2025年CFA《數(shù)量分析》客觀題練習(xí)考試時間：______分鐘總分：______分姓名：______試卷內(nèi)容1.Asampleof30observationsistakenfromapopulationwithmean75andstandarddeviation12.Thesamplingdistributionofthesamplemeanhasameanof:A.0.4B.12C.75D.36002.IfZisastandardnormalrandomvariable,thentheprobabilitythatZislessthan1.96isapproximately:A.0.025B.0.475C.0.950D.0.9753.Thecentrallimittheoremstatesthatasthesamplesizeincreases,thesamplingdistributionofthesamplemeanapproachesa:A.uniformdistributionB.normaldistributionwithmeanequaltothepopulationmeanC.normaldistributionwithmeanequaltothepopulationstandarddeviationD.exponentialdistribution4.Astatisticusedtoestimateapopulationparameteriscalleda:A.parameterB.populationC.sampleD.statistic5.Thestandarddeviationofthesamplingdistributionofthesamplemeaniscalledthe:A.standarderrorB.samplingerrorC.standarddeviationofthepopulationD.meansquareerror6.Inahypothesistest,thenullhypothesisis:A.alwaystrueB.alwaysfalseC.maybetrueorfalseD.nevertested7.Thelevelofsignificanceinahypothesistestistheprobabilityof:A.rejectingthenullhypothesiswhenitistrueB.failingtorejectthenullhypothesiswhenitisfalseC.acceptingthenullhypothesiswhenitistrueD.failingtorejectthenullhypothesiswhenitistrue8.ATypeIerroroccurswhen:A.thenullhypothesisistrueandwefailtorejectitB.thenullhypothesisisfalseandwefailtorejectitC.thenullhypothesisistrueandwerejectitD.thenullhypothesisisfalseandwerejectit9.Thep-valueinahypothesistestistheprobabilityofobtainingateststatisticasextremeas,ormoreextremethan,theobservedvalue,assuming:A.thenullhypothesisistrueB.thealternativehypothesisistrueC.thepopulationstandarddeviationisunknownD.thesamplesizeissmall10.A95%confidenceintervalforthemeansuggeststhat:A.thereisa95%probabilitythatthepopulationmeanfallswithintheintervalB.thereisa95%probabilitythatthesamplemeanfallswithintheintervalC.weare95%confidentthatthesamplemeanfallswithintheintervalD.weare95%confidentthatthepopulationstandarddeviationfallswithintheinterval11.Thewidthofaconfidenceintervaldependson:A.thesamplesizeB.thelevelofconfidenceC.thestandarddeviationofthesampleD.alloftheabove12.Whencomparingtwopopulationmeansusingindependentsamples,theassumptionofequalpopulationvariancesisrequiredfor:A.thepooledvariancet-testB.theseparatevariancet-testC.boththepooledvariancet-testandtheseparatevariancet-testD.neitherthepooledvariancet-testnortheseparatevariancet-test13.Aregressionanalysisresultsinthefollowingequation:yhat=5+3x.Theslopeoftheregressionlineis:A.5B.3C.-3D.