数据分析33.docx

数据分析33.docx

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数据分析33

Question1

WewanttoestimatetheaveragecoffeeintakeofCourserastudents,measuredincupsofcoffee.Asurveyof1,000studentsyieldsanaverageof0.55cupsperday,withastandarddeviationof1cupperday.Whichofthefollowingisnotnecessarilytrue?

YourAnswer

Score

Explanation

μ=0.55,σ=1

Correct

1.00

Justbecausethesamplestatisticsarethesevaluesdoesn'tmeanthepopulationvalueswillbeexactlyequaltothem,thereforeit'snotnecessarilytruethatμ=0.55,σ=1.

x¯=0.55,s=1

Thesampledistributionisrightskewed.

0.55isapointestimateforthepopulationmean.

Total

1.00/1.00

QuestionExplanationThisquestionreferstothefollowinglearningobjective（s）:

Definesamplestatisticasapointestimateforapopulationparameter,forexample,thesamplemeanisusedtoestimatethepopulationmean,andnotethatpointestimateandsamplestatisticaresynonymous.

Question2

Researchersstudyinganthropometrycollectedvariousbodyandskeletalmeasurementsfor507physicallyactiveindividuals.Thehistogrambelowshowsthesampledistributionofheightsincentimeters.Ifthe507individualsareasimplerandomsample-andlet’sassumetheyare-thenthesamplemeanisapointestimateforthemeanheightofallactiveindividuals.Whatmeasuredoweusetoquantifythevariabilityofsuchanestimate?

Computethisquantityusingthedatafromthissampleandchoosethebestanswerbelow.

YourAnswer

Score

Explanation

standarddeviation=0.417

standarderror=0.417

meansquarederror=0.105

standarddeviation=0.019

standarderror=0.019

Inorrect

0.00

Wequantifyvariabilityinthesamplemeanbycalculatingthestandarderror（ofthemean）SE=σ/n√.

Total

0.00/1.00

QuestionExplanationThisquestionreferstothefollowinglearningobjective（s）:

Calculatethesamplingvariabilityofthemean,thestandarderror,asSE=σ/n√.

Question3

Thestandarderrormeasures:

YourAnswer

Score

Explanation

thevariabilityofsamplestatistics

thevariabilityofpopulationparameters

thevariabilityinthepopulation

thevariabilityofthesampledobservations

Inorrect

0.00

The``variabilityofthesampledobservations"ismeasuredbythesamplestandarddeviations.

Total

0.00/1.00

QuestionExplanationThisquestionreferstothefollowinglearningobjective（s）:

Distinguishstandarddeviation（σors）andstandarderror（SE）:

standarddeviationmeasuresthevariabilityinthedata,whilestandarderrormeasuresthevariabilityinpointestimatesfromdifferentsamplesofthesamesizeandfromthesamepopulation,i.e.measuresthesamplingvariability.

Question4

Supposeyoutookalargenumberofrandomsamplesofsizenfromalargepopulationandcalculatedthemeanofeachsample.Thensupposeyouplottedthedistributionofyoursamplemeansinahistogram.Nowconsiderthefollowingpossibleattributesofyourcollecteddataandthepopulationfromwhichtheyweresampled.Forwhichofthefollowingsetsofattributeswouldyounotexpectyourhistogramofyoursamplemeanstofollowanearlynormaldistribution?

YourAnswer

Score

Explanation

n=120.Thepopulationdistributionisunknown,butthedistributionofdataineachsampleisslightlyskewed.

n=20.Thepopulationdistributionisnearlynormal.

n=120.Thepopulationdistributionisslightlyskewed.

n=10.Thepopulationdistributionisunknown,butthedistributionofdataineachsampleisheavilyskewed.

Correct

1.00

Samplesizeissmallandthepopulationdistributionmightbeskewed,hencelikelynotgoingtoyieldnearlynormalsamplingdistribution.

Total

1.00/1.00

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

TheGeneralSocialSurvey（GSS）isasociologicalsurveyusedtocollectdataondemographiccharacteristicsandattitudesofresidentsoftheUnitedStates.In2010,thesurveycollectedresponsesfromoverathousandUSresidents.Thesurveyisconductedface-to-facewithanin-personinterviewofarandomly-selectedsampleofadults.Oneofthequestionsonthesurveyis“Forhowmanydaysduringthepast30dayswasyourmentalhealth,whichincludesstress,depression,andproblemswithemotions,notgood?

