2025年英國牛津大學(xué)面試題庫及答案

一、單項選擇題（總共10題，每題2分）1.Whichofthefollowingisacharacteristicofabinomialdistribution?A.Thetrialsareindependent.B.Theprobabilityofsuccessremainsconstant.C.Thenumberoftrialsisfixed.D.Alloftheabove.2.Inanormaldistribution,whatisthevalueofthemean?A.0B.1C.ThemedianD.Themode3.Whatistheprimarypurposeofhypothesistesting?A.Toestimatethepopulationparameter.B.Tomakeadecisionaboutapopulationparameter.C.Todescribethedata.D.Topredictfutureoutcomes.4.Whichofthefollowingisameasureofcentraltendency?A.VarianceB.StandarddeviationC.MedianD.Correlationcoefficient5.Inaregressionanalysis,whatdoesthecoefficientofdetermination(R-squared)represent?A.Thestrengthoftherelationshipbetweenvariables.B.Theproportionofthevarianceinthedependentvariablethatispredictablefromtheindependentvariable.C.Theslopeoftheregressionline.D.Theinterceptoftheregressionline.6.Whatistheexpectedvalueofadiscreterandomvariable?A.Themeanofthevariable.B.Themedianofthevariable.C.Themodeofthevariable.D.Therangeofthevariable.7.WhichofthefollowingisapropertyofaPoissondistribution?A.Itisusedformodelingthenumberofeventsoccurringinafixedintervaloftime.B.Itissymmetric.C.Ithasameanandvariancethatareequal.D.Alloftheabove.8.Inat-test,whatisthedegreesoffreedom?A.Thenumberofobservationsminusone.B.Thenumberofobservations.C.Thenumberofvariables.D.Thenumberofgroups.9.Whatisthepurposeofaconfidenceinterval?A.Toestimatethepopulationparameter.B.Totestahypothesis.C.Topredictfutureoutcomes.D.Todescribethedata.10.Whichofthefollowingisatypeofnon-parametrictest?A.t-testB.ANOVAC.Chi-squaretestD.Pearsoncorrelation二、填空題（總共10題，每題2分）1.Themeasureofcentraltendencythatismostaffectedbyoutliersisthe________.2.Theprobabilityofaneventoccurringatleastonceintwoindependenttrialsisgivenby________.3.Thestandarddeviationofanormaldistributionisequalto________.4.AtypeIerroroccurswhenthenullhypothesisis________.5.Thecoefficientofdetermination(R-squared)rangesfrom________to________.6.Theexpectedvalueofabinomialrandomvariableisgivenby________.7.Thedegreesoffreedomforat-testwith20observationsis________.8.Aconfidenceintervalprovidesarangeofvalueswithinwhichthepopulationparameterislikelytofallwithacertainlevelofconfidence.9.Thechi-squaretestisusedtodetermineifthereisasignificantassociationbetweentwo________variables.10.Anon-parametrictestisastatisticaltestthatdoesnotmakeassumptionsaboutthe________ofthedata.三、判斷題（總共10題，每題2分）1.Themeanisalwaysgreaterthanthemedianinanormaldistribution.2.Thestandarddeviationisameasureofcentraltendency.3.ThePoissondistributionisusedformodelingthenumberofeventsoccurringinafixedintervaloftime.4.AtypeIIerroroccurswhenthenullhypothesisistrue.5.Thecoefficientofdetermination(R-squared)measuresthestrengthoftherelationshipbetweenvariables.6.Theexpectedvalueofadiscreterandomvariableisthesameasitsmean.7.Thedegreesoffreedomforachi-squaretestarecalculatedasthenumberofrowsminusonetimesthenumberofcolumnsminusone.8.Aconfidenceintervalprovidesarangeofvalueswithinwhichthesamplemeanislikelytofall.9.ThePearsoncorrelationcoefficientmeasuresthestrengthanddirectionofthelinearrelationshipbetweentwovariables.10.Anon-parametrictestisusedwhenthedatadoesnotfollowanormaldistribution.四、簡答題（總共4題，每題5分）1.ExplainthedifferencebetweenatypeIerrorandatypeIIerrorinhypothesistesting.2.Describetheconditionsunderwhichabinomialdistributionisappropriate.3.Whatisthepurposeofaconfidenceinterval,andhowisitcalculated?4.Discusstheadvantagesanddisadvantagesofusingnon-parametrictests.五、討論題（總共4題，每題5分）1.HowdoestheCentralLimitTheoreminfluencetheuseofthenormaldistributioninstatisticalanalysis?2.Inwhatscenarioswouldyouprefertouseat-testoveranANOVA?3.Explaintheconceptofap-valueanditsroleinhypothesistesting.4.Discusstheimportanceofunderstandingtheassumptionsbehindstatisticaltestsandtheconsequencesofviolatingtheseassumptions.答案和解析一、單項選擇題答案1.D2.A3.B4.C5.B6.A7.A8.A9.A10.C二、填空題答案1.mean2.1-(1-p)^23.thesameasthestandarddeviation4.false5.0,16.np7.198.parameter9.categorical10.distribution三、判斷題答案1.False2.False3.True4.False5.True6.True7.True8.False9.True10.True四、簡答題答案1.AtypeIerroroccurswhenthenullhypothesisistruebutisincorrectlyrejected.AtypeIIerroroccurswhenthenullhypothesisisfalsebutisincorrectlynotrejected.Theprimarydifferenceisinthedecisionmadeaboutthenullhypothesis.2.Abinomialdistributionisappropriatewhenthereareafixednumberoftrials,eachtrialhasonlytwopossibleoutcomes(successorfailure),theprobabilityofsuccessisconstantforeachtrial,andthetrialsareindependent.3.Thepurposeofaconfidenceintervalistoestimatethepopulationparameterwithacertainlevelofconfidence.Itiscalculatedbytakingthesamplemeanandaddingorsubtractingamarginoferror,whichisdeterminedbythestandarderrorandthedesiredconfidencelevel.4.Advantagesofnon-parametrictestsincludetheirabilitytobeusedwithnon-normaldata,fewerassumptions,andapplicabilitytoordinalornominaldata.Disadvantagesincludegenerallyhavinglesspowerthanparametrictestswhentheassumptionsaremetandbeinglessefficient.五、討論題答案1.TheCentralLimitTheoremstatesthatthedistributionofsamplemeansapproximatesanormaldistributionasthesamplesizebecomeslarge,regardlessofthepopulationdistribution.Thistheoremallowsfortheuseofthenormaldistributioninstatisticalanalysisevenwhenthepopulationdistributionisnotnormal.2.At-testispreferredoverANOVAwhencomparingthemeansoftwogroupsonly.