统计学英文模拟试题及答案

统计学英文模拟试题及答案

一、单选题（每题1分，共10分）

1.Themeasureofcentraltendencythatismostaffectedbyoutliersis:A.MeanB.MedianC.ModeD.Range【答案】A【解析】Mean平均数ishighlyinfluencedbyoutliersbecauseitinvolvessummingallvaluesandthendividingbythenumberofvalues.

2.WhatistheprobabilityofgettingaheadwhenflippingafaircoinA.0B.

0.5C.1D.-

0.5【答案】B【解析】Afaircoinhastwooutcomes:headsortails.Theprobabilityofgettingaheadis1outof2,whichis

0.

5.

3.Theprocessoforganizingdataintogroupsorclassesiscalled:A.CentraltendencyB.DispersionC.FrequencydistributionD.Standarddeviation【答案】C【解析】Frequencydistributioninvolvesorganizingdataintodifferentgroupsorclassestoshowhowofteneachgroupoccurs.

4.Acorrelationcoefficientof-

0.8indicates:A.AstrongpositiverelationshipB.AweakpositiverelationshipC.AstrongnegativerelationshipD.Norelationship【答案】C【解析】Acorrelationcoefficientrangesfrom-1to

1.Avalueof-

0.8indicatesastrongnegativerelationshipbetweentwovariables.

5.Themeasureofhowspreadoutthedataiscalled:A.CentraltendencyB.VariabilityC.FrequencyD.Standarddeviation【答案】B【解析】Variabilityreferstohowspreadoutthedatapointsareinadataset.Standarddeviationisacommonmeasureofvariability.

6.Theshapeofanormaldistributionis:A.SkewedB.BimodalC.SymmetricalD.Uniform【答案】C【解析】Anormaldistributionissymmetrical,withthemean,median,andmodeallatthecenter.

7.Thenullhypothesisinhypothesistestingis:A.ThehypothesisthatisacceptedifthealternativehypothesisisrejectedB.ThehypothesisthatthereisnosignificantdifferenceoreffectC.ThehypothesisthatthereisasignificantdifferenceoreffectD.Thehypothesisthatisalwaystrue【答案】B【解析】ThenullhypothesisH0isastatementthatthereisnosignificantdifferenceoreffect,whichistestedagainstthealternativehypothesis.

8.Themeanofadatasetis50andthestandarddeviationis

10.WhatvalueistwostandarddeviationsabovethemeanA.60B.70C.80D.90【答案】C【解析】Twostandarddeviationsabovethemeaniscalculatedas:Mean+2StandardDeviation=50+210=

70.

9.Astudyinvolvescollectingdatafromasampleof100people.Thisisanexampleof:A.DescriptivestatisticsB.InferentialstatisticsC.ParametricstatisticsD.Non-parametricstatistics【答案】B【解析】Inferentialstatisticsinvolvesmakinginferencesaboutapopulationbasedonasample.Collectingdatafromasampleof100peopleisanexampleofinferentialstatistics.

10.Themedianofthedataset3,7,7,9,10is:A.7B.8C.9D.10【答案】B【解析】Themedianisthemiddlevaluewhenthedataisarrangedinascendingorder.Thedatasetarrangedinascendingorderis3,7,7,9,10,sothemedianis

7.

二、多选题（每题4分，共20分）

1.WhatarethemeasuresofcentraltendencyA.MeanB.MedianC.ModeD.VarianceE.Standarddeviation【答案】A、B、C【解析】Measuresofcentraltendencyincludethemean,median,andmode.Varianceandstandarddeviationaremeasuresofvariability.

2.WhatarethetypesofsamplingmethodsA.RandomsamplingB.StratifiedsamplingC.ClustersamplingD.ConveniencesamplingE.Standarddeviation【答案】A、B、C、D【解析】Typesofsamplingmethodsincluderandomsampling,stratifiedsampling,clustersampling,andconveniencesampling.Standarddeviationisameasureofvariability.

3.WhatarethepropertiesofanormaldistributionA.SymmetricalB.Mean,median,andmodeareequalC.Bell-shapedD.SkewedE.Meaniszero【答案】A、B、C【解析】Propertiesofanormaldistributionincludebeingsymmetrical,havingthemean,median,andmodeequal,andbeingbell-shaped.

4.WhatarethestepsinhypothesistestingA.StatethenullhypothesisB.CollectdataC.CalculatetheteststatisticD.MakeadecisionE.Calculatethemean【答案】A、B、C、D【解析】Stepsinhypothesistestingincludestatingthenullhypothesis,collectingdata,calculatingtheteststatistic,andmakingadecision.

5.WhatarethetypesofcorrelationA.PositivecorrelationB.NegativecorrelationC.NocorrelationD.PerfectcorrelationE.Mean【答案】A、B、C【解析】Typesofcorrelationincludepositivecorrelation,negativecorrelation,andnocorrelation.Perfectcorrelationisnotastandardtypeofcorrelation.