”

Basedonresponsesfrom1,151USresidents,thesurveyreporteda95%confidenceintervalof3.40to4.24daysin2010.Giventhisinformation,whichofthefollowingstatementswouldbemostappropriatetomakeregardingthetrueaveragenumberofdaysof“notgood”mentalhealthin2010forUSresidents?

YourAnswer

Score

Explanation

ForallUSresidentsin2010,thereisa95%probabilitythatthetrueaveragenumberofdaysof“notgood”mentalhealthisbetween3.40and4.24days.

ForallUSresidentsin2010,basedonthis95%confidenceinterval,wewouldrejectanullhypothesisstatingthatthetrueaveragenumberofdaysof“notgood”mentalhealthis5days.

Thereisnotsufficientinformationtocalculatethemarginoferrorofthisconfidenceinterval.

Forthese1,151residentsin2010,weare95%confidentthattheaveragenumberofdaysof“notgood”mentalhealthisbetween3.40and4.24days.

Inorrect

0.00

Theconfidenceintervalsonlytrytocapturepopulationparameters,notsamplemeans.Wecancalculateexactlywhatthesamplemeanis.

Total

0.00/1.00

QuestionExplanationThisquestionreferstothefollowinglearningobjective（s）:

∙Interpretaconfidenceintervalas“WeareXX%confidentthatthetruepopulationparameterisinthisinterval”,whereXX%isthedesiredconfidencelevel.

∙Definemarginoferrorasthedistancerequiredtotravelineitherdirectionawayfromthepointestimatewhenconstructingaconfidenceinterval.

Question6

Astudysuggeststhattheaveragecollegestudentspends2hoursperweekcommunicatingwithothersonline.Youbelievethatthisisanunderestimateanddecidetocollectyourownsampleforahypothesistest.Yourandomlysample60studentsfromyourdormandfindthatonaveragetheyspent3.5hoursaweekcommunicatingwithothersonline.Whichofthefollowingisthecorrectsetofhypothesesforthisscenario?

YourAnswer

Score

Explanation

H0:

μ=2HA:

μ>2

Correct

1.00

H0:

μ=2HA:

μ<2

H0:

μ=3.5HA:

μ<3.5

H0:

x¯=2HA:

x¯<2

H0:

x¯=2HA:

x¯>2

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（observedormoreextremesamplestatistic|H0true）

P（H0true）

P（H0true|HAfalse）

P（H0true|observeddata）

Inorrect

0.00

Reviewtheassociatedlearningobjective.Thissoundsmoreliketheposteriorprobability:

P（hypothesis|data）.

Total

0.00/1.00

QuestionExplanationThisquestionreferstothefollowinglearningobjective（s）:

Defineap-valueastheconditionalprobabilityofobtainingasamplestatisticatleastasextremeastheoneobservedgiventhatthenullhypothesisistrue.

 p-value=P（observedormoreextremesamplestatistic|H0true）

Question8

Allbutoneofthefollowingconfidenceintervalshasamarginoferrorof0.7.Whichistheconfidenceintervalwiththedifferentmarginoferror?

YourAnswer

Score

Explanation

（−4.7,−3.3）

（1.6,4.4）

Correct

1.00

Thewidthofaconfidenceintervalis2timesthemarginoferror,sinceweaddandsubtractthesamemarginoferrortothesamplestatisticstoobtaintheboundsoftheconfidenceinterval.Tosolvethisquestionweneedtocalculatethemarginoferrorusingthisruleforeachchoice:

|（1.6−4.4）/2|=1.4

（20.3,21.7）

（−0.5,0.9）

Total

1.00/1.00

QuestionExplanationThisquestionreferstothefollowinglearningobjective（s）:

∙Recognizethatwhenthesamplesizeincreaseswewouldexpectthesamplingvariabilitytodecrease.

∙Definemarginoferrorasthedistancerequiredtotravelineitherdirectionawayfromthepointestimatewhenconstructingaconfidenceinterval,i.e.z⋆×SE.

Question9

Aresearcherfounda2006-2010surveyshowingthattheaverageageof