数据分析6.docx
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数据分析6
Question1
Whichofthefollowingisnotrequiredforthedistributionofthesampleproportiontobenearlynormal?
YourAnswer
Score
Explanation
Samplesizeshouldbeatleast30andthepopulationdistributionshouldnotbeextremelyskewed.
Correct
1.00
Whenconsideringthedistributionofthesampleproportion,wedon’thavearequirementofn≥30.Todetermineifthesamplesizeofcategoricaldataishighenough,weinsteadcheckthesuccess-failurecondition.
Observationsshouldbeindependent.
Thereshouldbeatleast10failures.
Thereshouldbeatleast10successes.
Total
1.00/1.00
QuestionExplanationRecognizethattheCentralLimitTheorem（CLT）isaboutthedistributionofpointestimates,andthatgivencertainconditions,thisdistributionwillbenearlynormal.
InthecaseoftheproportiontheCLTtellsusthatif
（1）theobservationsinthesampleareindependent,
（2）thesamplesizeissufficientlylarge（checkedusingthesuccess/failurecondition:
np≥10andn（1−p）≥10）,thenthedistributionofthesampleproportionwillbenearlynormal,centeredatthetruepopulationproportionandwithastandarderrorofp（1−p）n−−−−−√.p^∼N（mean=p,SE=p（1−p）n−−−−−−−√）
Question2
Whencheckingconditionsforcalculatingaconfidenceintervalforaproportion,youshouldusewhichnumberofsuccessesandfailures?
YourAnswer
Score
Explanation
Dependsonthecontext
Notapplicable.Thenumberofsuccessesandfailures（observedorotherwise）isnotpartoftheconditionsrequiredforcalculatingaconfidenceintervalforaproportion.
Observed
Correct
1.00
Usetheobservednumberofsuccessesandfailureswhencalculatingaconfidenceintervalforaproportion,butnotwhendoingahypothesistest.Inahypothesistestforaproportion,youshouldusenp0andn（1−p0）successesandfailures;thatis,theexpectednumberbasedonthenullproportion.
Expected（basedonthenullvalue）
Total
1.00/1.00
QuestionExplanationForconfidenceintervalsusep^（observedsampleproportion）whencalculatingthestandarderrorandcheckingthesuccess/failurecondition.Forhypothesistestsusep0（nullvalue）whencalculatingthestandarderrorandcheckingthesuccess/failurecondition.
Question3
InMay2011,Gallupasked1,721studentsingradesfivethroughtwelveiftheirschoolteachesthemaboutmoneyandbanking.Researchersareinterestedinfindingoutifamajorityofstudentsreceivesucheducation.Whichofthefollowingisthecorrectsetofhypotheses?
YourAnswer
Score
Explanation
H0:
p^=0.5;HA:
p^≠0.5
H0:
p=0.5;HA:
p>0.5
Correct
1.00
Thewordingofthequestiontellsuswe’reinterestedinwhetherthetrueproportionofstudentsreceivingthiseducationisgreaterthan50%（i.e.makesthem“amajority”）.
H0:
p<0.5;HA:
p>0.5
H0:
μ=0.5;HA:
μ>0.5
Total
1.00/1.00
QuestionExplanationThisquestionrevisitsthesetupofhypothesistestingwithinthecategoricaldata/proportionsofUnit5.
Question4
Youandafriendareabouttovisittheaviaryatthelocalzooforthefirsttime.Atrustworthyzookeepersaystheaviaryholdsabout3,000birds.Yourfriendreadsomewherethat10%ofthosebirdsarecardinals,buthethinkstherearereallymorecardinalsthanthat.You’rebothgreatatidentifyingcardinalssoyoudecidetotestthisclaimwithahypothesistestonthetrueproportionpofcardinalsintheaviary.Youwalkaroundtheaviarytogetherandgetasimplerandomsamplebyspotting250birds.Ofthese,35werecardinalsand215werenotcardinals.Thep-valueis0.0175.Whichofthefollowingisfalse?
YourAnswer
Score
Explanation
p^=0.14
H0:
p=0.10
Thesuccess-failureconditionismet.
Ifinfact10%ofthebirdsintheaviaryarecardinals,theprobabilityofobtainingarandomsampleof250birdswhereexactly14%arecardinalsis0.027.
Correct
1.00
p-value=P（observedormoreextremeteststatistic|H0true）
Total
1.00/1.00
QuestionExplanationp-value=P（observedormoreextremeteststatistic|H0true）
Question5
Whendoweusethepooledproportionincalculationofthestandarderrorofthedifferenceoftwoproportions（SE（p^1−p^2））?
YourAnswer
Score
Explanation
whenusingarandomizationtesttocomparep1−p2
whencomparingp1andp2usingatheoreticalapproach,andthenullhypothesisisH0:
p1−p2=（somevalueotherthan0）
Inorrect
0.00
Reviewtheassociatedlearningobjective.
whenconstructingaconfidenceintervalforp1−p2
whencomparingp1andp2usingatheoreticalapproach,andthenullhypothesisisH0:
p1−p2=0
Total
0.00/1.00
∙QuestionExplanationNotethatthestandarderrorcalculationfortheconfidenceintervalandthehypothesistestaredifferentwhendealingwithproportions,sinceinthehypothesistestweneedtoassumethatthenullhypothesisistrue.
