《AP统计学讲义.ppt》由会员分享，可在线阅读，更多相关《AP统计学讲义.ppt（69页珍藏版）》请在taowenge.com淘文阁网|工程机械CAD图纸|机械工程制图|CAD装配图下载|SolidWorks_CaTia_CAD_UG_PROE_设计图分享下载上搜索。
1、统计学精讲精练主讲老师：黄逸昆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 grade751TheEarthsMoonhasmanyimpactcratersthatwerecreatedwhentheinnersolarsystemwassubjectedtoheavybombardmentofsmallcelestial
2、bodies.Scientistsstudied11impactcratersontheMoontodeterminewhethertherewasanyrelationshipbetweentheageofthecraters(basedonradioactivedatingoflunarrocks)andtheimpactrate(asdeducedfromthedensityofthecraters).Thedataaredisplayedinthescatterplotbelow.(a)Describethenatureoftherelationshipbetweenimpactrat
3、eandage.Priortofittingalinearregressionmodel,theresearcherstransformedbothimpactrateandagebyusinglogarithms.Thefollowingcomputeroutputandresidualplotwereproduced.(b)Interpretthevalueofr 2.(c)Commentontheappropriatenessofthislinearregressionformodelingtherelationshipbetweenthetransformedvariables.2At
4、acertainuniversity,studentswholiveinthedormitorieseatatacommondininghall.Recently,somestudentshavebeencomplainingaboutthequalityofthefoodservedthere.Thedininghallmanagerdecidedtodoasurveytoestimatetheproportionofstudentslivinginthedormitorieswhothinkthatthequalityofthefoodshouldbeimproved.Oneevening
5、,themanageraskedthefirst100studentsenteringthedininghalltoanswerthefollowingquestion.(a)Inthissetting,explainhowbiasmayhavebeenintroducedbasedonthewaythisconveniencesamplewasselectedandsuggesthowthesamplecouldhavebeenselecteddifferentlytoavoidthatbias.(b)Inthissetting,explainhowbiasmayhavebeenintrod
6、ucedbasedonthewaythequestionwaswordedandsuggesthowitcouldhavebeenwordeddifferentlytoavoidthatbias.3TrainscarrybauxiteorefromamineinCanadatoanaluminumprocessingplantinnorthernNewYorkstateinhoppercars.Fillingequipmentisusedtoloadoreintothehoppercars.Whenfunctioningproperly,theactualweightsoforeloadedi
7、ntoeachcarbythefillingequipmentatthemineareapproximatelynormallydistributedwithameanof70tonsandastandarddeviationof0.9ton.Ifthemeanisgreaterthan70tons,theloadingmechanismisoverfilling.(a)Ifthefillingequipmentisfunctioningproperly,whatistheprobabilitythattheweightoftheoreinarandomlyselectedcarwillbe7
8、0.7tonsormore?Showyourwork.(b)Supposethattheweightoforeinarandomlyselectedcaris70.7tons.Wouldthatfactmakeyoususpectthattheloadingmechanismisoverfillingthecars?Justifyyouranswer.(c)Ifthefillingequipmentisfunctioningproperly,whatistheprobabilitythatarandomsampleof10carswillhaveameanoreweightof70.7tons
9、ormore?Showyourwork.(d)Basedonyouranswerinpart(c),ifarandomsampleof10carshadameanoreweightof70.7tons,wouldyoususpectthattheloadingmechanismwasoverfillingthecars?Justifyyouranswer.4.TheprincipalatCrestMiddleSchool,whichenrollsonlysixth-gradestudentsandseventh-gradestudents,isinterestedindeterminingho
10、wmuchtimestudentsatthatschoolspendonhomeworkeachnight.Thetablebelowshowsthemeanandstandarddeviationoftheamountoftimespentonhomeworkeachnight(inminutes)forarandomsampleof20sixth-gradestudentsandaseparaterandomsampleof20seventh-gradestudentsatthisschool.Basedondotplotsofthesedata,itisnotunreasonableto
11、assumethatthedistributionoftimesforeachgradewereapproximatelynormallydistributed.(a)Estimatethedifferenceinmeantimesspentonhomeworkforallsixth-andseventh-gradestudentsinthisschoolusinganinterval.Besuretointerpretyourinterval.(b)Anassistantprincipalreasonedthatamuchnarrowerconfidenceintervalcouldbeob
12、tainedifthestudentswerepairedbasedontheirresponses;forexample,pairingthesixth-gradestudentandtheseventh-gradestudentwiththehighestnumberofminutesspentonhomework,thesixth-gradestudentandseventh-gradestudentwiththenexthighestnumberofminutesspentonhomework,andsoon.Istheassistantprincipalcorrectinthinki
