunch40Ping-Pongballsfromeachcatapultandmeasurethedistancethattheballtravelsbeforelanding.Distancestothenearestcentimeteraregraphedinthedotplotsbelow.(a)Commentonanysimilaritiesandanydifference
24、sinthetwodistributionsofdistancestraveledbyballslaunchedfromcatapultAandcatapultB.(b)IftheparentswanttomaximizetheprobabilityofhavingthePing-Pongballslandwithintheband,whichoneofthetwocatapults,AorB,wouldbebettertousethantheother?Justifyyourchoice.(c)Usingthecatapultthatyouchoseinpart(b),howmanycent
25、imetersfromthetargetlineshouldthiscatapultbeplaced?Explainwhyyouchosethisdistance.2.Amanufacturerofdishdetergentbelievestheheightofsoapsudsinthedishpandependsontheamountofdetergentused.Astudyofthesudsheightsforanewdishdetergentwasconducted.Sevenpansofwaterwereprepared.Allpanswereofthesamesizeandtype
26、andcontainedthesameamountofwater.Thetemperatureofthewaterwasthesameforeachpan.Anamountofdishdetergentwasassignedatrandomtoeachpan,andthatamountofdetergentwasaddedtothepan.Thenthewaterinthedishpanwasagitatedforasetamountoftime,andtheheightoftheresultingsudswasmeasured.Aplotofthedataandthecomputeroutp
27、utfromfittingaleastsquaresregressionlinetothedataareshownbelow.(a)Writetheequationofthefittedregressionline.Defineanyvariablesusedinthisequation.(b)Notethats = 1.99821 in the computer output. Interpret this value in the context of this study.(c)Identifyandinterpretthestandarderroroftheslope.3.Thedep
28、thfromthesurfaceofEarthtoarefractinglayerbeneaththesurfacecanbeestimatedusingmethodsdevelopedbyseismologists.Onemethodisbasedonthetimerequiredforvibrationstotravelfromadistantexplosiontoareceivingpoint.Thedepthmeasurement(M)isthesumofthetruedepth(D)andtherandommeasurementerror(E). That is, M - D + E
29、. The measurement error (E) is assumed to be normally distributed with mean 0 feet and standard deviation 1.5 feet.(a)Ifthetruedepthatacertainpointis2feet,whatistheprobabilitythatthedepthmeasurementwillbenegative?(b)Supposethreeindependentdepthmeasurementsaretakenatthepointwherethetruedepthis2feet.W
30、hatistheprobabilitythatatleastoneofthesemeasurementswillbenegative?(c)Whatistheprobabilitythatthemeanofthethreeindependentdepthmeasurementstakenatthepointwherethetruedepthis2feetwillbenegative?4.Patientswithheart-attacksymptomsarriveatanemergencyroomeitherbyambulanceorself-transportationprovidedbyth
31、emselves,family,orfriends.Whenapatientarrivesattheemergencyroom,thetimeofarrivalisrecorded.Thetimewhenthepatientsdiagnostictreatmentbeginsisalsorecorded.Anadministratorofalargehospitalwantedtodeterminewhetherthemeanwaittime(timebetweenarrivalanddiagnostictreatment)forpatientswithheart-attacksymptoms
32、differsaccordingtothemodeoftransportation.Arandomsampleof150patientswithheart-attacksymptomswhohadreportedtotheemergencyroomwasselected.Foreachpatient,themodeoftransportationandwaittimewererecorded.Summarystatisticsforeachmodeoftransportationareshowninthetablebelow.(a)Usea99percentconfidenceinterval
33、toestimatethedifferencebetweenthemeanwaittimesforambulance-transportedpatientsandself-transportedpatientsatthisemergencyroom.(b)Basedonlyonthisconfidenceinterval,doyouthinkthedifferenceinthemeanwaittimesisstatisticallysignificant?Justifyyouranswer.5.Abiologistisinterestedinstudyingtheeffectofgrowth-
34、enhancingnutrientsanddifferentsalinity(salt)levelsinwateronthegrowthofshrimps.Thebiologisthasorderedalargeshipmentofyoungtigershrimpsfromasupplyhouseforuseinthestudy.Theexperimentistobeconductedinalaboratorywhere10tigershrimpsareplacedrandomlyintoeachof12similartanksinacontrolledenvironment.Thebiolo
