新编数据分析

Whichofthefollowingstatesthattheproportionofoccurrenceswithaparticularoutcomeconvergestotheprobabilityofthatoutcome?

YourAnswer

Score

Explanation

Lawoflargenumbers

Correct

1.00

Lawofaverages

Generaladditionrule

Bayes’theorem

Total

1.00/1.00

QuestionExplanationThisquestionreferstothefollowinglearningobjective:Explainwhythelong-runrelativefrequencyofrepeatedindependenteventssettlesdowntothetrueprobabilityasthenumberoftrialsincreases,i.e.whythelawoflargenumbersholds.

Question2

ShownbelowarefourVenndiagrams.InwhichofthediagramsdoestheshadedarearepresentAandBbutnotC?

YourAnswer

Score

Explanation

Correct

1.00

WeneedtheareacommontoeventsAandBtobeentirelyshadedexceptforthatportioncommontoeventC:“AandBbutnotC”.

Total

1.00/1.00

QuestionExplanationThisquestionreferstothefollowinglearningobjective:DrawVenndiagramsrepresentingeventsandtheirprobabilities.

Question3

Eachchoicebelowshowsasuggestedprobabilitydistributionforthemethodofaccesstoonlinecoursematerials(desktopcomputer,laptopcomputer,tablet,smartphone).Determinewhichisaproperprobabilitydistribution.

YourAnswer

Score

Explanation

desktopcomputer:0.15,laptopcomputer:0.50,tablet:0.30,smartphone:0.20

desktopcomputer:0.25,laptopcomputer:0.35,tablet:0.15,smartphone:0.25

Correct

1.00

Sumofallprobabilitiesmustequal1andeachprobabilitymustbeavaluebetween0and1.

desktopcomputer:0.20,laptopcomputer:0.20,tablet:0.20,smartphone:0.20

desktopcomputer:0.30,laptopcomputer:0.40,tablet:0.35,smartphone:-0.05

Total

1.00/1.00

QuestionExplanationThisquestionreferstothefollowinglearningobjective:Defineaprobabilitydistributionasalistofthepossibleoutcomeswithcorrespondingprobabilitiesthatsatisfiesthreerules:

-Theoutcomeslistedmustbedisjoint.

-Eachprobabilitymustbebetween0and1.

-Theprobabilitiesmusttotal1.

Question4

Lastsemester,outof170studentstakingaparticularstatisticsclass,71studentswere“majoring”insocialsciencesand53studentsweremajoringinpre-medicalstudies.Therewere6studentswhoweremajoringinbothpre-medicalstudiesandsocialsciences.Whatistheprobabilitythatarandomlychosenstudentismajoringinpre-medicalstudies,giventhats/heismajoringinsocialsciences?

YourAnswer

Score

Explanation

6/53

6/170

6/71

Correct

1.00

IfMistheeventastudentismajoringinpre-medicalstudiesandSistheevents/heismajoringinsocialsciences,thencalculateP(M|S)=P(M&S)P(S)=671.

(71+53−6)/170

Total

1.00/1.00

QuestionExplanationThisquestionreferstothefollowinglearningobjective:Distinguishmarginalandconditionalprobabilities.

Question5

Whichofthefollowingisfalse?

YourAnswer

Score

Explanation

Iftwooutcomesofarandomprocess(bothwithprobabilitygreaterthan0)aremutuallyexclusive,theyarenotnecessarilycomplements.

Iftwoevents(bothwithprobabilitygreaterthan0)aremutuallyexclusive,theycouldbeindependent.

Correct

1.00

Mutuallyexclusiveeventsmaybecomplements(e.g.ifacoinisflippedtheprobabilityofaHeadandaTailareboth0.5,addingupto1)buttheyalsomightnotbeiftherearemorethantwopossibleoutcomesoftherandomprocess(e.g.avotermightbeDemocrat,Republican,orIndependent,sincebeingDemocratandRepublicanaremutuallyexclusivebutnotcomplements).Howevermutuallyexclusiveeventscannotbeindependent;theeventsarealwaysdependentsinceifoneeventoccursweknowtheotheronecannot.

Iftheprobabilitiesoftwomutuallyexclusiveoutcomesofarandomprocessaddupto1,theyarecomplements.