三、填空题（每题2分，共16分）

1.Theprocessoforganizingdataintogroupsorclassesiscalled______.【答案】frequencydistribution

2.Acorrelationcoefficientof1indicatesa______correlation.【答案】perfect

3.Themeasureofcentraltendencythatisleastaffectedbyoutliersisthe______.【答案】median

4.Thenullhypothesisinhypothesistestingisdenotedby______.【答案】H

05.Theprocessofmakinginferencesaboutapopulationbasedonasampleiscalled______.【答案】inferentialstatistics

6.Themeasureofhowspreadoutthedataiscalled______.【答案】variability

7.Theshapeofanormaldistributionis______.【答案】symmetrical

8.Themeanofadatasetis20andthestandarddeviationis

5.Whatvalueisonestandarddeviationbelowthemean【答案】15

四、判断题（每题1分，共10分）

1.Themeanisalwaysequaltothemedianinanormaldistribution.（）【答案】（√）【解析】Inanormaldistribution,themean,median,andmodeareallequal.

2.Acorrelationcoefficientof0indicatesnorelationshipbetweentwovariables.（）【答案】（√）【解析】Acorrelationcoefficientof0indicatesnolinearrelationshipbetweentwovariables.

3.Thenullhypothesisisalwaystrue.（）【答案】（×）【解析】Thenullhypothesisisastatementthatthereisnosignificantdifferenceoreffect,anditisnotalwaystrue.

4.Thestandarddeviationisameasureofcentraltendency.（）【答案】（×）【解析】Thestandarddeviationisameasureofvariability,notcentraltendency.

5.Asampleof100peopleisalwaysrepresentativeofapopulation.（）【答案】（×）【解析】Asampleof100peoplemaynotberepresentativeofapopulation,dependingonhowitisselected.

6.Themedianisthemiddlevalueinadataset.（）【答案】（√）【解析】Themedianisthemiddlevaluewhenthedataisarrangedinascendingorder.

7.Themeanisthemostcommonmeasureofcentraltendency.（）【答案】（√）【解析】Themeanisthemostcommonlyusedmeasureofcentraltendency.

8.Acorrelationcoefficientof-1indicatesaperfectnegativerelationship.（）【答案】（√）【解析】Acorrelationcoefficientof-1indicatesaperfectnegativerelationshipbetweentwovariables.

9.Thenullhypothesisisrejectedifthep-valueislessthan

0.

05.（）【答案】（√）【解析】Ifthep-valueislessthan

0.05,thenullhypothesisistypicallyrejected.

10.Thestandarddeviationisalwaysgreaterthanorequaltozero.（）【答案】（√）【解析】Thestandarddeviationisameasureofvariabilityandisalwaysgreaterthanorequaltozero.

五、简答题（每题2分，共10分）

1.Whatisthedifferencebetweendescriptiveandinferentialstatistics【答案】Descriptivestatisticssummarizeanddescribethefeaturesofadataset,whileinferentialstatisticsmakeinferencesaboutapopulationbasedonasample.

2.Whatisahypothesistest【答案】Ahypothesistestisastatisticalmethodusedtomakedecisionsaboutapopulationbasedonasample.Itinvolvesstatinganullhypothesis,collectingdata,calculatingateststatistic,andmakingadecision.

3.Whatisanormaldistribution【答案】Anormaldistributionisaprobabilitydistributionthatissymmetricalandbell-shaped,withthemean,median,andmodeallatthecenter.

4.Whatisthepurposeofastandarddeviation【答案】Thepurposeofastandarddeviationistomeasurehowspreadoutthedataisinadataset.Itprovidesinformationaboutthevariabilityofthedata.

5.Whatisthedifferencebetweenapopulationandasample【答案】Apopulationistheentiregroupofindividualsoritemsthatarebeingstudied,whileasampleisasubsetofthepopulationthatisselectedforthestudy.

六、分析题（每题10分，共20分）

1.Aresearcherisstudyingtheheightsofstudentsinaschool.Theycollectdatafromasampleof50studentsandfindthatthemeanheightis170cmwithastandarddeviationof10cm.Whatcantheresearcherconcludeabouttheheightsofallstudentsintheschool【答案】Theresearchercaninferthattheheightsofallstudentsintheschoolarelikelytobecenteredaround170cmwithavariabilityofapproximately10cm.However,thisinferenceisbasedonthesampleandmaynotbeexact.

2.Astudyisconductedtodetermineifthereisacorrelationbetweenthenumberofhoursstudiedandexamscores.Thedatacollectedfrom100studentsshowsacorrelationcoefficientof

0.

6.Whatcanbeconcludedfromthiscorrelationcoefficient【答案】Acorrelationcoefficientof

0.6indicatesamoderatepositiverelationshipbetweenthenumberofhoursstudiedandexamscores.Thissuggeststhatasthenumberofhoursstudiedincreases,examscorestendtoincreaseaswell.

