stat final review supplemental

ElementsofStatisticsISupplementalFinalExamReview

1. ResearchersareconductingastatewidesurveyfortheU.SPostalService.Thesurveyrecordsmanydifferentvariablesofinterest.Whichoftheseiscategorical?

A)CountyofResidenceB)Numberofpeople,bothadultsandchildren,livinginthehouseholdC)Totalhouseholdincome,beforetaxes.D)Ageofrespondent

2. Asampleofemployeesofalargepharmaceuticalcompanyhasbeenobtained.Thelengthoftime(inmonths)theyhaveworkedforthecompanywasrecordedforeachemployee.Astemplotofthesedataisshownbelow.Stem:Tensdigit,Leaf:Onesdigit.

6223345789700023444567888980011234445799990001112358Whatwouldbeabetterwaytorepresentthisdataset?A)Displaythedatainatimeplot.B)Displaythedatainaboxplot.C)Splitthestems.D)Useahistogramwithclasswidthsequalto10.3.AdistributorofappliancesisdoingacustomersatisfactionsurveyforamanufacturerofDVDplayers.Asampleof68clientsisaskedtorateaparticularDVDplayeronappearance,functionality,easeofuse,andpriceona1to10scale,where1correspondstotheworstratingand10tothebestpossiblerating.Abargraphoftheeaseofuseratingsclassifiedbygenderisgivenbelow:

WhatpercentageofthesampledfemaleclientsratedtheDVDplayerasnotsoeasytouse(aratingof4orlower)?

A)28%B)29%C)38%D)62%

1JDiaco


Usethefollowinginformationtoanswerquestions46.Inastatisticsclasswith136students,theprofessorrecordshowmuchmoneyeachstudenthasintheirpossessionduringthefirstclassofthesemester.Thehistogramshownbelowrepresentsthedatahecollected:

4. Whatisapproximatelythepercentageofstudentswithunder$10.00intheirpossession?A) 35% C) 45%B) 40% D) 50%5. Whichofthefollowingdescription(s)is/arecorrectregardingtheshapeofthehistogram?A) Skewedright D) Anoutlierispresent.B) Skewedleft E) UnimodalC) Symmetric F) Bimodal6. Whatisapproximatelythenumberofstudentswith$30.00ormoreintheirpossession?A) Lessthan5 C) About30B) About10 D) Morethan100Usethefollowinginformationtoanswerquestions78.Duringtheearlypartofthe1994baseballseason,manysportsfansandbaseballplayersnoticedthatthenumberofhomerunsbeinghitseemedtobeunusuallylarge.BelowareseparatestemplotsforthenumberofhomerunsbyAmericanLeagueandNationalLeagueteamsbasedontheteambyteamstatisticsonhomerunshitthroughFriday,June3,1994(fromtheColumbusDispatchsportssection,Sunday,June5,1994)AmericanLeague NationalLeague2 2 93 5 3 1 4 0 3 9 4 2 6 7 8 8 5 1 4 7 8 8 5 3 5 5 5 6 4 8 8 6 3 3 7 7 5 7 7 7. WhatisthemedianforthenumberofhomerunsfortheAmericanLeagueteams?A) 45B) 50C) 50.5D) 57.5

2JDiaco


8. Determinewhethereachofthefollowingstatementsistrueorfalse.A) TheAmericanLeagueplotisreasonablysymmetric.B) TheNationalLeagueplotisbimodal.C) ThemediannumberofhomerunshitbyNationalLeagueteamsforthistimeperiodwashigher

thanthemedianfortheAmericanLeagueteams.D) Thelowestnumberofhomerunshitbyany teamforthistimeperiodis29.9. WhichofthefollowingstatementsisFALSE?A) Thedistributionofacategoricalvariableliststhecategoriesandgivesthecountsorthe

percentofindividualsineachcategory.B) Abarchartisausefulgraphicaltoolfordescribingtheshapeofthedistributionofacategorical

variable.C) Astemplotisparticularlyvaluablefordisplayingtheshapeofthedistributionofacategorical

variablewhentherearefewobservations.D) Ahistogramshowsthedistributionofcountsorpercentsamongthevaluesofasingle

quantitativevariable.E) Bargraphs,unlikehistograms,haveblankspacesbetweenthebarstoseparatetheitemsbeing

compared.10 Inthefuelefficiencystudyof2007compactmodelautomobilesthefollowinghistogramofthe

distributionofthemilespergallonfuelefficiencyratingincitydriving(MPGCity)forautomobilesmanufacturedinEuropewasobtained:

Fromthehistogramabove,showingthedistributionofMPGCity,wecanseethatA) theshapeofthedistributionisroughlysymmetricwithonepeak.B) thedistributionisskewedtotheleft.C) thedistributionisskewedtotheright.D) thedistributionisroughlysymmetricwithoutliervaluestotheleft.E) theshapeofthedistributionwouldbeeasiertoseeifastemplothadbeenconstructedinstead

ofthehistogram.

