数据分析32.docx
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数据分析32.docx
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数据分析32
Question1
SupposeweareinterestedinstudyinghowmuchchocolateisconsumedbyCourserastudents,measuredingramsperweek.Aftersurveying500students,wecalculateanaverageof175gramsperweekwithastandarddeviationof195gramsperweek.Whichofthefollowingisnotnecessarilytrue?
YourAnswer
Score
Explanation
Ahistogramofthesampleswillbeskewedtotheright.
x¯=175,s=195
μ=175,σ=195
Correct
1.00
Justbecausethesamplestatisticsarethesevaluesdoesn'tmeanthepopulationvalueswillbeexactlyequaltothem,thereforeit'snotnecessarilytruethatμ=175,σ=195.
Apointestimateforthepopulationstandarddeviationis195.
Total
1.00/1.00
QuestionExplanationThisquestionreferstothefollowinglearningobjective(s):
Definesamplestatisticasapointestimateforapopulationparameter,forexample,thesamplemeanisusedtoestimatethepopulationmean,andnotethatpointestimateandsamplestatisticaresynonymous.
Question2
Researchersstudyinganthropometrycollectedvariousbodyandskeletalmeasurementsfor507physicallyactiveindividuals.Thehistogrambelowshowsthesampledistributionofheightsincentimeters.Ifthe507individualsareasimplerandomsample-andlet’sassumetheyare-thenthesamplemeanisapointestimateforthemeanheightofallactiveindividuals.Whatmeasuredoweusetoquantifythevariabilityofsuchanestimate?
Computethisquantityusingthedatafromthissampleandchoosethebestanswerbelow.
YourAnswer
Score
Explanation
meansquarederror=0.105
standarderror=0.019
standarddeviation=0.019
standarddeviation=0.417
Inorrect
0.00
Wequantifyvariabilityinthesamplemeanbycalculatingthestandarderror(ofthemean)SE=σ/n√.
standarderror=0.417
Total
0.00/1.00
QuestionExplanationThisquestionreferstothefollowinglearningobjective(s):
Calculatethesamplingvariabilityofthemean,thestandarderror,asSE=σ/n√.
Question3
Studentsareaskedtocountthenumberofchocolatechipsin22cookiesforaclassactivity.Theyfoundthatthecookiesonaveragehad14.77chocolatechipswithastandarddeviationof4.37chocolatechips.Aftercollectingthedata,astudentreportsthestandarderrorofthemeantobe0.93chocolatechips.Whatisthebestwaytointerpretthestudent’sresult?
YourAnswer
Score
Explanation
0.93chocolatechipsisameasureofthevariabilitywe’dexpectincalculationsofthemeannumberofchocolatechipsifwetookrepeatedrandomsamplesof22cookies.
Thestudenteithermadeacalculationerrororhisresultismeaningless,becauseitdoesnotmakesensetotalkabout0.93chocolatechips.
Inorrect
0.00
Standarderrormeasuresthevariabilityinpointestimatesfromdifferentsamplesofthesamesizeandfromthesamepopulation,i.e.measuresthesamplingvariability.
0.93isthestandarddeviationofthenumberofchocolatechipsinachocolatechipcookie.
0.93chocolatechipsisameasureofthevariabilityinthemeannumberofchocolatechipsacrossallchocolatechipcookies.
Total
0.00/1.00
QuestionExplanationThisquestionreferstothefollowinglearningobjective(s):
Distinguishstandarddeviation(σors)andstandarderror(SE):
standarddeviationmeasuresthevariabilityinthedata,whilestandarderrormeasuresthevariabilityinpointestimatesfromdifferentsamplesofthesamesizeandfromthesamepopulation,i.e.measuresthesamplingvariability.
Question4
Whichofthefollowingisfalseaboutthecentrallimittheorem(CLT)?
YourAnswer
Score
Explanation
Ifwetakemoresamplesfromtheoriginalpopulation,thesamplingdistributionismorelikelytobenearlynormal.
Ifthepopulationdistributionisnormal,thesamplingdistributionofthemeanwillalsobenearlynormal,regardlessofthesamplesize.
Asthesamplesizeincreases,thesamplingdistributionofthemeanismorelikelytobenearlynormal,regardlessoftheshapeoftheoriginalpopulationdistribution.
Inorrect
0.00
Reviewtheassociatedlearningobjective.
TheCLTstatesthatthesamplingdistributionwillbecenteredatthetruepopulationparameter.
Total
0.00/1.00
QuestionExplanationThisquestionreferstothefollowinglearningobjective(s):
RecognizethattheCentralLimitTheorem(CLT)isaboutthedistributionofpointestimates,andthatgivencertainconditions,thisdistributionwillbenearlynormal.
InthecaseofthemeantheCLTtellsusthatif
(1a)thesamplesizeissufficientlylarge(n≥30)andthedataarenotextremelyskewedor
(1b)thepopulationisknowntohaveanormaldistribution,and
(2)theobservationsinthesampleareindependent,
thenthedistributionofthesamplemeanwillbenearlynormal,centeredatthetruepopulationmeanandwithastandarderrorofσn√.x¯∼N(mean=μ,SE=σn√)
∙Whenthepopulationdistributionisunknown,condition(1a)canbecheckedusingahistogramorsomeothervisualizationofthedistributionoftheobserveddatainthesample.
