2025年CFA《數(shù)量方法》專項訓(xùn)練資料考試時間：______分鐘總分：______分姓名：______試卷內(nèi)容1.Consideradatasetconsistingofthefollowingvalues:5,7,9,13,15.Themeanofthisdatasetis_______andthemedianis_______.2.Foranormallydistributedrandomvariablewithameanof100andastandarddeviationof15,theprobabilitythatthevariableisgreaterthan130isapproximately_______.3.Thevarianceofadatasetis25.Thestandarddeviationofthesamedatasetis_______.4.IfthecorrelationcoefficientbetweentwovariablesXandYis-0.6,whatcanbeinferredabouttherelationshipbetweenXandY?A)Astrongpositivelinearrelationship.B)Aweakpositivelinearrelationship.C)Astrongnegativelinearrelationship.D)Aweaknegativelinearrelationship.5.Afinancialanalystwantstoestimatetheaveragereturnofastockportfolio.Shetakesarandomsampleof30daysandcalculatesthesamplemeanreturntobe1.5%withasamplestandarddeviationof0.8%.Ifshewantstoconstructa95%confidenceintervalforthepopulationmeanreturn,theintervalwillbeapproximately_______.6.Aresearcheristestingthenullhypothesisthatthemeanheightofapopulationis170cmagainstthealternativehypothesisthatthemeanheightisgreaterthan170cm.Sheusesasignificancelevelof0.05andcalculatesap-valueof0.03.Basedonthisp-value,whatistheresearcher'sconclusion?A)Failtorejectthenullhypothesis.B)Rejectthenullhypothesis.7.Supposeacompany'sdailysalesfollowaPoissondistributionwithameanof10units.Whatistheprobabilitythatthecompanysellsexactly8unitsonagivenday?8.Theconceptofaconfidenceintervalimpliesthat:A)Ifwetakemanysamples,about95%ofthesamplemeanswillbewithintheinterval.B)Thereisa95%probabilitythatthetruepopulationmeaniswithinthecalculatedinterval.C)Theintervaliscertaintocontainthetruepopulationmean.D)Thesamplemeanisguaranteedtobethetruepopulationmean.9.ConsiderasimplelinearregressionmodelwhereYisthedependentvariableandXistheindependentvariable.AcoefficientestimateforXis2.5,andthestandarderrorofthisestimateis0.5.Totestthenullhypothesisthatthetruecoefficientiszero(H0:β1=0)againstthealternativehypothesisthatitisnotzero(H1:β1≠0)atthe0.05significancelevel,theteststatistic(t)isapproximately_______.10.Thestandarddeviationofthesamplingdistributionofthesamplemeanincreasesasthesamplesize_______.A)Increases.B)Decreases.11.Amarketingfirmwantstodetermineifthereisasignificantdifferenceintheaveragespendingbetweentwogroupsofcustomers,GroupAandGroupB.GroupAconsistsof50customerswithameanspendingof$80andastandarddeviationof$10.GroupBconsistsof60customerswithameanspendingof$85andastandarddeviationof$12.Usingasignificancelevelof0.01,theappropriateteststatistic(torz)forcomparingthetwomeansis_______.12.IfarandomvariableXfollowsastandardnormaldistribution(mean=0,standarddeviation=1),theprobabilitythatXislessthan1.96isapproximately_______.13.ThemeanofadiscreterandomvariableXis5anditsvarianceis4.TheexpectedvalueofthesquareofX,E[X^2],is_______.14.Whenusingthemethodofleastsquarestofitaregressionline,whichofthefollowingisalwaystrue?A)Thesumoftheresidualsiszero.B)Thesumofthesquaredresidualsisminimized.C)Theregressionlinepassesthroughthepoint(mean(X),mean(Y)).D)Thecorrelationcoefficientisalwayspositive.15.Aninvestorbelievesthatthereisa30%probabilitythatthestockmarketwillriseby10%nextmonthanda70%probabilitythatitwillfallby5%.Theexpectedchangeinthestockmarket,accordingtotheinvestor'sbeliefs,isapproximately_______.16.Afinancialanalystisconductingahypothesistestatthe5%significancelevel.Ifthep-valueofthetestis0.06,whatisthedecisionregardingthenullhypothesis?A)Rejectthenullhypothesis.B)Failtorejectthenullhypothesis.17.Theskewnessofaprobabilitydistributionmeasuresits:A)Centraltendency.B)Variability.C)Symmetry.D)Kurtosis.18.Asampleof100observationsistakenfromapopulation.Thesamplemeanis50,andthesamplestandarddeviationis5.A90%confidenceintervalforthepopulationmeanisapproximately_______.19.IfXandYareindependentrandomvariables,thecovariancebetweenXandYis_______.20.Inasimplelinearregressionanalysis,R-squared(R2)measurestheproportionofthevarianceinthedependentvariablethatisexplainedbytheindependentvariable(s).IfR2=0.64,itmeansthat_______.21.Astatisticusedtomeasurethestrengthanddirectionofthelinearrelationshipbetweentwovariablesisthe_______.22.Themeanofastandardnormaldistributionis_______anditsstandarddeviationis_______.23.Whenconductingahypothesistest,aTypeIerroroccursif:A)Thenullhypothesisistrueandwerejectit.B)Thenullhypothesisisfalseandwefailtorejectit.C)Thealternativehypothesisistrueandwefailtorejectit.D)Thealternativehypothesisisfalseandwerejectit.24.Afinancialresearchercollectsdataontheannualreturnsoftwostocks,StockAandStockB,overthepast10years.TodetermineifthereisasignificantlinearrelationshipbetweenthereturnsofStockAandStockB,whichtestshouldbeprimarilyused?A)t-testfortwoindependentmeans.B)Chi-squaretestforindependence.C)ANOVA.D)Pearsoncorrelationcoefficienttest.25.Thecentrallimittheoremstatesthatasthesamplesizeincreases,thesamplingdistributionofthesamplemeanbecomesapproximately_______.26.ForadiscreterandomvariableXwithpossiblevalues1,2,3,andtheircorrespondingprobabilities0.2,0.5,0.3,theexpectedvalueofX,E[X],is_______.27.Acompanywantstoestimatetheaveragetimeitscustomersspendonitswebsiteperday.Ittakesarandomsampleof40customersandcalculatesthesamplemeantimetobe15minuteswithasamplestandarddeviationof5minutes.Ifthecompanywantstoconstructa99%confidenceintervalforthepopulationmeantime,thecriticalvalue(zort)usedwillbegreaterthanthecriticalvalueusedfora95%confidenceinterval.A)True.B)False.28.Thestandarderrorofthemeandecreasesasthesamplesizeincreases.Thisimpliesthat:A)Largersamplesprovidemorepreciseestimatesofthepopulationmean.B)Smallersamplesprovidemorepreciseestimatesofthepopulationmean.C)Thevariabilityofthesamplemeansdecreaseswithlargersamplesizes.D)Thevariabilityofthesamplemeansincreaseswithlargersamplesizes.29.Aprobabilitydistributionthatisskewedtotherightissaidtohavea:A)Positiveskewness.B)Negativeskewness.C)Zeroskewness.D)Skewnessequalto1.30.Iftheestimatedcoefficientofdetermination(R2)inaregression