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statistics21bykeller
CHAPTER21
NONPARAMETRICSTATISTICS
SECTIONS1
MULTIPLECHOICEQUESTIONS
Inthefollowingmultiple-choicequestions,pleasecirclethecorrectanswer.
1.Considerthefollowingdataset:
14,14,15,16,18,19,19,20,21,22,23,25,25,25,25,and28.Therankassignedtothefourobservationsofvalue25is:
a.12
b.12.5
c.13
d.13.5
ANSWER:
d
2.ToapplytheWilcoxonranksumtesttodeterminewhetherthelocationofpopulation1isdifferentfromthelocationofpopulation2,thesamplesmustbe:
a.drawnfromnormalpopulations
b.drawnfrommatchedpairsexperiment
c.independent
d.largerthan30
ANSWER:
c
3.TheWilcoxonranksumteststatisticTisapproximatelynormallydistributedwheneverthesamplesizesarelargerthan:
a.10
b.15
c.20
d.25
ANSWER:
a
4.AWilcoxonranksumtestforcomparingtwopopulationsinvolvestwoindependentsamplesofsizes5and7.Thealternativehypothesisisstatedas:
Thelocationofpopulation1isdifferentfromthelocationofpopulation2.Theappropriatecriticalvaluesatthe5%significancelevelare:
a.20and45
b.22and43
c.33and58
d.35and56
ANSWER:
a
5.Considerthefollowingtwoindependentsamples:
SampleA:
1617192247
SampleB:
2731343740
Thevalueoftheteststatisticforaleft-tailWilcoxonranksumtestis:
a.6
b.20
c.35
d.55
ANSWER:
b
6.Anonparametricmethodtocomparetwopopulations,whenthesamplesareindependentandthedataareeitherordinalorinterval,andwherethenormalityrequirementnecessarytoperformtheparametrictestisnotsatisfied,isthe:
a.Wilcoxonranksumtest
b.signtest
c.Wilcoxonsignedranksumtest
d.equal-variancet-testof
ANSWER:
a
7.Statisticalmethodsthatrequirefewassumptions,ifany,aboutthepopulationdistributionareknownas:
a.parametrictechniques
b.nonparametrictechniques
c.freeagenttechniques
d.Alloftheabove
ANSWER:
b
8.Whichofthefollowingstatementsaboutnonparametrictestsisfalse?
a.Wecansafelyemploynonparametrictestsevenwhenweknownothingatallaboutthepopulationsfromwhichsampledataarebeingdrawn
b.Wecanconductnonparametrictestswithnominaldata
c.Wecanconductnonparametrictestswithordinaldata
d.Wecanonlyconductnonparametrictestswithdataofahigherorderthannominalorordinal
ANSWER:
d
9.Whichofthefollowingstatementsisfalse?
a.Wecanconductnonparametrictestsevenwithnominalandordinaldata
b.Whenparametricassumptionsarevalidand,therefore,eithertypeoftestcouldbeused,nonparametrictestsarelesspowerfulthanparametrictests
c.Givensamplesizeandspecifiedsignificancelevel
theprobabilityofaTypeIIerror
islargerforanonparametrictest
d.Usinganonparametrictestwhenwecouldemployaparametrictestcanbelessefficient:
Anonparametrictestoftentendstoignoreavailablesampleinformation-forexample,byfocusingonlyonthedirectionsratherthanthesizesofobserveddifferences.
ANSWER:
c
10.Considerthefollowingtwoindependentsamples:
SampleA:
151718
SampleB:
14161919202223
Thevalueoftheteststatisticforaright-tailWilcoxonranksumtestis:
a.3
b.7
c.11
d.44
ANSWER:
c
11.Thenonparametrictestsdiscussedinyourbook(Wilcoxonranksumtest,signtest,Wilcoxonsignedranksumtest,Kruskal-WallistestandFriedmantest)allrequirethattheprobabilitydistributionsbe:
a.identicalexceptwithrespecttolocation
b.identicalexceptwithrespecttospread(variance)
c.identicalexceptwithrespecttoshape(distribution)
d.differentwithrespecttolocation,spread,andshape
ANSWER:
a
12.Statisticalmethodsthatrequire,amongotherassumptions,thatthepopulationsbenormallydistributedareknownas:
a.distribution-freetechniques
b.nonparametrictechniques
c.parametrictechniques
d.both(a)and(b)arecorrect
ANSWER:
c
13.InaWilcoxonranksumtest,thetwosamplesizesare4and6,andthevalueoftheWilcoxonteststatisticisT=20.Ifthetestisatwo-tailandthelevelofsignificanceis
then:
a.thenullhypothesiswillberejected
b.thenullhypothesiswillnotberejected
c.thealternativehypothesiswillnotberejected
d.notenoughinformationhasbeengiventoanswerthisquestion
ANSWER:
b
14.ComparingtheoutputofstrawberriesgrownonplotsusingfertilizerAwiththatgrownonotherwiseidenticalplotsusingfertilizerB,inordertomakeageneralassessmentofrelativefertilizereffectiveness,maywellcallfora
a.Friedmantest
b.Kruskal-Wallistest
c.Wilcoxonrank-sumtest
d.Spearmanrankcorrelationtest
ANSWER:
c
15.AWilcoxonranksumtestforcomparingtwopopulationsinvolvestwoindependentsamplesofsizes15and20.Theun-standardizedteststatistic(thatistheranksum)isT=210.Thevalueofthestandardizedteststatisticzis:
a.14.0
b.10.5
c.6.0
d.–2.0
ANSWER:
d
16.Theappropriatemeasureofcentrallocationofordinaldataisthe:
a.mean
b.median
c.mode
d.Alloftheabove
ANSWER:
b
17.YouareperformingtheWilcoxonrank-sumtest.The13ththrough15thvaluesinanorderedarrayofpooledsampledataallequal$180(whilethe12thvalueislessandthe16thvalueismore).Theappropriateranksforthethree$180valuesare
a.13,14,15
b.14,14,14
c.12.5,13,14.5
d.12.5,13,15
ANSWER:
b
18.InanormalapproximationtotheWilcoxonranksumtest,thestandardizedteststatisticiscalculatedasz=1.80.Foratwo-tailtest,thep-valueis:
a.0.0359
b.0.4641
c.0.2321
d.0.0718
ANSWER:
d
19.Whichofthefollowingwillneverbearequiredconditionofanonparametrictest?