3JDiaco


11 Theagesofthe667peopleparticipatinginalargeworkshop(tothenearestyear)aresummarizedasfollows:Age 18 19 20 21 22 23 24 25 32Numberofstudents 14 120 200 200 90 30 10 2 1Whatistrueaboutthemedianage?

A) Itcouldbeanynumberbetween19and20.B) Itmustbe20.C) Itmustbe21.D) Itmustbeover21.12 Areporterwishestoportraybaseballplayersasoverpaid.Whichmeasureofcentershouldhe

reportastheaveragesalaryofmajorleagueplayers?A) Themean.B) Themedian.C) Eitherthemeanormedian.Theywillbeequalinthiscase.D) Neitherthemeannorthemedian.Bothwillbemuchlowerthantheactualaveragesalary.Usethefollowinginformationtoanswerquestions1317.TheInsuranceInstituteforHighwaySafetypublishesdataonthetotaldamagesufferedbycompactautomobilesinaseriesofcontrolled,lowspeedcollisions.Thecostforasampleof9cars,inhundredsofdollars,isprovidedbelow.

10681043.57.58913 Whatisthemediancostofthetotaldamagesufferedforthissampleofcars?A) $400 C) $800B) $730 D) $100014 Whatisthefirstquartilefortheabovedata?A) $350 C) $600B) $500 D) $80015 Whatistheinterquartilerangeoftheabovedata?A) $300 C) $400B) $350 D) $45016 Whatisthemeanofthetotaldamagesufferedforthissampleofcars?A) $239B) $733C) $800D) $95017 Usingthecorrectunits,whatisthevalueofthevariance?A) 224.85dollarsB) 238.48dollars2

C) 50,555.54dollars2

D) 56,875dollars2

Usethefollowinginformationtoanswerquestions1819.

TheMichiganDepartmentofTransportation(MDOT)isworkingonamajorproject:80%ofthehighwaysinMichiganneedtoberepaved.Tospeedcompletionofthisproject,manycontractorswillbeworkingforMDOT.Contractorsarecurrentlybiddingonthenextpartoftheproject.Tohelpmakeadecisionaboutwhichcontractortohire,MDOTcollectsmanyvariablesbesidesjusttheestimatedcost.

4JDiaco


Oneofthosevariablesisthecontractorsestimateofthenumberofworkdaysrequiredtofinishthejob.Twentycontractorshavebidonthenextjob.Theboxplotbelowrepresentstheirestimatesofthenumberofworkdaysrequired:

18 Whatis(approximately)theinterquartilerange,basedontheboxplot?A) 140daysB) 270daysC) 360daysD) 760days

19 Determinewhethereachofthefollowingstatementsistrueorfalse.A) Themediannumberofdaysisapproximately180.B) Theminimumnumberofdaysisapproximately40.C) Themaximumnumberofdaysisapproximately750.D) Twentyfivepercentofcontractorsestimatedthenumberofdaystobemorethan100.20 Agriculturalfairsoftenholdcompetitionsforproducegrownbylocalgardeners.Thefollowing

dataaretheweight(inpounds)oftomatoesenteredintoanannualfairinRoland,Manitoba,Canadain2007:2.481.521.151.131.000.990.960.940.75TheInterquartileRange(IQR)forthesedatais:

A) 1.73poundsB) 0.58poundsC) 0.19poundsD) 1.00poundsE) 0.385pounds21 Applythe1.5IQRruletothedatainquestion#20tocheckforoutliervalues.InthiscaseA) therearenooutliers.B) thevalue0.75istheonlyoutlier.C) thevalues0.75and2.48arebothoutliers.D) thevalue2.48istheonlyoutlier.E) thevalues1.52and2.48arebothoutliers.

5JDiaco


22 TheNewEnglandPatriotsareatoprankedteamintheNationalFootballLeague(NFL)andtheSaskatchewanRoughridersarethe2007championsoftheCanadianFootballLeague(CFL).Fromthe2007rostersofthesetwoteamstheweightoftheplayerswasdeterminedandthefollowingsidebysideboxplotsoftheirweightsisprovidedbelow:

Whichofthefollowingstatementsaboutthesesidebysideboxplotsis(are)TRUE?