35、gistisplanningtouse3differentgrowth-enhancingnutrients(A,B,andC)andtwodifferentsalinitylevels(lowandhigh).(a)Listthetreatmentsthatthebiologistplanstouseinthisexperiment.(b)Usingthetreatmentslistedinpart(a),describeacompletelyrandomizeddesignthatwillallowthebiologisttocomparetheshrimpsgrowthafter3wee
36、ks.(c)Giveonestatisticaladvantagetohavingonlytigershrimpsintheexperiment.Explainwhythisisanadvantage.(d)Giveonestatisticaldisadvantagetohavingonlytigershrimpsintheexperiment.Explainwhythisisadisadvantage.2006 AP STATISTICS FREE-2006 AP STATISTICS FREE-RESPONSE QUESTIONSRESPONSE QUESTIONSSTATISTICS S
37、TATISTICS SECTION SECTION Part B Part B Questions 6 Questions 6 Spend about 25 minutes on this part Spend about 25 minutes on this part of the exam. of the exam. Percent of Section II grade25Percent of Section II grade256.Amanufacturerofthermostatsisconcernedthatthereadingsofitsthermostatshavebecome
38、lessreliable(morevariable).Inthepast,thevariancehasbeen1.52degreesFahrenheit(F)squared.Arandomsampleof10recentlymanufacturedthermostatswasselectedandplacedinaroomthatwasmaintainedat68F.Thereadingsforthose10thermostatsaregiveninthetablebelow.(a)Statethenullandalternativehypothesesthatthemanufactureri
39、sinterestedintesting.(b)Calculatethevalueof(n-1)S2/1.52forthesedata.(c)Assumethatthepopulationofthermostattemperaturesfollowsanormaldistribution.Usetheteststatistic (n-1)S2/1.52frompart(b)andthechi-squaredistributiontotestthehypothesesinpart(a).(d)Forthetestconductedinpart(c),whatisthesmallestvalueo
40、ftheteststatisticthatwouldhaveledtotherejectionofthenullhypothesisatthe5percentsignificancelevel?Markthisvalueoftheteststatisticonthegraphofthechi-squaredistributionbelow.Indicatetheregionthatcontainsallofthevaluesthatwouldhaveledtotherejectionofthenullhypothesis.(e)Usingsimulation,1,000samples,each
41、ofsize10,wererandomlygeneratedfrom3populationswithdifferentvariances.Eachpopulationwasnormallydistributedwithmean68andvariancegreaterthan1.52.Thehistogramsbelowshowthesimulatedsamplingdistributionof(n-1)S2/1.52foreachpopulation.Marktheregionidentifiedinpart(d)oneachofthehistogramsbelow.2006 AP STATI
42、STICS FREE-2006 AP STATISTICS FREE-RESPONSE QUESTIONSRESPONSE QUESTIONS(f)Basedontheregionsthatyoumarkedinpart(e),identifythesimulatedsamplingdistributionthatcorrespondstothepopulationwiththelargestvariance.Thenidentifythesimulatedsamplingdistributionthatcorrespondstothepopulationwiththesmallestvari
43、ance.Justifyyourchoices.2005 AP STATISTICS FREE-2005 AP STATISTICS FREE-RESPONSE QUESTIONSRESPONSE QUESTIONSSTATISTICS STATISTICS SECTION SECTION Part A Part A Questions 1-5 Questions 1-5 Spend about 65 minutes on this part Spend about 65 minutes on this part of the exam. of the exam. Percent of Sec
44、tion II grade75Percent of Section II grade751.ThegoalofanutritionalstudywastocomparethecaloricintakeofadolescentsIrvinginruralareasoftheUnitedStateswiththecaloricintakeofadolescentslivinginurbanareasoftheUnitedStates.Arandomsampleofninth-gradestudentsfromonehighschoolinaruralareawasselected.Anotherr
45、andomsampleofninthgradersfromonehighschoolinanurbanareawasalsoselected.Eachstudentineachsamplekeptrecordsofallthefoodheorsheconsumedinoneday.Theback-to-backstemplotbelowdisplaysthenumberofcaloriesoffoodconsumedperkilogramofbodyweightforeachstudentonthatday.(a)Writeafewsentencescomparingthedistributi