七、综合应用题（每题25分，共50分）

1.Acompanywantstodetermineifthereisadifferenceintheaveragesalesbetweentwodifferentsalesstrategies.Theycollectdatafrom30salesrepresentativesusingeachstrategyandfindthefollowingresults:-StrategyA:Meansales=$10,000,Standarddeviation=$2,000-StrategyB:Meansales=$9,500,Standarddeviation=$1,500Usingasignificancelevelof

0.05,canthecompanyconcludethatthereisasignificantdifferenceintheaveragesalesbetweenthetwostrategies【答案】Todetermineifthereisasignificantdifferenceintheaveragesalesbetweenthetwostrategies,wecanperformatwo-samplet-test.ThenullhypothesisH0isthatthereisnosignificantdifferenceintheaveragesales,andthealternativehypothesisH1isthatthereisasignificantdifference.-Step1:StatethehypothesesH0:μA=μBThereisnosignificantdifferenceintheaveragesalesH1:μA≠μBThereisasignificantdifferenceintheaveragesales-Step2:CalculatetheteststatisticUsingtheformulaforthetwo-samplet-test:t=meanA-meanB/sqrtsA^2/nA+sB^2/nBwheremeanAandmeanBarethesamplemeans,sAandsBarethesamplestandarddeviations,andnAandnBarethesamplesizes.t=10000-9500/sqrt2000^2/30+1500^2/30t=500/sqrt4000000/30+2250000/30t=500/sqrt

133333.33+75000t=500/sqrt

208333.33t=500/

456.41t≈

1.09-Step3:DeterminethecriticalvalueForatwo-tailedtestwithasignificancelevelof

0.05anddegreesoffreedomdf=nA+nB-2=30+30-2=58,thecriticalvaluefromthet-distributiontableisapproximately

2.

002.-Step4:MakeadecisionSincethecalculatedteststatistic

1.09islessthanthecriticalvalue

2.002,wefailtorejectthenullhypothesis.Therefore,thereisnotenoughevidencetoconcludethatthereisasignificantdifferenceintheaveragesalesbetweenthetwostrategies.

2.AresearcherisstudyingtherelationshipbetweenthenumberofhoursspentexercisingperweekandthebodymassindexBMIofindividuals.Theycollectdatafrom50individualsandfindthefollowingresults:-Numberofhoursexercisedperweek:Mean=5,Standarddeviation=2-BMI:Mean=25,Standarddeviation=5ThecorrelationcoefficientbetweenthenumberofhoursexercisedperweekandBMIis-

0.

4.Whatcantheresearcherconcludefromthiscorrelationcoefficient【答案】Thecorrelationcoefficientof-

0.4indicatesamoderatenegativerelationshipbetweenthenumberofhoursspentexercisingperweekandBMI.Thissuggeststhatasthenumberofhoursspentexercisingperweekincreases,BMItendstodecrease.However,itisimportanttonotethatcorrelationdoesnotimplycausation,andtheremaybeotherfactorsinfluencingtherelationshipbetweenexerciseandBMI.-TheresearchercanconcludethatthereisaninverserelationshipbetweenthenumberofhoursspentexercisingperweekandBMI,butfurtherstudieswouldbeneededtodeterminetheunderlyingreasonsforthisrelationshipandtoestablishcausation.---标准答案

一、单选题

1.A

2.B

3.C

4.C

5.B

6.C

7.B

8.C

9.B

10.B

二、多选题

1.A、B、C

2.A、B、C、D

3.A、B、C

4.A、B、C、D

5.A、B、C

三、填空题

1.frequencydistribution

2.perfect

3.median

4.H

05.inferentialstatistics

6.variability

7.symmetrical

8.15

四、判断题

1.（√）

2.（√）

3.（×）

4.（×）

5.（×）

6.（√）

7.（√）

8.（√）

9.（√）

10.（√）

五、简答题

1.Descriptivestatisticssummarizeanddescribethefeaturesofadataset,whileinferentialstatisticsmakeinferencesaboutapopulationbasedonasample.

2.Ahypothesistestisastatisticalmethodusedtomakedecisionsaboutapopulationbasedonasample.Itinvolvesstatinganullhypothesis,collectingdata,calculatingateststatistic,andmakingadecision.

3.Anormaldistributionisaprobabilitydistributionthatissymmetricalandbell-shaped,withthemean,median,andmodeallatthecenter.

4.Thepurposeofastandarddeviationistomeasurehowspreadoutthedataisinadataset.Itprovidesinformationaboutthevariabilityofthedata.

5.Apopulationistheentiregroupofindividualsoritemsthatarebeingstudied,whileasampleisasubsetofthepopulationthatisselectedforthestudy.

六、分析题

1.Theresearchercaninferthattheheightsofallstudentsintheschoolarelikelytobecenteredaround170cmwithavariabilityofapproximately10cm.However,thisinferenceisbasedonthesampleandmaynotbeexact.

2.Acorrelationcoefficientof

0.6indicatesamoderatepositiverelationshipbetweenthenumberofhoursstudiedandexamscores.Thissuggeststhatasthenumberofhoursstudiedincreases,examscorestendtoincreaseaswell.

七、综合应用题

1.Thecompanycanconcludethatthereisnotenoughevidencetoconcludethatthereisasignificantdifferenceintheaveragesalesbetweenthetwostrategies.

2.TheresearchercanconcludethatthereisaninverserelationshipbetweenthenumberofhoursspentexercisingperweekandBMI,butfurtherstudieswouldbeneededtodeterminetheunderlyingreasonsforthisrelationshipandtoestablishcausation.。