商务统计习题

本文格式为Word版，下载可任意编辑——商务统计习题PracticeTest1BusinessStatistics:

MultipleChoice:Eachisworthtwopoints

Identifytheletterofthechoicethatbestcompletesthestatementoranswersthequestion.**Skip15-17,18,20Ch10-12,13Material____1.Thesumoftherelativefrequenciesforallclasseswillalwaysequal

a.thesamplesize

b.thenumberofclassesc.one

d.anyvaluelargerthanone

____

2.Theinterquartilerangeis

a.the50thpercentile

b.anothernameforthevariance

c.thedifferencebetweenthelargestandsmallestvalues

d.thedifferencebetweenthethirdquartileandthefirstquartile

____

3.Thestandarddeviationofasampleof100observationsequals64.Thevarianceofthesampleequals

a.8b.10c.6400d.4,096

4.Thenumericalvalueofthestandarddeviationcanneverbe

a.largerthanthevariance

____

b.zeroc.negative

d.smallerthanthevariance

____

5.Thesetofallpossiblesamplepoints(experimentaloutcomes)iscalled

a.asample

b.aneventc.thesamplespaced.apopulation

____

6.Arandomvariablethatcanassumeonlyafinitenumberofvaluesisreferredtoasa(n)

a.infinitesequence

b.finitesequence

c.discreterandomvariabled.discreteprobabilityfunction

____

Exhibit5-11

Alocalbottlingcompanyhasdeterminedthenumberofmachinebreakdownspermonthandtheirrespectiveprobabilitiesasshownbelow:

NumberofBreakdownsProbability

00.1210.3820.2530.1840.07

7.RefertoExhibit5-11.Theprobabilityofatleast3breakdownsinamonthis

a.0.5

b.0.10c.0.30d.0.90

____

8.Anormalprobabilitydistribution

a.isacontinuousprobabilitydistribution

b.isadiscreteprobabilitydistributionc.canbeeithercontinuousordiscreted.musthaveastandarddeviationof1

Exhibit6-6

____

ThestartingsalariesofindividualswithanMBAdegreearenormallydistributedwithameanof$40,000andastandarddeviationof$5,000.

9.RefertoExhibit6-6.WhatpercentageofMBA'swillhavestartingsalariesof$34,000to$46,000?

a.38.49%

b.38.59%c.50%d.76.98%

____

10.GiventhatZisastandardnormalrandomvariable,whatisthevalueofZiftheareabetween-ZandZis0.901?

a.1.96b.-1.96

c.0.4505d.?1.65

____

11.Whichofthefollowingisnotameasureofcentrallocation?

a.mean

b.medianc.varianced.mode

____

12.Thedescriptivemeasureofdispersionthatisbasedontheconceptofadeviationaboutthemeanis

a.therange

b.theinterquartilerange

c.theabsolutevalueoftheranged.thestandarddeviation

____

13.Whichofthefollowingsymbolsrepresentsthemeanofthepopulation?

a.?2

b.?c.?

____

14.Whichofthefollowingsymbolsrepresentsthesizeofthesample

a.?2

d.

b.?c.Nd.n

____

15.Iftwoeventsareindependent,then

a.theymustbemutuallyexclusive

b.thesumoftheirprobabilitiesmustbeequaltoonec.theirintersectionmustbezerod.Noneofthesealternativesiscorrect..

____

16.Whichofthefollowingstatementsis(are)alwaystrue?

a.-1?P(Ei)?1

b.P(A)=1-P(Ac)c.P(A)+P(B)=1d.?P?1

____

17.Ameasureoftheaveragevalueofarandomvariableiscalleda(n)

a.variance

b.standarddeviationc.expectedvalued.coefficientofvariation

____

18.Fourpercentofthecustomersofamortgagecompanydefaultontheirpayments.Asampleoffivecustomersisselected.Whatis

theprobabilitythatexactlytwocustomersinthesamplewilldefaultontheirpayments?a.0.2592b.0.0142

c.0.9588

d.0.7408

____

19.Theexpectedvalueofadiscreterandomvariable

a.isthemostlikelyorhighestprobabilityvaluefortherandomvariable

b.willalwaysbeoneofthevaluesxcantakeon,althoughitmaynotbethehighestprobabilityvaluefor

therandomvariable

c.istheaveragevaluefortherandomvariableovermanyrepeatsoftheexperimentd.Noneofthesealternativesiscorrect.