46、onofthedailycaloricintakeofninth-gradestudentsintheruralhighschoolwiththedistributionofthedailycaloricintakeofninth-gradestudentsintheurbanhighschool.(b)Isitreasonabletogeneralizethefindingsofthisstudytoallruralandurbanninth-gradestudentsintheUnitedStates?Explain.Researcherswhowanttoconductasimilars
47、tudyaredebatingwhichofthefollowingtwoplanstouse.PlanI:Haveeachstudentinthestudyrecordallthefoodheorsheconsumedinoneday.Thenresearcherswouldcomputethenumberofcaloriesoffoodconsumedperkilogramofbodyweightforeachstudentforthatday.PlanII:Haveeachstudentinthestudyrecordallthefoodheorsheconsumedoverthesam
48、e7-dayperiod.Thenresearcherswouldcomputetheaveragedailynumberofcaloriesoffoodconsumedperkilogramofbodyweightforeachstudentduringthat7-dayperiod.Assumingthatthestudentskeepaccuraterecords,whichplan,IorII,wouldbettermeetthegoalofthestudy?Justifyyouranswer.2.LettherandomvariableX representthenumberofte
49、lephonelinesinusebythetechnicalsupportcenterofasoftwaremanufactureratnooneachday.TheprobabilitydistributionofX isshowninthetablebelow.(a)Calculatetheexpectedvalue(themean)ofX.(b)Usingpastrecords,thestaffatthetechnicalsupportcenterrandomlyselected20daysandfoundthatanaverageof1.25telephonelineswereinu
50、seatnoononthosedays.Thestaffproposestoselectanotherrandomsampleof1,000daysandcomputetheaveragenumberoftelephonelinesthatwereinuseatnoononthosedays.Howdoyouexpecttheaveragefromthisnewsampletocomparetothatofthefirstsample?Justifyyourresponse.(c)Themedianofarandomvariableisdefinedasanyvaluex suchthatP(
51、X 0.5andP(X x) 0.5.Fortheprobabilitydistributionshowninthetableabove,determinethemedianofX.(d)Inasentenceortwo,commentontherelationshipbetweenthemeanandthemedianrelativetotheshapeofthisdistribution.3.TheGreatPlainsRailroadisinterestedinstudyinghowfuelconsumptionisrelatedtothenumberofrailcarsforitstr
52、ainsonacertainroutebetweenOklahomaCityandOmaha.Arandomsampleof10trainsonthisroutehasyieldedthedatainthetablebelow.Ascatterplot,aresidualplot,andtheoutputfromtheregressionanalysisforthesedataareshownbelow.(a)Isalinearmodelappropriateformodelingthesedata?Clearlyexplainyourreasoning.(b)Supposethefuelco
53、nsumptioncostis$25perunit.Giveapointestimate(singlevalue)forthechangeintheaveragecostoffuelpermileforeachadditionalrailcarattachedtoatrain.Showyourwork.(c)Interpretthevalueofr2 inthecontextofthisproblem.(d)Woulditbereasonabletousethefittedregressionequationtopredictthefuelconsumptionforatrainonthisr
54、outeifthetrainhad65railcars?Explain.4Someboxesofacertainbrandofbreakfastcerealincludeavoucherforafreevideorentalinsidethebox.Thecompanythatmakesthecerealclaimsthatavouchercanbefoundin20percentoftheboxes.However,basedontheirexperienceseatingthiscerealathome,agroupofstudentsbelievesthattheproportionof
55、boxeswithvouchersislessthan0.2.Thisgroupofstudentspurchased65boxesofthecerealtoinvestigatethecompanysclaim.Thestudentsfoundatotalof11vouchersforfreevideorentalsinthe65boxes.Supposeitisreasonabletoassumethatthe65boxespurchasedbythestudentsarearandomsampleofallboxesofthiscereal.Basedonthissample,isthe
56、resupportforthestudentsbeliefthattheproportionofboxeswithvouchersislessthan0.2?Providestatisticalevidencetosupportyouranswer.AsurveywillbeconductedtoexaminetheeducationallevelofadultheadsofhouseholdsintheUnitedStates.Eachrespondentinthesurveywillbeplacedintooneofthefollowingtwocategories:Doesnothave