∙Thelargerthesamplesize(n),thelessimportanttheshapeofthedistributionbecomes,i.e.whennisverylargethesamplingdistributionwillbenearlynormalregardlessoftheshapeofthepopulationdistribution.
Question5
TogetanestimateofconsumerspendingintheU.S.followingtheThanksgivingholiday,436randomlysampledAmericanadultsweresurveyed.Theirdailyspendingforthesix-dayperiodfollowingThanksgivingaveraged$84.71.A95%confidenceintervalbasedonthissampleis($80.31,$89.11).Whichofthefollowingaretrue?
1Weare95%confidentthattheaveragespendingofthe436Americanadultsinthissampleisbetween$80.31and$89.11.
1Ifwecollectedmanyrandomsamplesofthesamesizeandcalculatedaconfidenceintervalfordailyspendingforeachsample,thenwewouldexpect95%oftheintervalstocontainthetruepopulationparameter.
1Weare95%confidentthattheaveragespendingofallAmericanadultsisbetween$80.31and$89.11.
YourAnswer
Score
Explanation
IandII
IandIII
IIandIII
I,II,andIII
None
Inorrect
0.00
Someofthesestatementsarecorrect.
Total
0.00/1.00
QuestionExplanationThisquestionreferstothefollowinglearningobjective(s):
∙Interpretaconfidenceintervalas“WeareXX%confidentthatthetruepopulationparameterisinthisinterval”,whereXX%isthedesiredconfidencelevel.
∙Definemarginoferrorasthedistancerequiredtotravelineitherdirectionawayfromthepointestimatewhenconstructingaconfidenceinterval.
Question6
Aninsurancecompanyisreviewingitscurrentpolicyrates.Whenoriginallysettingtheratestheybelievedthattheaverageclaimamountwas$1,800.Theyareconcernedthatthetruemeanisactuallyhigherthanthis,becausetheycouldpotentiallylosealotofmoney.Theyrandomlyselect40claims,whichyieldasamplemeanof$1,950.Whichofthefollowingisthecorrectsetofhypothesesforthisscenario?
YourAnswer
Score
Explanation
H0:
μ=1,800
HA:
μ>1,800
Correct
1.00
H0:
μ=1,950
HA:
μ>1,800
H0:
μ=1,800
HA:
μ>1,950
H0:
x¯=1,800
HA:
x¯>1,800
Total
1.00/1.00
QuestionExplanationThisquestionreferstothefollowinglearningobjective(s):
∙Alwaysconstructhypothesesaboutpopulationparameters(e.g.populationmean,μ)andnotthesamplestatistics(e.g.samplemean,x¯).Notethatthepopulationparameterisunknownwhilethesamplestatisticismeasuredusingtheobserveddataandhencethereisnopointinhypothesizingaboutit.
∙Definethenullvalueasthevaluetheparameterissettoequalinthenullhypothesis.
∙Notethatthealternativehypothesismightbeone-sided(μthenullvalue)ortwo-sided(μ≠thenullvalue),andthechoicedependsontheresearchquestion.
Question7
Whichofthefollowingisthecorrectdefinitionofthep-value?
YourAnswer
Score
Explanation
P(H0true)
P(H0true|observeddata)
P(observedormoreextremesamplestatistic|H0true)
Correct
1.00
Defineap-valueastheconditionalprobabilityofobtainingasamplestatisticatleastasextremeastheoneobservedgiventhatthenullhypothesisistrue.
P(H0true|HAfalse)
Total
1.00/1.00
QuestionExplanationThisquestionreferstothefollowinglearningobjective(s):
Defineap-valueastheconditionalprobabilityofobtainingasamplestatisticatleastasextremeastheoneobservedgiventhatthenullhypothesisistrue.
p-value=P(observedormoreextremesamplestatistic|H0true)
Question8
Supposewecollectedasampleofsizen=100fromsomepopulationandusedthedatatocalculatea95%confidenceintervalforthepopulationmean.Nowsupposewearegoingtoincreasethesamplesizeton=300.Keepingallelseconstant,whichofthefollowingwouldweexpecttooccurasaresultofincreasingthesamplesize?
1Thestandarderrorwoulddecrease.
1Widthofthe95%confidenceintervalwouldincrease.
1Themarginoferrorwoulddecrease.
YourAnswer
Score
Explanation
IIandIII
IandIII
Correct
1.00
Increasingthesamplesize(whilekeepingthesameconfidencelevel)willdecreasethestandarderror,whichdecreasesthemarginoferrorandhencethewidthofintervals.
IandII
I,II,andIII
None
Total
1.00/1.00
QuestionExplanationThisquestionreferstothefollowinglearningobjective(s):
∙Recognizethatwhenthesamplesizeincreaseswewouldexpectthesamplingvariabilitytodecrease.
∙Definemarginoferrorasthedistancerequiredtotravelineitherdirectionawayfromthepointestimatewhenconstruct
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