a.Dataareordinal
b.Dataareinterval
c.Thesamplesaredrawnfromnormallydistributedpopulations
d.Thepopulationsbeingcomparedareidenticalinspreadandshape
ANSWER:
c
20.AnonparametricmethodthatisequivalenttotheWilcoxonranksumtestisthe:
a.Wilcoxonsignedranksumtest
b.Friedmantest
c.Kruskal-Wallistest
d.Mann-Whitneytest
ANSWER:
d
21.Considerthefollowingdataset:
2.2,2.3,2.3,2.5,2.6,2.7,2.8,2.8,2.8,2.9,3.1,3.2,and3.5.Therankassignedtothethreeobservationsofvalue2.8is:
a.6
b.7
c.8
d.9
ANSWER:
c
22.TheWilcoxonranksumtest(likemostofthenonparametrictestspresentedinyourbook)actuallyteststodeterminewhetherthepopulationdistributionshaveidentical:
a.locations
b.spreads(variances)
c.shapes
d.Alloftheabove
ANSWER:
d
23.Inferentialproceduresthatarefreefromrestrictiveassumptionsaboutthesampledpopulationsareknownas
a.Distribution-freetests(becausenoassumptionaboutthenatureofthepopulationdistributionisbeingmade).
b.Distribution-freetests(becausenoassumptionaboutthenatureofthesamplingdistributionsofteststatisticsisbeingmade).
c.Parametrictests
d.Alloftheabove
ANSWER:
a
24.TousetheWilcoxonRankSumTestasatestforlocation,wemustassumethat
a.theobtaineddataareeitherordinalorintervalwherethenormalityrequirementnecessarytoperformtheequal-variancesttestof
isunsatisfied
b.bothsamplesarerandomlyandindependentlydrawnfromtheirrespectivepopulations
c.bothunderlyingpopulationsfromwhichthesamplesweredrawnareequivalentinshapeanddispersion
d.Alloftheabove
ANSWER:
d
25.WhichofthefollowingcorrectlydescribestheWilcoxonrank-sumtest?
a.Itisanonparametrictestbasedontwoindependentsimplerandomsamples
b.Itisdesignedtodeterminewhethertherelativefrequencydistributionsoftwostatisticalpopulationsofcontinuousvaluesareidenticaltoordifferentfromoneanother
c.Itisequivalenttoaparametrict-testofthedifferencebetweentwomeans.
d.Alloftheabove.
ANSWER:
d
26.ThefirststepinaWilcoxonranksumtestistocombinethedatavaluesinthetwosamplesandassignarankof1tothe:
a.smallestobservation
b.middleobservation
c.largestobservation
d.observationthatoccursmostfrequently
ANSWER:
a
TRUE/FALSEQUESTIONS
27.Aparametrictestisahypothesistestthatdependsoncertainspecificassumptionsabouttheprobabilitydistributionofpopulationvaluesorthesizesofpopulationparameters.
ANSWER:
T
28.Nonparametrictestsaremethodsofinferencethatmakenoassumptionswhatsoeveraboutthenatureofunderlyingpopulationdistributionsortheirparameters.
ANSWER:
T
29.Anonparametrictestisonethatmakesnoassumptionsaboutthespecificshapeofthepopulationfromwhichasampleisdrawn.
ANSWER:
T
30.Nonparametricproceduresareoften,andperhapsmoreaccurately,calledfree-agentstatistics.
ANSWER:
F
31.AWilcoxonranksumtestforcomparingtwoindependentsamplesinvolvestwosamplesofsizes6and9.Thealternativehypothesisisthatthelocationofpopulation1istotheleftofthelocationofpopulation2.Usinga0.05significancelevel,theappropriatecriticalvaluesare31and65.
ANSWER:
F
32.InaWilcoxonranksumtestforindependentsamples,thetwosamplesizesare4and6,andthevalueoftheWilcoxonteststatisticisT=25.Ifthetestisatwo-tailandthelevelofsignificanceis0.05,thenthenullhypothesiswillberejected.
ANSWER:
F
33.AWilcoxonranksumtestforcomparingtwopopulationsinvolvestwoindependentsamplesofsizes15and20.Ifthevalueofun-standardizedteststatisticisT=225,thenthevalueofthestandardizedteststatisticisz=–1.50.
ANSWER:
T
34.Statisticalteststhatarenotverysensitivetoerrorsinassumptionsarecalledparametrictests.
ANSWER:
F
35.Nonparametrictestsareoftenmoreefficientthanparametrictests.
ANSWER:
F
36.Thestatisticalmethodsdiscus