13、ngthatmatchingstudentsinthiswayandthencomputingamatched-pairsconfidenceintervalforthemeandifferenceintimespentonhomeworkisabetterprocedurethantheoneusedinpart(a)?Explainwhyorwhynot.5.AresearcherthinksthatmodernThaidogsmaybedescendantsofgoldenjackals.Arandomsampleof16animalswascollectedfromeachofthet
14、wopopulations.Thelength(inmillimeters)ofthemandible(jawbone)wasmeasuredforeachanimal.Thelowerquartile,median,andupperquartileforeachsampleareshowninthetablebelow,alongwithallvaluesbelowthelowerquartileandallvaluesabovetheupperquartile.(a)Displayparallelboxplotsofmandiblelengths(showingoutliers,ifany
15、)forthemodernThaidogsandthegoldenjackalsonthegridbelow.Basedontheboxplots,writeafewsentencescomparingthedistributionsofmandiblelengthsforthetwotypesofdogs.(b)IsitreasonabletousethesampleofmandiblelengthsofmodernThaidogstoconstructanintervalestimateofthemeanmandiblelengthforthepopulationofmodernThaid
16、ogs?Justifyyouranswer.(Note:Youdonothavetocomputetheinterval.)(c)IsitreasonabletousethesampledataofmandiblelengthsofmodernThaidogsandthesampledataofmandiblelengthsofgoldenjackalstoperformatwo-samplef-testforthedifferenceinmeanmandiblelengthsforthetwotypesofdogs?Justifyyouranswer.(Note:Youdonothaveto
17、conductthetest.)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,thefollowingprocedurewasimplemented.Researchers
18、capturedaninitialsampleof200birdsofthespeciesonIslandA;theyattachedlegbandstoeachofthebirds,andthenreleasedthebirds.Similarly,asampleof250birdsofthesamespeciesonIslandBwascaptured,banded,andreleased.Sufficienttimewasallowedforthebirdstoreturntotheirnormalroutineandlocation.Subsequentsamplesofbirdsof
19、thespeciesofinterestwerethentakenfromeachisland.Thenumberofbirdscapturedandthenumberofbirdswithlegbandswererecorded.Theresultsaresummarizedinthefollowingtable.Assumethatboththeinitialsampleandthesubsequentsamplesthatweretakenoneachislandcanberegardedasrandomsamplesfromthepopulationofbirdsofthisspeci
20、es.(a)Dothedatafromthesubsequentsamplesindicatethatthereisadifferenceinproportionsofthebandedbirdsonthesetwoislands?Givestatisticalevidencetosupportyouranswer.(b)Researcherscanestimatethetotalnumberofbirdsofthisspeciesonanislandbyusinginformationonthenumberofbirdsintheinitialsampleandtheproportionof
21、bandedbirdsinthesubsequentsample.UsethisinformationtoestimatethetotalnumberofbirdsofthisspeciesonIslandA.Showyourwork.(c)Theanalysesinparts(a)and(b)assumethatthesamplesofbirdscapturedinboththeinitialandsubsequentsamplescanberegardedasrandomsamplesofthepopulationofbirdsofthisspeciesthatliveontherespe
22、ctiveislands.Thisisacommonassumptionmadebywildliferesearchers.Describetwoconcernsthatshouldbeaddressedbeforemakingthisassumption.2006 AP 2006 AP STATISSTATISQUESTIONSQUESTIONSSTATISTICS STATISTICS SECTION SECTION Part A Part A Questions 1-5 Questions 1-5 Spend about 65 minutes on this part Spend abo
23、ut 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-Pongballsfromthecatapultssothatthe
24、ballslandwithina5-centimeterband.Atargetlinewillbedrawnthroughthemiddleoftheband,asshowninthefigurebelow.Allpointsonthetargetlineareequidistantfromthelaunchinglocation.Ifaballlandswithintheshadedband,thestudentwillwinaprize.Theparentshaveconstructedthetwocatapultsaccordingtoslightlydifferentplans.Th
25、eywanttotestthesecatapultsbeforebuildingadditionalones.Underidenticalconditions,theparentslaunch40Ping-Pongballsfromeachcatapultandmeasurethedistancethattheballtravelsbeforelanding.Distancestothenearestcentimeteraregraphedinthedotplotsbelow.(a)Commentonanysimilaritiesandanydifferencesinthetwodistrib