∙Notethatthecalculationofthestandarderrorofthedistributionofthedifferenceintwoindependentsampleproportionsisdifferentforaconfidenceintervalandahypothesistest.
Question6
Toevaluatethefollowinghypotheses
H0:
p=0.3
HA:
p≠0.3
weusearandomsampleof50observationswherep^=0.36.Whichofthefollowingisthecorrectstandarderror?
Choosetheclosestanswer.
YourAnswer
Score
Explanation
0.0648
0.0679
Inorrect
0.00
Forahypothesistest,SE=p0（1−p0）n−−−−−−√
0.0096
0.0297
0.0042
0.0092
Total
0.00/1.00
QuestionExplanationNotethatthereasonforthedifferenceincalculationsofstandarderroristhesameasinthecaseofthesingleproportion:
whenthenullhypothesisclaimsthatthetwopopulationproportionsareequal,weneedtotakethatintoconsiderationwhencalculatingthestandarderrorforthehypothesistest,anduseacommonproportionforbothsamples.
Question7
Anintroductorystatsprofessorhypothesizesthat50%ofstudentslearnbestbywatchingthevideos,10%byreadingthebook,20%bysolvingquestions,andtherestfromthediscussionforums.Shesurveysarandomsampleofalargesampleofstudentsaskingthemhowtheylearnbest,andwantstousethesedatatoevaluateherhypothesis.Whichmethodshouldsheuse?
YourAnswer
Score
Explanation
Z-test
t-test
χ2testofgoodnessoffit
Correct
1.00
ANOVA
Total
1.00/1.00
∙QuestionExplanationUseachi-squaretestofgoodnessoffittoevaluateifthedistributionoflevelsofasinglecategoricalvariablefollowsahypothesizeddistribution.
∙Whenevaluatingtheindependenceoftwocategoricalvariableswhereatleastonehasmorethantwolevels,useachi-squaretestofindependence.
Question8
Whendoingahypothesistestonasingleproportion（i.e.foronecategoricalvariable）,wehavestudiedhowtocalculatethep-valueforthehypothesistest,beginningwithgeneratingsimulatedsamples.Whichofthefollowingisthebestdescriptionforhowyoushouldgeneratethesimulatedsamples,andwhy?
YourAnswer
Score
Explanation
Generatesimulatedsamplesbasedonthealternativehypothesisbecausethatisthehypothesiswe’retryingtoprovewhendoingthehypothesistest.
Generatesimulatedsamplesbasedonthenullhypothesisbecausethatisthehypothesiswe’retryingtoprovewhendoingthehypothesistest.
Generatesimulatedsamplesbasedonthenullhypothesisbecauseweneedtoseehowextremeourobserveddatalooksifthenullhypothesiswerereallytrue.
Correct
1.00
Generatesimulatedsamplesbasedonthealternativehypothesisbecauseweneedtoseehowextremeourobserveddatalooksifthealternativehypothesiswerereallytrue.
Total
1.00/1.00
QuestionExplanationInhypothesistestingforonecategoricalvariable,generatesimulatedsamplesbasedonthenullhypothesis,andthencalculatethenumberofsamplesthatareatleastasextremeastheobserveddata.
Question9
Trueorfalse:
Incalculationoftherequiredsamplesizeforagivenmarginoferroroftheconfidenceintervalforapopulationproportion,weshouldusep^=0.5ifwedon’thaveanyknowledgeaboutthecharacteristicsofthepopulation.
YourAnswer
Score
Explanation
True
Correct
1.00
False
Total
1.00/1.00
Question10
Supposeinapopulation20%ofpeoplewearcontactlenses.Whatistheexpectedshapeofthesamplingdistributionofproportionofcontactlenswearersinrandomsamplesof30peoplefromthispopulation?
YourAnswer
Score
Explanation
right-skewed
Correct
1.00
S-Fconditionnotmet,andthetruepopulationiscloserto0than1,sothesamplingdistributionwillberightskewed.
uniform
left-skewed
nearlynormal
Total
1.00/1.00
QuestionExplanationNotethatiftheCLTdoesn'tapplyandthesampleproportionislow（closeto0）thesamplingdistributionwilllikelyberightskewed,ifthesampleproportionishigh（closeto1）thesamplingdistributionwilllikelybeleftskewed.
Question11
Atastopsign,somedriverscometoafullstop,somecometoa‘rollingstop’（notafullstop,butslowdown）,andsomedonotstopatall.Wewouldliketotestifthereisanassociationbetweengenderandtypeofstop（full,rolling,ornostop）.Wecollectdatabystandingafewfeetfromastopsignandtakingnoteoftypeofstopandthegenderofthedriver.Whatarethehypothesesfortestingforanassociationbetweengenderandtypeofstop?
YourAnswer
Score
Explanation
H0:
Genderandtypeofstopareindependent.
HA:
Genderandtypeofstopareassociated.
H0:
Malesandfemalesareequallylikelytocometoarollingstop.
HA:
Males
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