____

20.Whichofthefollowingisnotapropertyofabinomialexperiment?a.theexperimentconsistsofasequenceofnidenticaltrials

b.eachoutcomecanbereferredtoasasuccessorafailure

c.theprobabilitiesofthetwooutcomescanchangefromonetrialtothenextd.thetrialsareindependent

____

Exhibit5-9

TheprobabilitydistributionforthedailysalesatMichael'sCo.isgivenbelow.

DailySales(In$1,000s)Probability

400.1500.4600.3700.2

21.RefertoExhibit5-9.Theexpecteddailysalesare

a.$55,000b.$56,000

c.$50,000d.$70,000

____

22.Forastandardnormaldistribution,theprobabilityofz?0isa.zerob.-0.5

c.0.5d.one

Exhibit6-2

Theweightoffootballplayersisnormallydistributedwithameanof200poundsandastandarddeviationof25pounds.23.RefertoExhibit6-2.Whatpercentofplayersweighbetween180and220pounds?

a.28.81%b.0.5762%

c.0.281%d.57.62%

____

Exhibit6-6

ThestartingsalariesofindividualswithanMBAdegreearenormallydistributedwithameanof$40,000andastandarddeviationof$5,000.

____24.RefertoExhibit6-6.WhatistheprobabilitythatarandomlyselectedindividualwithanMBAdegreewillgetastartingsalaryofat

least$47,500?a.0.4332b.0.9332c.0.0668d.0.5000

ShortAnswer/Problems

1.Thefollowingdatarepresentthedailydemand(yinthousandsofunits)andtheunitprice(xindollars)foraproduct.

DailyDemand(y)UnitPrice(x)

473935443420

135368

1530

166

a.b.

Computeandinterpretthesamplecovariancefortheabovedata.Computeandinterpretthesamplecorrelationcoefficient.

2.Thedailydinnerbillsinalocalrestaurantarenormallydistributedwithameanof$28andastandarddeviationof$6.

a.Whatistheprobabilitythatarandomlyselectedbillwillbeatleast$39.10?b.Whatpercentageofthebillswillbelessthan$16.90?

c.Whataretheminimumandmaximumofthemiddle95%ofthebills?

d.Iftwelveofoneday'sbillshadavalueofatleast$43.06,howmanybillsdidtherestaurantcollectonthatday?

3.Belowyouaregivenapartialcomputeroutputbasedonasampleof7observations,relatinganindependentvariable(x)andadependent

variable(y).PredictorCoefficientStandardErrorConstant24.1128.376x-0.2520.253AnalysisofVarianceSOURCESSRegression196.893Error94.822a.Developtheestimatedregressionline.

b.Ifyouaregiventhatx=50,findtheestimateofybasedonyourregressionequation.c.Determinethecoefficientofdeterminationandinterpretyouranswer.

SolutionstoMC1.ANS:C2.ANS:D3.ANS:D4.ANS:C5.ANS:C6.ANS:C7.ANS:D8.ANS:A9.ANS:D10.ANS:D11.ANS:C12.ANS:D13.ANS:C14.ANS:D15.ANS:D16.ANS:B17.ANS:C18.ANS:B19.ANS:C20.ANS:C21.ANS:B22.ANS:C23.ANS:D24.ANS:C25.ANS:C26.ANS:A27.ANS:B28.ANS:D29.ANS:CSolutionstoShortAnswer1.ANS:

a.-47(rounded).Sincethecovarianceisnegative,itindicatesanegativerelationshipbetweenxandy.b.-0.922.Thereisastrongnegativerelationshipbetweenxandy.

2.ANS:

a.0.0322b.0.0322

c.minimum=$16.24maximum=$39.06d.2,000

3.ANS:

a.

=24.112+0.816xb.