26、utionsofdistancestraveledbyballslaunchedfromcatapultAandcatapultB.(b)IftheparentswanttomaximizetheprobabilityofhavingthePing-Pongballslandwithintheband,whichoneofthetwocatapults,AorB,wouldbebettertousethantheother?Justifyyourchoice.(c)Usingthecatapultthatyouchoseinpart(b),howmanycentimetersfromtheta
27、rgetlineshouldthiscatapultbeplaced?Explainwhyyouchosethisdistance.2.Amanufacturerofdishdetergentbelievestheheightofsoapsudsinthedishpandependsontheamountofdetergentused.Astudyofthesudsheightsforanewdishdetergentwasconducted.Sevenpansofwaterwereprepared.Allpanswereofthesamesizeandtypeandcontainedthes
28、ameamountofwater.Thetemperatureofthewaterwasthesameforeachpan.Anamountofdishdetergentwasassignedatrandomtoeachpan,andthatamountofdetergentwasaddedtothepan.Thenthewaterinthedishpanwasagitatedforasetamountoftime,andtheheightoftheresultingsudswasmeasured.Aplotofthedataandthecomputeroutputfromfittingale
29、astsquaresregressionlinetothedataareshownbelow.(a)Writetheequationofthefittedregressionline.Defineanyvariablesusedinthisequation.(b)Notethats=1.99821 in the computer output.Interpret this value in the context of this study.(c)Identifyandinterpretthestandarderroroftheslope.3.ThedepthfromthesurfaceofE
30、arthtoarefractinglayerbeneaththesurfacecanbeestimatedusingmethodsdevelopedbyseismologists.Onemethodisbasedonthetimerequiredforvibrationstotravelfromadistantexplosiontoareceivingpoint.Thedepthmeasurement(M)isthesumofthetruedepth(D)andtherandommeasurementerror(E).That is,M-D+E.The measurement error(E)
31、is assumed to be normally distributed with mean 0 feet and standard deviation 1.5 feet.(a)Ifthetruedepthatacertainpointis2feet,whatistheprobabilitythatthedepthmeasurementwillbenegative?(b)Supposethreeindependentdepthmeasurementsaretakenatthepointwherethetruedepthis2feet.Whatistheprobabilitythatatlea
32、stoneofthesemeasurementswillbenegative?(c)Whatistheprobabilitythatthemeanofthethreeindependentdepthmeasurementstakenatthepointwherethetruedepthis2feetwillbenegative?4.Patientswithheart-attacksymptomsarriveatanemergencyroomeitherbyambulanceorself-transportationprovidedbythemselves,family,orfriends.Wh
33、enapatientarrivesattheemergencyroom,thetimeofarrivalisrecorded.Thetimewhenthepatientsdiagnostictreatmentbeginsisalsorecorded.Anadministratorofalargehospitalwantedtodeterminewhetherthemeanwaittime(timebetweenarrivalanddiagnostictreatment)forpatientswithheart-attacksymptomsdiffersaccordingtothemodeoft
34、ransportation.Arandomsampleof150patientswithheart-attacksymptomswhohadreportedtotheemergencyroomwasselected.Foreachpatient,themodeoftransportationandwaittimewererecorded.Summarystatisticsforeachmodeoftransportationareshowninthetablebelow.(a)Usea99percentconfidenceintervaltoestimatethedifferencebetwe
35、enthemeanwaittimesforambulance-transportedpatientsandself-transportedpatientsatthisemergencyroom.(b)Basedonlyonthisconfidenceinterval,doyouthinkthedifferenceinthemeanwaittimesisstatisticallysignificant?Justifyyouranswer.5.Abiologistisinterestedinstudyingtheeffectofgrowth-enhancingnutrientsanddiffere
36、ntsalinity(salt)levelsinwateronthegrowthofshrimps.Thebiologisthasorderedalargeshipmentofyoungtigershrimpsfromasupplyhouseforuseinthestudy.Theexperimentistobeconductedinalaboratorywhere10tigershrimpsareplacedrandomlyintoeachof12similartanksinacontrolledenvironment.Thebiologistisplanningtouse3differen
37、tgrowth-enhancingnutrients(A,B,andC)andtwodifferentsalinitylevels(lowandhigh).(a)Listthetreatmentsthatthebiologistplanstouseinthisexperiment.(b)Usingthetreatmentslistedinpart(a),describeacompletelyrandomizeddesignthatwillallowthebiologisttocomparetheshrimpsgrowthafter3weeks.(c)Giveonestatisticaladva