A) TheweightsoftheNewEnglandteamexhibitlessoverallvariationthantheSaskatchewanteam.B) ThemedianweightfortheNewEnglandteamishigherthanthemedianweightforSaskatchewan.C) TheIQRfortheSaskatchewanteamisgreaterthantheIQR oftheNewEnglandteam.D) AandBE) BandC23 WhichofthefollowingstatementsabouttheMeanandtheMedianofadensitycurveareFALSE?A) TheMedianisthepointontheaxisthatdividestheareaunderthedensitycurveintwoequalhalves.B) TheMedianandtheMeanhavethesamevalueifthedensitycurveissymmetric.C) TheMeanisthebalancepointofthedensitycurve.D) TheMedianofaskeweddensitycurveispulledawayfromtheMeaninthedirectionofthelongtail.E) ForasymmetricdensitycurveboththeMeanandtheMedianareatthecenterofthecurve.Usethefollowinginformationtoanswerquestions2425.Manyresidentsofsuburbanneighborhoodsownmorethanonecarbutconsideroneoftheircarstobethemainfamilyvehicle.TheageofthesefamilyvehiclescanbemodeledbyaNormaldistributionwithmean2yearsandstandarddeviation6months.24 Whatpercentageoffamilyvehiclesisbetween1and3yearsold?A) Cannotbedeterminedbasedontheinformationgiven.B) 68%C) 95%D) 99.7%

6JDiaco


25 Whatisthestandardizedvalueforafamilyvehiclethatis3yearsand3monthsold?A) 0.22B) 2.5C) 2.6D) 2.9226 UsingthestandardNormaldistributiontables,whatistheareaunderthestandardNormalcurve

correspondingtoZ1.22?

A) 0.1151B) 0.1112C) 0.8849D) 0.8888

28 UsingthestandardNormaldistributiontables,whatistheareaunderthestandardNormalcurvecorrespondingto0.5


31 WhichofthefollowingstatementsaboutthestandardizedzscoreofavalueofavariableX,whichhasmeanmandstandarddeviations,is(are)TRUE?

A) Thezscorehasameanequalto0.B) Thezscorehasastandarddeviationequalto1.C) Thezscoretellsushowmanystandarddeviationunitstheoriginalobservationfallawayfromthe

mean.D) Thezscoretellsusthedirectiontheobservationfallsawayfromthemean.E) Alloftheabovestatementsaboutthezscorearetrue.32Aquantileplotofthehorsepowerofasampleof65carsisshownbelow:

3002001000

Nor

mal

Sco

res

300

200

100

0

Hor

sepo

wer

Y

8

Whichofthefollowingdescriptionsbestdescribestheshapeofthedistributionofhorsepower?

Normal scores

A) NormalB) NormalwithsomeoutliersC) LeftskewedD) Rightskewed33. Fillintheblank.TheEnvironmentalProtectionAgencyrecordsdataonthefueleconomyof

manydifferentmakesofcars.Theyareinterestedindeterminingifonecouldpredictthemileageofthecar(inmilespergallon)fromtheweightofthecar(inlbs).Thevariable istheresponsevariableinthisstudy.

34. Aphenomenonisobservedmany,manytimesunderidenticalconditions.Theproportionof

timesaparticulareventAoccursisrecorded.Whatdoesthisproportionrepresent?A) TheprobabilityoftheeventA.B) ThedistributionoftheeventA.C) ThecorrelationoftheeventA.D) ThevarianceoftheeventA.Usethefollowingtoanswerquestions35and36:Thestatisticsofaparticularbasketballplayerstatethathemakes4outof5freethrowattempts.

JDiaco


35. Thebasketballplayerisjustabouttoattemptafreethrow.Whatdoyouestimatetheprobabilitythattheplayermakesthisnextfreethrowtobe?

A) 0.16B) 5050.Eitherhemakesitorhedoesnt.C) 0.80D) 1.236. Duringaseason,thebasketballplayermakesanaverageofabout200freethrowattempts.On

howmanyofthesethrowswouldyouestimatehewillactuallyscoreapoint?A) 80 C) 120B) 100 D) 16037. Whichofthefollowingstatementsbestdescribeswhatismeantbytheprobabilityofthe

outcomeofarandomphenomenon?A) Thecountoftheshorttermoccurrencesoftheoutcomes.B) Thecountoftheoutcomesofthephenomenonthatoccurinahaphazardmanner.C) Theproportionofoutcomesthatcanbeexpectedtobeobservedduringashortexperiment.D) Theproportionoftimestheoutcomewouldoccurinaverylongseriesofrepetitions.E) Theproportionofrepetitionsthatresultintheoutcomewhenanexperimentisconducted

abouttherandomphenomenon.Usethefollowingtoanswerquestions3839:Astandarddeckofcardshas52cards.Thecardshaveoneof2colors:26cardsinthedeckareredand26areblack.Thecardshaveoneof4denominations:13cardsarehearts(red),13cardsarediamonds(red),13cardsareclubs(black),and13cardsarespades(black).38. Onecardisselectedatrandomandthedenominationisrecorded.Whichofthefollowingis

thecorrectsamplespaceSforthesetofpossibleoutcomes?A) S={red,black}B) S={red,red,black,black}C) S={hearts,diamonds,clubs,spades}D) S={red,black,hearts,diamonds,clubs,spades}39. Twocardsareselectedatrandomandthecolorisrecorded.Whichofthefollowingisthe