Ifx=50then=24.112+0.816x?24.1+0.82(50)=65.1

c.0.675Sothereisafairlystrongpositiverelationshipbetweenxandy.

PracticeTest2BusinessStatistics:

MultipleChoice:Eachisworthtwopoints

Identifytheletterofthechoicethatbestcompletesthestatementoranswersthequestion.____1.Thesamplestatisticsisthepointestimatorof

a.?b.?c.d.

____2.Asamplestatisticisanunbiasedestimatorofthepopulationparameterif

a.theexpectedvalueofthesamplestatisticisequaltozero

b.theexpectedvalueofthesamplestatisticisequaltoone

c.theexpectedvalueofthesamplestatisticisequaltothepopulationparameterd.itisequaltozero

____

3.Apropertyofapointestimatorthatoccurswheneverlargersamplesizestendtoprovidepointestimatesclosertothepopulation

parameterisknownasa.efficiency

b.unbiasedsamplingc.consistencyd.relativeestimation

____

4.Arandomsampleof121bottlesofcologneshowedanaveragecontentof4ounces.Itisknownthatthestandarddeviationofthecontents(i.e.,ofthepopulation)is0.22ounces.Inthisproblemthe0.22isa.aparameter

b.astatistic

c.thestandarderrorofthemean

d.theaveragecontentofcolognesinthelongrun

____

5.Asampleof92observationsistakenfromaninfinitepopulation.Thesamplingdistributionofisapproximately

a.normalbecauseisalwaysapproximatelynormallydistributed

b.normalbecausethesamplesizeissmallincomparisontothepopulationsizec.normalbecauseofthecentrallimittheorem

d.Noneofthesealternativesiscorrect.

____

6.Asthenumberofdegreesoffreedomforatdistributionincreases,thedifferencebetweenthetdistributionandthestandardnormal

distribution

a.becomeslarger

b.becomessmallerc.staysthesame

____

d.Noneofthesealternativesiscorrect.

7.Fromapopulationof200elements,asampleof49elementsisselected.Itisdeterminedthatthesamplemeanis56andthesample

standarddeviationis14.Thestandarderrorofthemeanisa.3b.2

c.greaterthan2d.lessthan2

____

8.Whichofthefollowingis(are)pointestimator(s)?

a.?b.?

c.sd.?

____

9.Apopulationcharacteristic,suchasapopulationmean,iscalled

a.astatistic

b.aparameterc.asample

d.themeandeviation

____

10.Thesamplestatistic,suchas,s,or,thatprovidesthepointestimateofthepopulationparameterisknownas

a.apointestimator

b.aparameter

c.apopulationparameterd.apopulationstatistic

____

11.Thefactthatthesamplingdistributionofsamplemeanscanbeapproximatedbyanormalprobabilitydistributionwheneverthe

samplesizeislargeisbasedonthea.centrallimittheorem

b.factthatwehavetablesofareasforthenormaldistribution

c.assumptionthatthepopulationhasanormaldistributiond.Noneofthesealternativesiscorrect.

____

12.Randomsamplesofsize17aretakenfromapopulationthathas200elements,ameanof36,andastandarddeviationof8.The

meanandthestandarddeviationofthesamplingdistributionofthesamplemeansarea.8.7and1.94

b.36and1.94c.36and1.86

d.36and8

____

13.Whenconstructingaconfidenceintervalforthepopulationmeanandasmallsampleisused,thedegreesoffreedomforthet