38、ntagetohavingonlytigershrimpsintheexperiment.Explainwhythisisanadvantage.(d)Giveonestatisticaldisadvantagetohavingonlytigershrimpsintheexperiment.Explainwhythisisadisadvantage.2006 AP STATISTICS FREE-2006 AP STATISTICS FREE-RESPONSE QUESTIONSRESPONSE QUESTIONSSTATISTICS STATISTICS SECTION SECTION Pa
39、rt 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.Amanufacturerofthermostatsisconcernedthatthereadingsofitsthermostatshavebecomelessreliable(morevariable).Int
40、hepast,thevariancehasbeen1.52degreesFahrenheit(F)squared.Arandomsampleof10recentlymanufacturedthermostatswasselectedandplacedinaroomthatwasmaintainedat68F.Thereadingsforthose10thermostatsaregiveninthetablebelow.(a)Statethenullandalternativehypothesesthatthemanufacturerisinterestedintesting.(b)Calcul
41、atethevalueof(n-1)S2/1.52forthesedata.(c)Assumethatthepopulationofthermostattemperaturesfollowsanormaldistribution.Usetheteststatistic(n-1)S2/1.52frompart(b)andthechi-squaredistributiontotestthehypothesesinpart(a).(d)Forthetestconductedinpart(c),whatisthesmallestvalueoftheteststatisticthatwouldhavel
42、edtotherejectionofthenullhypothesisatthe5percentsignificancelevel?Markthisvalueoftheteststatisticonthegraphofthechi-squaredistributionbelow.Indicatetheregionthatcontainsallofthevaluesthatwouldhaveledtotherejectionofthenullhypothesis.(e)Usingsimulation,1,000samples,eachofsize10,wererandomlygeneratedf
43、rom3populationswithdifferentvariances.Eachpopulationwasnormallydistributedwithmean68andvariancegreaterthan1.52.Thehistogramsbelowshowthesimulatedsamplingdistributionof(n-1)S2/1.52foreachpopulation.Marktheregionidentifiedinpart(d)oneachofthehistogramsbelow.2006 AP STATISTICS FREE-2006 AP STATISTICS F
44、REE-RESPONSE QUESTIONSRESPONSE QUESTIONS(f)Basedontheregionsthatyoumarkedinpart(e),identifythesimulatedsamplingdistributionthatcorrespondstothepopulationwiththelargestvariance.Thenidentifythesimulatedsamplingdistributionthatcorrespondstothepopulationwiththesmallestvariance.Justifyyourchoices.2005 AP
45、 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 Section II grade75Percent of Section
46、 II grade751.ThegoalofanutritionalstudywastocomparethecaloricintakeofadolescentsIrvinginruralareasoftheUnitedStateswiththecaloricintakeofadolescentslivinginurbanareasoftheUnitedStates.Arandomsampleofninth-gradestudentsfromonehighschoolinaruralareawasselected.Anotherrandomsampleofninthgradersfromoneh
47、ighschoolinanurbanareawasalsoselected.Eachstudentineachsamplekeptrecordsofallthefoodheorsheconsumedinoneday.Theback-to-backstemplotbelowdisplaysthenumberofcaloriesoffoodconsumedperkilogramofbodyweightforeachstudentonthatday.(a)Writeafewsentencescomparingthedistributionofthedailycaloricintakeofninth-
48、gradestudentsintheruralhighschoolwiththedistributionofthedailycaloricintakeofninth-gradestudentsintheurbanhighschool.(b)Isitreasonabletogeneralizethefindingsofthisstudytoallruralandurbanninth-gradestudentsintheUnitedStates?Explain.Researcherswhowanttoconductasimilarstudyaredebatingwhichofthefollowin
49、gtwoplanstouse.PlanI:Haveeachstudentinthestudyrecordallthefoodheorsheconsumedinoneday.Thenresearcherswouldcomputethenumberofcaloriesoffoodconsumedperkilogramofbodyweightforeachstudentforthatday.PlanII:Haveeachstudentinthestudyrecordallthefoodheorsheconsumedoverthesame7-dayperiod.Thenresearcherswould
50、computetheaveragedailynumberofcaloriesoffoodconsumedperkilogramofbodyweightforeachstudentduringthat7-dayperiod.Assumingthatthestudentskeepaccuraterecords,whichplan,IorII,wouldbettermeetthegoalofthestudy?Justifyyouranswer.2.LettherandomvariableX representthenumberoftelephonelinesinusebythetechnicalsu