WhencomputingtheprobabilitythatacarddrawnrandomlyfromastandarddeckiseitheraJackora4,youcanusetheadditionrule.

Total

1.00/1.00

QuestionExplanationThisquestionreferstothefollowinglearningobjective:

•Definedisjoint(mutuallyexclusive)eventsaseventsthatcannotbothhappenatthesametime:IfAandBaredisjoint,P(AandB)=0.

•Distinguishbetweendisjointandindependentevents.

-IfAandBareindependent,thenhavinginformationonAdoesnottellus

anythingaboutB(andviceversa).

-IfAandBaredisjoint,thenknowingthatAoccurstellsusthatBcannotoccur(andviceversa).

-Disjoint(mutuallyexclusive)eventsarealwaysdependentsinceifoneeventoccursweknowtheotheronecannot.

Question6

Heightsof10year-olds,regardlessofgender,closelyfollowanormaldistributionwithmean55inchesandstandarddeviation6inches.Whichofthefollowingistrue?

YourAnswer

Score

Explanation

Anormalprobabilityplotofheightsofarandomsampleof50010year-oldspeopleshouldshowafairlystraightline.

Correct

1.00

Sincethedistributionofheightsof10year-oldscloselyfollowanormaldistributionwewouldexpectthenormalprobabilityplotofheightsofalargesampleofsuchkidstoshowastraightline.

Roughly95%of10year-oldsarebetween37and73inchestall.

Wewouldexpectmore10year-oldstobeshorterthan55inchesthantaller.

A10year-oldwhois65inchestallwouldbeconsideredmoreunusualthana10year-oldwhois45inchestall.

Total

1.00/1.00

QuestionExplanationThisquestionreferstothefollowinglearningobjective:UsetheZscore

 -ifthedistributionisnormal:todeterminethepercentilescoreofadatapoint(usingtechnologyornormalprobabilitytables)

 -regardlessoftheshapeofthedistribution:toassesswhetherornottheparticularobservationisconsideredtobeunusual(morethan2standarddeviationsawayfromthemean).

Question7

TheNationalVaccineInformationCenterestimatesthat90%ofAmericanshavehadthediseasechickenpoxbythetimetheyreachadulthood.Whatistheprobabilitythatexactly92outof100randomlysampledAmericanadultshadchickenpoxduringchildhood?

YourAnswer

Score

Explanation

0.07

0.02

0.14

0.11

Correct

1.00

Usethebinomialdistributionwithn=100,k=92,andp=0.9.ThenP(k=92)=()0.9920.18=0.114892

0.10

Total

1.00/1.00

QuestionExplanationThisquestionreferstothefollowinglearningobjective:Calculatetheprobabilityofagivennumberofsuccessesinagivennumberoftrialsusingthebinomialdistribution.

Question8

YourroommatelovestoeatChinesefoodfordinner.Heestimatesthatonanygivennight,there’sa30%chancehe’llchoosetoeatChinesefood.AlthoughhelovesChinesefood,hedoesn’tliketoeatittoomuchinashortperiodoftime,soonmostweeksheeatsseveraldifferentkindsoffoodsfordinner.Supposeyouwantedtocalculatetheprobabilitythat,overthenext7days,youfriendeatsChinesefoodatleast3times.Whichofthefollowingisthemostaccuratestatementaboutcalculatingthisprobability?

YourAnswer

Score

Explanation

Becausewedonotknowtheprobabilitiesofyourroommateeatinganyothertypesoffoods,wecannotusethebinomialdistributiontocalculatethedesiredprobability.

Because“success”or“failure”havenorealmeaninginthecontextofthisproblem,wecannotusethebinomialdistributiontocalculatethedesiredprobability.

Becausehedoesn’tliketoeatChinesefoodtoomuchinashortperiodoftime,pisnotreallythesameforeachtrialandsowecannotusethebinomialdistributiontocalculatethedesiredprobability.

Becauseweknown=3,k=7,andp=0.30,wecanusethebinomialdistributiontocalculatethedesiredprobability.

Becauseweknown=7,k=3,andp=0.30,wecanusethebinomialdistributiontocalculatethedesiredprobability.

Inorrect

0.00

Becausehedoesn’tliketoeatChinesefoodtoomuchinashortperiodoftime,pisnotreallythesameforeachtrialandsowecannotusethebinomialdistributiontocalculatethedesiredprobability.