correctsamplespaceSforthesetofpossibleoutcomes?A) S={red,black}B) S={(red,red),(red,black),(black,red),(black,black)}C) S={0,1,2}D) S={red,black,hearts,diamonds,clubs,spades}40. Twocardsareselectedatrandomandthedenominationisrecorded.TheeventHisdefinedas

theeventthatthefirstcardishearts.WhichofthefollowingcorrectlydefineseventH?A) H={diamonds,clubs,spades}B) H={hearts,diamonds,clubs,spades}C) H={(hearts,diamonds),(hearts,clubs),(hearts,spades)}D) H={(hearts,diamonds),(hearts,clubs),(hearts,spades),(hearts,hearts)}

9JDiaco


41. Twocardsareselectedatrandomandthedenominationisrecorded.TheeventDisdefinedastheeventthatthefirstcardisdiamondsandthesecondcardisred.WhichofthefollowingcorrectlydefineseventDC?DC= {(diamonds,clubs),(diamonds,spades)}A)DC= {(hearts,clubs),(hearts,spades)}B)DC= {(hearts,clubs),(hearts,spades),(spades,clubs),(spades,spades), (clubs,clubs),(clubs,spades)}

C)

D) Noneoftheabove.42. Twocardsareselectedatrandom.EventCisdefinedastheeventthatthefirstcardisclubs,

eventRastheeventthatthefirstcardisred,andeventBastheeventthatthesecondcardisblack.Whicheventsaredisjoint?

A) RandBonly.B) RandConly.C) RandB,RandC,butnotBandC.D) Noneoftheeventsaredisjoint.Usethefollowingtoanswerquestions4346:

ConsiderthefollowingprobabilityhistogramforadiscreterandomvariableX:

43. ThisprobabilityhistogramcorrespondstowhichofthefollowingdistributionsforX?A)

ValueofX 1 2 3 4 5Probability 0.06 0.25 0.38 0.25 0.06

B) ValueofX 1 2 3 4 5Probability 0.10 0.25 0.30 0.20 0.15

C) ValueofX 1 2 3 4 5Probability 0.10 0.25 0.30 0.25 0.10

D) Noneoftheabove.44. WhatistheP(X=3)?A) 0 C) 0.25B) 0.20 D) 0.30

10JDiaco


45. WhatisP(X$400)?A) 0.2119 C) 0.7881B) 0.2881 D) 0.845048. Theprobabilityisapproximately0.6thatonarandomlyselecteddaythestorewillmakeless

thanhowmuch?A) $0.30 C) $361.30B) $347.40 D) $372.6049. Bicyclesarriveatabikeshopaspartsinabox.Beforetheycanbesold,theymustbeunpacked

andassembled.Basedonpastexperience,thebikeshopownerknowsthatassemblytimesfollow(roughly)aNormaldistributionwithameanof25minutesandastandarddeviationof3minutes.Acustomerwalksintothebikeshopandwishestobuyabikeliketheoneinthewindow,butinadifferentcolor.Theshophasone,butitisstillinthebox,soitwillneedtobeassembled.Whatistheprobabilitythatthebikewillbereadywithinahalfhour?

A) 0.0478 C) 0.8413B) 0.1587 D) 0.952250. Considerthefollowingthreescenariosanddetermineiftherandomvariabledescribedineach

iseitherdiscreteorcontinuous.I. Theincreaseinlengthoflifeofacancerpatientfollowingchemotherapy.II. Thevolumeofgasolinelostduetoevaporationduringthefillingofagastank.III. Thenumberofcracksthatexceed1.5centimetersin10kilometersofa

majorhighway.TherandomvariableinscenariosI,II,andIII,respectively,is:

A) Continuous,discrete,discrete.B) Continuous,continuous,discrete.C) Continuous,continuous,continuous.D) Discrete,continuous,discrete.E) Discrete,discrete,continuous.

11JDiaco


51. ThefollowingtabledescribestheprobabilitydistributionfortherandomvariableXthatcountsthenumberoftimesacustomervisitsagrocerystoreina1weekperiod:

Visits 0 1 2 3 4ormoreP(Visits) 0.1 0.25 0.3 ? 0.1

Thevalueoftheentryinthetablefor3Visitsshouldbe:A) 0.2B) 0.55C) 0.75D) 0.25E) 0.35

Usethefollowingtoanswerquestions5254:Supposetherearethreeballsinabox.Ononeoftheballsisthenumber1,onanotheristhenumber2,andonthethirdisthenumber3.Youselecttwoballsatrandomandwithoutreplacementfromtheboxandnotethetwonumbersobserved.ThesamplespaceSconsistsofthethreeequallylikelyoutcomes{(1,2),(1,3),(2,3)}(disregardingorder).LetXbethesumofthetwoballsselected.