distributionequalsa.n-1

b.nc.29d.30

_____14.Thecollectionofallpossiblesamplepointsinanexperimentisa.thesamplespaceb.asamplepointc.anexperimentd.thepopulation_____15.Offiveletters(A,B,C,D,andE),twolettersaretobeselectedatrandom.Howmanypossibleselectionsarethere?a.20b.7c.5!d.10_____16.The“TopThree〞ataracetrackconsistsofpickingthecorrectorderofthefirstthreehorsesinarace.Ifthereare10horsesinaparticularrace,howmany“TopThree〞outcomesarethere?a.302,400b.720c.1,814,400d.10_____17.GiventhateventEhasaprobabilityof0.25,theprobabilityofthecomplementofeventEa.cannotbedeterminedwiththeaboveinformationb.canhaveanyvaluebetweenzeroandonec.mustbe0.75d.is0.25_____18.Thesymbol?ersectionofeventsc.sumoftheprobabilitiesofeventsd.samplespace_____19.IfP(A)=0.38,P(B)=0.83,andP(A?B)=0.57;thenP(A?B)=a.1.21b.0.64c.0.78d.1.78_____20.IfP(A)=0.62,P(B)=0.47,andP(A?B)=0.88;thenP(A?B)=a.0.2914b.1.9700c.0.6700d.0.2100_____21.IfP(A)=0.85,P(A?B)=0.72,andP(A?B)=0.66,thenP(B)=a.0.15b.0.53c.0.28d.0.15_____22.Twoeventsaremutuallyexclusiveifa.theprobabilityoftheirintersectionis1b.theyhavenosamplepointsincommonc.theprobabilityoftheirintersectionis0.5d.theprobabilityoftheirintersectionis1andtheyhavenosamplepointsincommon_____23.IfAandBaremutuallyexclusiveeventswithP(A)=0.3andP(B)=0.5,thenP(A?B)=a.0.30b.0.15c.0.00d.0.20_____24.IfAandBaremutuallyexclusiveeventswithP(A)=0.3andP(B)=0.5,thenP(A?B)=a.0.00b.0.15c.0.8d.0.2_____25.Asubsetofapopulationselectedtorepresentthepopulationisaa.subsetb.samplec.smallpopulationd.Noneofthealternativeanswersiscorrect._____26.AsimplerandomsampleofsizenfromaninfinitepopulationofsizeNistobeselected.Eachpossiblesampleshouldhavea.thesameprobabilityofbeingselectedb.aprobabilityof1/nofbeingselectedc.aprobabilityof1/Nofbeingselectedd.aprobabilityofN/nofbeingselected_____27.Aprobabilitydistributionforallpossiblevaluesofasamplestatisticisknownasaa.samplestatisticb.parameterc.simplerandomsampled.samplingdistribution

_____28.Fromapopulationof200elements,thestandarddeviationisknowntobe14.Asampleof49elementsisselected.Itisdeterminedthatthesamplemeanis56.Thestandarderrorofthemeanisa.3b.2c.greaterthan2d.lessthan2_____29.Fromapopulationof500elements,asampleof225elementsisselected.Itisknownthatthevarianceofthepopulationis900.Thestandarderrorofthemeanisapproximatelya.1.1022b.2c.30d.1.4847

ShortAnswer/Problems

Directions:Clearlydesignateyoursolutiontoeachportionofthequestionsaskedandshowyourentireworkandmethodforarrivingatthesolution.

1.Thesalesrecordsofarealestateagencyshowthefollowingsalesoverthepast200days:

#HousesSoldNumberofDays06018024031644a.Howmanysamplepointsarethere?

b.Assignprobabilitiestothesamplepointsandshowtheirvalues.c.Whatistheprobabilitythattheagencywillnotsellanyhousesinagivenday?d.Whatistheprobabilityofsellingatleast2houses?e.Whatistheprobabilityofselling1or2houses?f.Whatistheprobabilityofsellinglessthan3houses?

2.AssumetwoeventsAandBaremutuallyexclusiveand,furthermore,P(A)=0.2andP(B)=0.4.

a.FindP(A?B).b.FindP(A?B).c.FindP(A?B).

3.YouaregiventhefollowinginformationonEventsA,B,C,andD.P(A)=.4,P(B)=.2,P(C)=.1,P(A?D)=.6,P(A?B)=.3,P(A?C)=.04,P(A?D)=.03

a.ComputeP(D).b.ComputeP(A?B).c.ComputeP(A?C).d.ComputetheprobabilityofthecomplementofC.e.AreAandBmutuallyexclusive?Explainyouranswer.f.AreAandBindependent?Explainyouranswer.g.AreAandCmutuallyexclusive?Explainyouranswer.h.AreAandCindependent?Explainyouranswer.

4.Considerapopulationoffiveweightsidenticalinappearancebutweig