Total

0.00/1.00

QuestionExplanationThisquestionreferstothefollowinglearningobjective:Determineifarandomvariableisbinomialusingthefourconditions.

 -Thetrialsareindependent.

 -Thenumberoftrials,n,isfixed.

 -Eachtrialoutcomecanbeclassifiedasasuccessorfailure.

 -Theprobabilityofasuccess,p,isthesameforeachtrial.

Question9

Whichofthefollowing,onitsown,istheleastusefulmethodforassessingifthedatafollowanormaldistribution?

YourAnswer

Score

Explanation

Checkifthepointsareonastraightlineonanormalprobabilityplot.

Checkif68%ofthedataarewithin1SDofthemean,95%ofdataarewithin2SDsofthemean,and99.7%ofdataarewithin3SDsofthemean.

Checkifthedistributionisunimodalandsymmetric.

Inorrect

0.00

Allofthesearefeasiblemethodsforcheckingfornormalityofadistribution,buttheleastusefuliswhetherthemeanandmedianareequalsincethiswillbetrueforanysymmetricdistributionregardlessofwhetherit’snormalornot.Forexample,imagineaperfectlysymmetricbimodaldistribution(likeanmshape),themeanandthemedianofthisdistributionwillbeequalhowevertheshapeiscertainlynotnormal.

Checkifthemeanandmedianareequal.

Total

0.00/1.00

QuestionExplanationThisquestionreferstothefollowinglearningobjective:Assesswhetherornotadistributionisnearlynormalusingthe68-95-99.7%ruleorgraphicalmethodssuchasanormalprobabilityplot.

Question10

Whichofthefollowingistrue?Hint:Itmightbeusefultosketchthedistributions.

YourAnswer

Score

Explanation

TheZscoreforthemedianisundefinedifthedistributionisbimodal.

TheZscoreforthemedianisapproximately0ifthedistributionisbimodalandsymmetric.

Correct

1.00

NotetheZscoreisalwaysdefined,regardlessoftheshapeandskewofadistribution.Inasymmetricbimodaldistribution,themedianwillroughlyequalthemeanandsotheZscoreforthemedianwillbeapproximately0.

TheZscoreforthemedianwillusuallybe0ifthedistributionisunimodalandright-skewed.

TheZscoreforthemeanisundefinedifthedistributionisbimodalandskewed.

Total

1.00/1.00

QuestionExplanationThisquestionreferstothefollowinglearningobjective:Dependingontheshapeofthedistributiondeterminewhetherthemedianwouldhaveanegative,positive,or0ZscorekeepinginmindthatthemeanalwayshasaZscoreof0.

Question11

Atanygiventimeabout5.5%ofwomen(age15-45)arepregnant.Ahomepregnancytestisaccurate99%ofthetimeifthewomantakingthetestisactuallypregnantand99.5%accurateifthewomanisnotpregnant.Ifthetestyieldsapositiveresult,whatistheposteriorprobabilityofthehypothesisthatthewomanispregnant?

YourAnswer

Score

Explanation

0.92

Correct

1.00

LetPandNdenotetheevents“ispregnant”and“isnotpregnant”respectively.Let“+”and“−”denoteapositiveandnegativetestresult.WearegiventhatP(P)=0.055,P(+|P)=0.99,P(−|N)=0.995.Nowlet’swritedownthedesiredquantity,useBayes’Theoremonit,andseewhatwehave.WeareaskedtocalculateP(P|+),whichwewriteas.Weweren’tgivenP(N)orP(+|N),butwecancalculatethemusinggiveninformation.SpecificallyP(N)=1−P(P)=0.945andP(+|N)=1−P(−|N)=0.005.ThenplugintoBayes’TheoremtofindP(P|+)==0.92.Youranswermayvaryslightlyduetorounding.

0.995

0.99

0.08

Total

1.00/1.00

QuestionExplanationThisquestionreferstothefollowinglearningobjective:Distinguishbetweenmarginalandconditionalprobabilities.Constructtreediagramstocalculateconditionalprob-abilitiesandprobabilitiesofintersectionofnon-independenteventsusingBayes’the-orem:P(A|B)=P(AandB).P(B)

Question12

OnestrangephenomenonthatsometimesoccursatU.S.airportsecu