52. WhichofthefollowingisthecorrectdistributionforX?A)

ValueofX 1 2 3

Probability

B) ValueofX 3 4 5

Probability

C) ValueofX 1 2 3

Probability

6361 62

D) ValueofX 3 4 5

Probability

6361 62

53. Whatistheprobabilitythatthesumisatleast4?A) 0 C) B) D) 154. WhatisthemeanofX?A) 2.0 C) 4.0B) 2.33 D) 4.33

12JDiaco


55. Andyhasa(toy)garagethatissupposedtohavefourcarsinit.AccordingtoAndy,X=thenumberofcarsthatareactuallyinthegarageatanygiventimefollowsthefollowingdistribution:ValueofX 4 3 2 1 0Probability 0.90 0.05 0.03 0.02 0

Accordingtothismodel,whatistheaveragenumberofcarsthatareinthegarageatanygiventime?

A) 3cars C) 3.92carsB) 3.83cars D) 4carsUsethefollowingtoanswerquestions5659:SupposethatacollegedeterminesthefollowingdistributionforX=numberofcoursestakenbyafulltimestudentthissemester:

ValueofX 3 4 5 6Probability 0.07 0.25 0.28

56. TheprobabilityforX=4ismissing.Whatisit?A) 0.07 C) 0.40B) 0.25 D) 0.5057. Whatistheaveragenumberofcoursesfulltimestudentsatthiscollegetakethissemester?A) 4classes C) 4.74classesB) 4.26classes D) 5classes58. Whatisthestandarddeviationofthenumberofcoursesfulltimestudentsatthiscollegetake

thissemester?A) 0.89classesB) 0.94classesC) 1classD) 23.36classes59. WhatisP(X>4.74)?A) 0.25B) 0.28C) 0.53D) Impossibletocalculate,becauseXcannotbe4.74.60. Itisestimatedthatchemotherapyissuccessful70%ofthetimeincuringaparticulartypeof

cancer.Supposethat4patientswiththegiventypeofcanceraretreatedandletXbethenumberofthemthataresuccessfullycured.

X 0 1 2 3 4P(X=x) 0.01 0.08 0.27 0.40 0.24

Whatistheexpectedvalueofthenumberofpatientsthatwillbecured?A) 3B) 2C) 0.2D) 2.78E) 2.5

13JDiaco


TheBiologyDepartmentplanstorecruitanewfacultymember.Datacollectedbyadifferentuniversityonthe410possiblecandidatesareavailable.TheBiologyDepartmentisdebatingwhethertoputarequirementof10yearsofteachingexperienceinthejobadvertisement.Theavailabledataonthecandidatesareshownbelow:

Lessthan10years

experience10ormoreyears

experience TotalMale 178 112 290Female 99 21 120Total 277 133 410

61. Whatistheprobabilitythatacandidatehaslessthan10yearsexperience?62. Foreachofthefollowingscenarios,determinewhetherthebinomialdistributionisthe

appropriatedistributionfortherandomvariableX.A) Afaircoinisflippedtentimes.LetX=thenumberoftimesthecoincomesuptails.B) Afaircoinisflippedmultipletimes.LetX=thenumberoftimesthecoinneedstobeflipped

untilweseetentails.C) Aroulettewheelwithoneballinitisturnedsixtimes.LetX=thenumberoftimestheball

landsonred.D) Therearetenpeopleintheroom:fivemenandfivewomen.Threepeoplearetobeselectedat

randomtoformacommittee.LetX=thenumberofmenonthethreepersoncommittee.Usethefollowingtoanswerquestions6366:Theproportionofstudentswhoownacellphoneoncollegecampusesacrossthecountryhasincreasedtremendouslyoverthepastfewyears.Itisestimatedthatapproximately90%ofstudentsnowownacellphone.Fifteenstudentsaretobeselectedatrandomfromalargeuniversity.Assumethattheproportionofstudentswhoownacellphoneatthisuniversityisthesameasnationwide.LetX=thenumberofstudentsinthesampleof15whoownacellphone.63. WhatistheappropriatedistributionforX?A) XisN(15,0.9)B) XisB(15,0.9)C) XisB(15,13.5)D) XisN(13.5,1.16)64. Onaverage,howmanystudentswillownacellphoneinsimplerandomsamplesof15

students?A) 9B) 13C) 13.5D) 14

65. Whatisthestandarddeviationofthenumberofstudentswhoownacellphoneinsimple

randomsamplesof15students?A) 0.077B) 0.09C) 1.16D) 1.35

14JDiaco


66. Whatistheprobabilitythatallstudentsinasimplerandomsampleof15studentsownacellphone?

A) 0B) 0.1C) 0.206D) 0.967. Whichofthefollowingis(are)NOTpropertiesofabinomialsettingforsamplecounts?

I. Theobservationsareallindependent.II. Eachobservationiscategorizedasbeingaeithersuccessorafailure.III. Theproductofnandpmustbeatleast10.IV. Theprobabilityofasuccessisthesameforeachobservation.