-514.Insimplelinearregression,thecoefficientofdetermination(R-squared)measures:A.thestrengthofthelinearrelationshipbetweentheindependentanddependentvariablesB.theproportionofthevarianceinthedependentvariablethatisexplainedbytheindependentvariableC.themeanofthedependentvariableD.thestandarddeviationoftheerrorterm15.Theleastsquaresmethodisusedto:A.minimizethesumoftheabsolutevaluesoftheresidualsB.minimizethesumofthesquaredresidualsC.maximizethesumoftheresidualsD.minimizethesumoftheabsolutevaluesoftheerrors16.Thestandarderroroftheestimateinregressionanalysismeasures:A.theaveragedistancethattheobservedvaluesfallfromtheregressionlineB.thestandarddeviationoftheindependentvariableC.thestandarddeviationofthedependentvariableD.theslopeoftheregressionline17.Atimeseriesdataexhibitstrend,seasonality,andcyclicalcomponents.Toforecastfuturevalues,amethodthatisoftensuitableis:A.movingaverageB.exponentialsmoothingC.ARIMAmodelD.regressionanalysis18.Themovingaveragemethodisasmoothingtechniquethat:A.givesmoreweighttorecentobservationsB.givesequalweighttoallobservationsinthewindowC.ismosteffectivefordatawithnotrendorseasonalityD.isusedtoforecastfuturevalues19.Thecoefficientofcorrelation(r)cantakevaluesbetween:A.-1and1B.0and1C.-infinityandinfinityD.-1and020.Ifthecorrelationcoefficientbetweentwovariablesis-0.8,itindicates:A.astrongpositivelinearrelationshipB.aweakpositivelinearrelationshipC.astrongnegativelinearrelationshipD.nolinearrelationship21.Theformulaforthesamplecorrelationcoefficient(r)is:A.r=nΣxy/(Σx2Σy2)B.r=(nΣxy-ΣxΣy)/sqrt[(nΣx2-(Σx)2)(nΣy2-(Σy)2)]C.r=(Σx-Σy)/(nσxσy)D.r=σp/(σxσy)22.Achi-squaretestcanbeusedto:A.testfortheindependenceoftwocategoricalvariablesB.testforthegoodnessoffitofadatadistributionC.constructaconfidenceintervalforapopulationvarianceD.alloftheabove23.Thedegreesoffreedomforachi-squaretestofindependenceinacontingencytablewithrrowsandccolumnsis:A.r+cB.r*cC.r+c-1D.r*c-124.TheF-statisticinanalysisofvariance(ANOVA)isusedtotest:A.theequalityofpopulationmeansB.theequalityofpopulationvariancesC.thecorrelationbetweentwovariablesD.thelinearrelationshipbetweentwovariables25.Inasimplelinearregressionanalysis,iftheslopeoftheregressionlineissignificantlydifferentfromzero,wecanconclude:A.thereisasignificantlinearrelationshipbetweentheindependentanddependentvariablesB.theindependentvariableisagoodpredictorofthedependentvariableC.thedependentvariableisagoodpredictoroftheindependentvariableD.thecorrelationcoefficientissignificant26.Arandomvariablethatcantakeononlyafiniteorcountablyinfinitenumberofvaluesiscalleda:A.continuousrandomvariableB.discreterandomvariableC.binomialrandomvariableD.normalrandomvariable27.Theexpectedvalueofadiscreterandomvariableisthe:A.meanoftherandomvariableB.medianoftherandomvariableC.modeoftherandomvariableD.varianceoftherandomvariable28.Thevarianceofadiscreterandomvariablemeasures:A.thespreadoftherandomvariablearounditsmeanB.theprobabilityoftherandomvariabletakingonaspecificvalueC.theexpectedvalueoftherandomvariableD.thestandarddeviationoftherandomvariable29.AprobabilitydistributionthatisusedtomodelthenumberofsuccessesinafixednumberofindependentBernoullitrialsiscalledthe:A.normaldistributionB.PoissondistributionC.binomialdistributionD.exponentialdistribution30.Themeanofabinomialdistributionwithparametersnandpis:A.npB.npqC.sqrt(np)D.n/p試卷答案1.C解析思路：根據(jù)抽樣分布的性質(zhì)，樣本均值的抽樣分布的均值等于總體均值。因此，樣本均值的抽樣分布的均值為75。2.C解析思路：標(biāo)準(zhǔn)正態(tài)分布表或Z表查得，Z小于1.96的概率約為0.975。因此，P(Z<1.96)≈0.950。3.B解析思路：中心極限定理指出，當(dāng)樣本量足夠大時，樣本均值的抽樣分布近似服從正態(tài)分布，其均值等于總體均值，標(biāo)準(zhǔn)差等于總體標(biāo)準(zhǔn)差除以樣本量的平方根。因此，樣本均值的抽樣分布接近于一個以總體均值為中心，標(biāo)準(zhǔn)差逐漸縮小的正態(tài)分布。4.D解析思路：用于估計總體參數(shù)的樣本度量值稱為統(tǒng)計量。例如，樣本均值、樣本方差等都是統(tǒng)計量，它們是總體參數(shù)的估計值。5.A解析思路：樣本均值的標(biāo)準(zhǔn)誤差是指樣本均值的標(biāo)準(zhǔn)差，它衡量了樣本均值圍繞總體均值波動的程度。標(biāo)準(zhǔn)誤差的計算公式為總體標(biāo)準(zhǔn)差除以樣本量的平方根。6.C解析思路：原假設(shè)（nullhypothesis）是關(guān)于總體參數(shù)的一個假設(shè)，它可能為真，也可能為假，需要通過樣本數(shù)據(jù)來進行檢驗。7.A解析思路：顯著性水平（levelofsignificance）也稱為α，是指在原假設(shè)為真的情況下，錯誤地拒絕原假設(shè)的概率，即第一類錯誤（TypeIerror）的概率。8.C解析思路：第一類錯誤（TypeIerror）是指在原假設(shè)為真的情況下，由于樣本的隨機性，我們錯誤地拒絕了原假設(shè)，作出了錯誤的結(jié)論。9.A解析思路：p值是指在原假設(shè)為真的情況下，觀察到當(dāng)前樣本數(shù)據(jù)或更極端數(shù)據(jù)的概率。它是衡量樣本數(shù)據(jù)與原假設(shè)之間矛盾程度的一個指標(biāo)。10.A解析思路：置信區(qū)間（confidenceinterval）是對于未知總體參數(shù)的一個估計區(qū)間，置信水平（levelofconfidence）表示我們有多大的把握相信這個區(qū)間包含了真實的總體參數(shù)。因此，95%置信區(qū)間意味著我們有95%的置信水平相信真實的總體均值落在這個區(qū)間內(nèi)。11.D解析思路：置信區(qū)間的寬度受樣本量、置信水平和樣本標(biāo)準(zhǔn)差的影響。樣本量越大，置信水平越高，樣本標(biāo)準(zhǔn)差越大，置信區(qū)間的寬度都會增加。12.A解析思路：當(dāng)假設(shè)兩個總體的方差相等時，可以使用pooledvariancet-test（合并方差t檢驗）來比較兩個總體的均值。這種檢驗方法需要計算一個合并的樣本方差來估計總體方差。13.B解析思路：在回歸方程yhat=a+bx中，b表示回歸線的斜率，它反映了自變量x變化一個單位時，因變量y的平均變化量。14.B解析思路：判定系數(shù)（coefficientofdetermination），通常用R-squared表示，它衡量了回歸模型中自變量對因變量的解釋程度，即回歸模型能夠解釋的因變量總變異的比例。15.B解析思路：最小二乘法（leastsquaresmethod）是一種常用的回歸分析方法，其目標(biāo)是通過最小化殘差平方和來估計回歸方程的參數(shù)，即最小化觀測值與回歸線之間垂直距離的平方和。16.A解析思路：標(biāo)準(zhǔn)誤差oftheestimate（standarderroroftheestimate）也稱為residualstandarddeviation，它衡量了觀測值圍繞回歸線的散布程度，即回歸模型預(yù)測精度的一個指標(biāo)。17.C解析思路：ARIMA模型（AutoregressiveIntegratedMovingAveragemodel）是一種時間序列預(yù)測模型，它能夠處理具有趨勢、季節(jié)性和周期性成分的時間序列數(shù)據(jù)。18.B解析思路：移動平均法（movingaverage）是一種簡單的時間序列平滑技術(shù)，它通過對最近k個觀測值計算平均值來平滑時間序列數(shù)據(jù)，并假設(shè)這些觀測值具有相同的權(quán)重。19.A解析思路：相關(guān)系數(shù)（cor