57、ahighschooldiplomaHasahighschooldiplomaThesurveywillbeconductedusingatelephoneinterview.Random-digitdialingwillbeusedtoselectthesample.(a)Forthissurvey,stateonepotentialsourceofbiasanddescribehowitmightaffecttheestimateoftheproportionofadultheadsofhouseholdsintheUnitedStateswhodonothaveahighschooldi
58、ploma.(b)Apilotsurveyindicatedthatabout22percentofthepopulationofadultheadsofhouseholdsdonothaveahighschooldiploma.Usingthisinformation,howmanyrespondentsshouldbeobtainedifthegoalofthesurveyistoestimatetheproportionofthepopulationwhodonothaveahighschooldiplomatowithin0.03with95percentconfidence?Just
59、ifyyouranswer.(c)Sinceeducationislargelytheresponsibilityofeachstate,theagencywantstobesurethatestimatesareavailableforeachstateaswellasforthenation.Identifyasamplingmethodthatwillachievethisadditionalgoalandbrieflydescribeawaytoselectthesurveysampleusingthismethod.2005 AP STATISTICS FREE-2005 AP ST
60、ATISTICS FREE-RESPONSE QUESTIONSRESPONSE QUESTIONSSTATISTICS STATISTICS SECTION SECTION Part B Part B Questions 6 Questions 6 Spend about 25 minutes on this part Spend about 25 minutes on this part of the exam. of the exam. Percent of Section II grade25Percent of Section II grade256.Lead,foundinsome
61、paints,isaneurotoxinthatcanbeespeciallyharmfultothedevelopingbrainandnervoussystemofchildren.Childrenfrequentlyputtheirhandsintheirmouthaftertouchingpaintedsurfaces,andthisisthemostcommontypeofexposuretolead.Astudywasconductedtoinvestigatewhetherthereweredifferencesinchildrensexposuretoleadbetweensu
62、burbanday-carecentersandurbanday-carecentersinonelargecity.Forthisstudy,researchersusedarandomsampleof20childreninsuburbanday-carecenters.Tenofthese20childrenwererandomlyselectedtoplayoutside;theremaining10childrenplayedinside.Allchildrenhadtheirhandswipedcleanbeforebeginningtheirassignedone-hourpla
63、yperiodeitheroutsideorinside.Aftertheplayperiodended,theamountofleadinmicrograms(meg)oneachchildsdominanthandwasrecorded.Themeanamountofleadonthedominanthandforthechildrenplayinginsidewas3.75meg,andthemeanamountofleadforthechildrenplayingoutsidewas5.65meg.A95percentconfidenceintervalforthedifference
64、inthemeanamountofleadafteronehourinsideversusonehouroutsidewascalculatedtobe(-2.46,-1.34).Arandomsampleof18childreninurbanday-carecentersinthesamelargecitywasselected.Forthissample,thesameprocesswasused,includingrandomlyassigningchildrentoplayinsideoroutside.Thedatafortheamount(inmeg)ofleadoneachchi
65、ldsdominanthandareshowninthetablebelow.(a)Usea95percentconfidenceintervaltoestimatethedifferenceinthemeanamountofleadonachildsdominanthandafteranhourofplayinsideversusanhourofplayoutsideaturbanday-carecentersinthiscity.Besuretointerpretyourinterval.(b)Onthefigurebelow,Usingtheverticalaxisforthemeana
66、mountoflead,plotthemeanfortheamountsofleadonthedominanthandofchildrenwhoplayedinsideatthesuburbanday-carecenterandthenplotthemeanfortheamountsofleadonthedominanthandofchildrenwhoplayedinsideattheurbanday-carecenter.Connectthesetwopointswithalinesegment.Plotthetwomeans(suburbanandurban)forthechildren
67、whoplayedoutsideatthetwotypesofday-carecenters.Connectthesetwopointswithasecondlinesegment.(c)Fromthestudy,whatconclusionscanbedrawnabouttheimpactofsetting(inside,outside),environment(suburban,urban),andtherelationshipbetweenthetwoontheamountofleadonthedominanthandofchildrenafterplayinthiscity?Justifyyouranswer.Thanks