A) IB) IIC) IIID) IVE) Alloftheabovearerequiredpropertiesofthebinomialsetting.68. Aproductionprocess,whenfunctioningasitshould,willstillproduce2%defectiveitems.A

randomsampleof10itemsistobeselectedfromthe1000itemsproducedinaparticularproductionrun.LetXbethecountofthenumberofdefectiveitemsfoundintherandomsample.WhatcanbesaidaboutthevariableX?

A) WecanuseaNormaldistributionwithmean20andstandarddeviation4.43asanapproximationforthedistributionofX.XisapproximatelyNormalwith =10and =0.44.B)

C) Xhasanapproximatebinomialdistributionwithparameters1000and0.01.D) Xhasanapproximatebinomialdistributionwithmean0.2andstandarddeviation0.443.E) WithoutadditionalinformationweareunabletodetermineifXisapproximatelyNormally

distributedorifithasabinomialdistribution.69. LetXbearandomvariable,whichhasabinomialdistributionwithmean =8andstandard

deviation =2.19.TheparametersnandpforthisbinomialdistributionarerespectivelyA) n=16,p=0.5.B) n=13.3,p=0.6.C) n=10,p=0.8.D) n=20,p=0.6.E) n=20,p=0.4.

Usethefollowingtoanswerquestions77and71:Itisclaimedthat55%ofmarriagesinthestateofCaliforniaendindivorcewithinthefirst15years.Alargestudywasstarted15yearsagoandhasbeentrackinghundredsofmarriagesinthestateofCalifornia.

70. Supposetenmarriagesarerandomlyselected.Whatistheprobabilitythatlessthantwoofthemendedinadivorce?

A) 0.0021B) 0.0045C) 0.0130D) 0.0274

15JDiaco


71. Suppose100marriagesarerandomlyselected.Whatistheprobabilitythatlessthan20ofthemendedinadivorce?

A) Lessthan0.0001B) 0.0055C) 0.0130D) 0.0229

Usethefollowingtoanswerquestions7274:

ThescoresofindividualstudentsontheAmericanCollegeTesting(ACT)ProgramCompositeCollegeEntranceExaminationhaveaNormaldistributionwithmean18.6andstandarddeviation6.0.AtNorthsideHigh,36seniorstakethetest.Assumethescoresatthisschoolhavethesamedistributionasnationalscores.

72. Whatisthemeanofthesamplingdistributionofthesamplemeanscoreforarandomsampleof36students?

A) 1.0 C) 6.0B) 3.1 D) 18.6

73. Whatisthestandarddeviationofthesamplingdistributionofthesamplemeanscoreforarandomsampleof36students?

A) 1.0 C) 6.0B) 3.1 D) 18.674. Whatisthesamplingdistributionofthesamplemeanscoreforarandomsampleof36students?A) ApproximatelyNormal,buttheapproximationispoor.B) ApproximatelyNormal,andtheapproximationisgood.C) ExactlyNormal.D) NeitherNormalnornonNormal.Itdependsontheparticular36studentsselected.Usethefollowingtoanswerquestions7577:

Chocolatebarsproducedbyacertainmachinearelabeled8.0oz.ThedistributionoftheactualweightsofthesechocolatebarsisclaimedtobeNormalwithameanof8.1ozandastandarddeviationof0.1oz.

75. Aqualitycontrolmanagerinitiallyplanstotakeasimplerandomsampleofsizenfromtheproductionline.Ifheweretodoublehissamplesize(to2n),bywhatfactorwouldthestandard

deviationofthesamplingdistributionof X change?A) 1/2 C) 2 B) 21 D) 2

16JDiaco


76. Thequalitycontrolmanagerplanstotakeasimplerandomsampleofsizenfromthe

productionline.Howbigshouldnbesothatthesamplingdistributionof X hasstandarddeviation0.01oz?

A) 10B) 100C) 1000D) CannotbedeterminedunlessweknowthepopulationfollowsaNormaldistribution.77. Ifthequalitycontrolmanagertakesasimplerandomsampleoftenchocolatebarsfromthe

productionline,whatistheprobabilitythatthesamplemeanweightofthetensampledchocolatebarswillbelessthan8.0oz?

A) 0B) 0.00078C) 0.0316D) 0.158778. Asampleofsizenisselectedatrandomfromapopulationthathasmean andstandard

deviation .Thesamplemean x willbedeterminedfromtheobservationsinthesample.Whichofthefollowingstatementsaboutthesamplemean, x ,is(are)TRUE?Themeanof x isthesameasthepopulationmean,i.e., .A)

B)Thevarianceof x is 2 n .Thestandarddeviationof x decreasesasthesamplesizegrowslarger.C)

D) Alloftheabovearetrue.E) OnlyAandBaretrue.79. Intheconstructionindustry,compressivestrengthofconcreteisacrucialcharacteristic.

Supposeforaparticularresidentialconstructionjobtheconcretetestedafter3daysshouldhaveameancompressionstrengthof =3000psiwithastandarddeviationof =50psi.ItisknownthatcompressivestrengthofconcreteisNormallydistributed.Onaconstructionsiteasampleofn=5specimensisselectedandtestedafter3days.Iftheconcretehasthedesiredcharacteristicswhatistheprobabilitythatthesamplemean x willbelargerthan3060psi?

A) 0.996B) 0.004C) 0.885D) 0.115E) Unabletodeterminebecausethesamplesizen=5ismuchtoosmalltorelyontheNormal

distributionforcalculationoftherequiredprobability.Usethefollowingtoanswerquestions80and81:Duringthesummermonths,thepricesofnonsmokingroomswithakingsizebedinhotelsinacertainareaareroughlyNormallydistributedwithameanof$131.80andastandarddeviationof$29.12.80. Whatpercentageofnonsmokingroomswithakingsizebedcostmorethan$150?A) 0.77% C) 26.60%B) 11.25% D) 36.78%

17JDiaco


81. Atravelagentrandomlyselectspricesofnonsmokingroomswithakingsizebedfrom15hotelsinthearea.Whatistheprobabilitythattheiraveragecostwillbemorethan$150?

A) 0.0077 C) 0.2660B) 0.1125 D) 0.3678Usethefollowingtoanswerquestions8284:Thedistributionoftheamountofmoneyundergraduatestudentsspendonbooksforatermisslightlyrightskewed,withameanof$400andastandarddeviationof$80.82. Ifastudentisselectedatrandom,whatistheprobabilitythatthisstudentspendsmorethan

$425onbooks?A) 0.1125B) 0.3773C) 0.6227D) Thiscannotbedeterminedfromtheinformationgiven.83. Inasimplerandomsampleof100undergraduatestudents,whatistheexpectedvalueofthe

samplemeanamountofmoneyspentonbooks?A) $400B) Anywherebetween$320and$480.C) Anywherebetween$392and$408.D) Thiscannotbedeterminedfromtheinformationgiven.84. Ifasimplerandomsampleof100undergraduatestudentsisselected,whatistheprobability

thatthesestudentsspendmorethan$425onbooks,onaverage?A) 0.00089B) 0.2353C) 0.3773D) Thiscannotbedeterminedfromtheinformationgiven.Usethefollowingscenariotoanswerquestions85and86:Intheuniversitylibraryelevatorthereisasignindicatinga16personlimitaswellasaweightlimitof2500lbs.Supposethatweightofstudents,faculty,andstaffisapproximatelyNormallydistributedwithameanweightof150lbsandastandarddeviationof27lbs.85. Whentheelevatorisfull,wecanthinkofthe16peopleintheelevatorasasimple

randomsampleofpeopleoncampus.Whataverageweightforthese16peopleintheelevatorwillresultinthetotalweightexceedingtheweightlimitof2500lbs?

86. Whatistheprobabilitythattherandomsampleof16peopleintheelevatorwillexceed

theweightlimit?87. Asimplerandomsampleof100athletesisselectedfromalargehighschool.Inthesample,

thereare15footballplayers.Whatisthestandarderrorofthesampleproportionoffootballplayers?

A) 0.00128 C) 0.05B) 0.0357 D) 0.357

18JDiaco


88. Asimplerandomsampleof60blooddonorsistakentoestimatetheproportionofdonorswithtypeAbloodwitha95%confidenceinterval.Inthesample,thereare10peoplewithtypeAblood.Whatisthemarginoferrorforthisconfidenceinterval?

A) 0.048 C) 0.094B) 0.079 D) 1.96

89. Asimplerandomsampleof85studentsistakenfromalargeuniversityontheWestCoasttoestimatetheproportionofstudentswhoseparentsboughtacarforthemwhentheyleftforcollege.Wheninterviewed,51studentsinthesamplerespondedthattheirparentsboughtthemacar.Whatisa95%confidenceintervalforp,thepopulationproportionofstudentswhoseparentsboughtacarforthemwhentheyleftforcollege?

A) (0.296,0.504) C) (0.496,0.704)B) (0.463,0.737) D) (0.513,0.687)

90. Asimplerandomsampleof100bagsoftortillachipsproducedbycompanyXisselectedeveryhourforqualitycontrol.Inthecurrentsample,18bagshadmorechips(measuredinweight)thanthelabeledquantity.Thequalitycontrolinspectorwishestousethisinformationtocalculatea90%confidenceintervalforthetrueproportionofbagsoftortillachipsthatcontain

morethanthelabelstates.Whatisthevalueofthestandarderrorof ?pA) 0.0015 C) 0.063B) 0.038 D) 0.384

Usethefollowingtoanswerquestions9193:

Asimplerandomsampleof120vetclinicsintheMidwestrevealsthatthevastmajorityofthemonlytreatsmallpets(dogs,cats,rabbits,etc.)andnolargeanimals(cows,horses,etc.).Ofthe120clinicssampled,88respondedthattheydonottreatlargeanimalsattheirclinic.

91. Whatisthevalueofthestandarderrorof ?p

A) 0.02 C) 0.04B) 0.03 D) 0.05

92. Whatisa90%confidenceintervalforp,thepopulationproportionofvetclinicsthatdotreatlargeanimals?

A) (0.163,0.371) C) (0.200,0.333)B) (0.188,0.346) D) (0.667,0.800)

93. Ifa95%confidenceintervalwerecalculatedinstead,whatwouldhappentothewidthoftheconfidenceinterval?

A) Itwouldbenarrower.B) Itwouldstaythesame.C) Itwouldbewider.D) Thiscannotbedeterminedfromtheinformationgiven.

19JDiaco


94. TheInformationTechnologyDepartmentatalargeuniversitywishestoestimatep=theproportionofstudentslivinginthedormitorieswhoownacomputerwitha95%confidenceinterval.WhatistheminimumrequiredsamplesizetheITDepartmentshouldusetoestimatetheproportionpwithamarginoferrornolargerthan3percentagepoints?

A) 33 C) 1067B) 752 D) 1068Usethefollowingtoanswerquestions9598:ThecandycompanythatmakesM&Msclaimsthat10%oftheM&Msitproducesaregreen.Supposethatthecandiesarepackagedatrandominlargebagsof200M&Ms.WhenwerandomlypickabagofM&Mswemayassumethatthisrepresentsasimplerandomsampleofsizen=200.SupposewewishtotestH0:p=0.10versusH1:p0.10.95. Underthenullhypothesis,whatisthevalueofthestandarderrorof ,thesampleproportion

ofgreenM&Msinabagof200?

p

A) 0.0015 C) 0.09B) 0.021 D) 1896. SupposethatintherandomlyselectedbagofM&Msthereareonly12greenM&Ms.Whatis

thevalueofthelargesamplezstatistic?A) z=1.886 C) z=1.886B) z=0.444 D) z=0.44497. WhatisthevalueofthecorrespondingPvalue?A) Pvalue=0.0297 C) Pvalue=0.06B) Pvalue=0.0593 D) Pvalue=0.328498. Ifa90%confidenceintervalwerecalculatedfromthesamedata,woulditcontainthevalue

0.10?A) YesB) NoC) Thiscannotbedeterminedfromtheinformationgiven.Usethefollowingtoanswerquestions99102:

Anotedpsychicwastestedforextrasensoryperception.Thepsychicwaspresentedwith200cardsfacedownandaskedtodetermineifthecardwereoneoffivesymbols:astar,across,acircle,asquare,orthreewavylines.Thepsychicwascorrectin50cases.Letprepresenttheprobabilitythatthepsychiccorrectlyidentifiesthesymbolonthecardinarandomtrial.Assumethe200trialscanbetreatedasasimplerandomsamplefromthepopulationofallguessesthepsychicwouldmakeinhislifetime.99. Basedontheresultsofthetest,whatisa95%confidenceintervalforp?A) 0.250.004 C) 0.250.055B) 0.250.05 D) 0.250.060

20JDiaco


100. Supposeyouwishedtoseeiftherewereevidencethatthepsychicisdoingbetterthanjustguessing.Todothis,youtestthehypothesesH0:p=0.20versusH1:p>0.20.Whatisthevalueofthezteststatistic?

A) z=0.83 C) z=1.96B) z=1.77 D) z=4.17101. WhatdoweknowaboutthevalueofthePvalueforthehypothesistest?A) Pvalue


AnswerKey

1.A2.C3.C4.C5.A,D,E6.B7.D8.True,False,False,True9.C10.B11.B12.A13.C14.B15.D16.B17.D18.B19.True,True,False,False20.E21.D22.D23.D24.C25.B26.D27.D28.C29.D30.D31.E32.C33.Mileageofthecar34.A35.C36.D37.D38.C39.B40.D41.D42.B43.B44.D45.C46.D47.A48.D49.D50.B51.D52.B

53.C54.C55.B56.C57.C58.B59.C60.D61. 277 0.676410

= 62.Y,N,Y,N63.B64.C65.C66.C67.C68.D69.E70.B71.A72.D73.A74.C75.B76.B77.B78.D79.B80.C

81.A82.D83.A84.A85. 2500 156.2516

= 86.normalcdf(156.25,E99,150, 274 )=0.177287.B88.C89.C90.B91.C92.C93.C94.D95.B96.A97.B98.B99.D100.B101.C102.C103.D104.B105.C

22JDiaco

stat final review supplemental

Documents