商务统计学第八章习题chap08-TIF-BSAFC5

ConfidenceIntervalEstimation225Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallCHAPTER8:CONFIDENCEINTERVALESTIMATION1.Thewidthofaconfidenceintervalestimateforaproportionwillbea)narrowerfor99%confidencethanfor95%confidence.b)widerforasamplesizeof100thanforasamplesizeof50.c)narrowerfor90%confidencethanfor95%confidence.d)narrowerwhenthesampleproportionis0.50thanwhenthesampleproportionis0.20.ANSWER:cTYPE:MCDIFFICULTY:ModerateKEYWORDS:confidenceinterval,proportion,properties,width2.Whendeterminingthesamplesizeforaproportionforagivenlevelofconfidenceandsamplingerror,thecloserto0.50thatisestimatedtobe,thesamplesizerequired__________.a)issmallerb)islargerc)isnotaffectedd)canbesmaller,largerorunaffectedANSWER:bTYPE:MCDIFFICULTY:ModerateKEYWORDS:confidenceinterval,proportion,properties3.A99%confidenceintervalestimatecanbeinterpretedtomeanthata)ifallpossiblesamplesaretakenandconfidenceintervalestimatesaredeveloped,99%ofthemwouldincludethetruepopulationmeansomewherewithintheirinterval.b)wehave99%confidencethatwehaveselectedasamplewhoseintervaldoesincludethepopulationmean.c)Bothoftheabove.d)Noneoftheabove.ANSWER:cTYPE:MCDIFFICULTY:ModerateKEYWORDS:confidenceinterval,interpretation4.Ifyouwereconstructinga99%confidenceintervalofthepopulationmeanbasedonasampleofn=25wherethestandarddeviationofthesamples=0.05,thecriticalvalueoftwillbea)2.7969b)2.7874c)2.4922d)2.4851ANSWER:aTYPE:MCDIFFICULTY:EasyKEYWORDS:criticalvalue,tdistribution226ConfidenceIntervalEstimationCopyright©2010PearsonEducation,Inc.PublishingasPrenticeHall5.WhichofthefollowingisnottrueabouttheStudent’stdistribution?a)Ithasmoreareainthetailsandlessinthecenterthandoesthenormaldistribution.b)Itisusedtoconstructconfidenceintervalsforthepopulationmeanwhenthepopulationstandarddeviationisknown.c)Itisbellshapedandsymmetrical.d)Asthenumberofdegreesoffreedomincreases,thetdistributionapproachesthenormaldistribution.ANSWER:bTYPE:MCDIFFICULTY:EasyKEYWORDS:tdistribution,properties6.TrueorFalse:Thetdistributionisusedtoconstructconfidenceintervalsforthepopulationmeanwhenthepopulationstandarddeviationisunknown.ANSWER:TrueTYPE:TFDIFFICULTY:EasyKEYWORDS:confidenceinterval,mean,standarddeviationunknown7.Thetdistributiona)assumesthepopulationisnormallydistributed.b)approachesthenormaldistributionasthesamplesizeincreases.c)hasmoreareainthetailsthandoesthenormaldistribution.d)Alloftheabove.ANSWER:dTYPE:MCDIFFICULTY:EasyKEYWORDS:tdistribution,properties8.ItisdesiredtoestimatetheaveragetotalcompensationofCEOsintheServiceindustry.Datawererandomlycollectedfrom18CEOsandthe97%confidenceintervalwascalculatedtobe($2,181,260,$5,836,180).Whichofthefollowinginterpretationsiscorrect?a)97%ofthesampledtotalcompensationvaluesfellbetween$2,181,260and$5,836,180.b)Weare97%confidentthatthemeanofthesampledCEOsfallsintheinterval$2,181,260to$5,836,180.c)InthepopulationofServiceindustryCEOs,97%ofthemwillhavetotalcompensationsthatfallintheinterval$2,181,260to$5,836,180.d)Weare97%confidentthattheaveragetotalcompensationofallCEOsintheServiceindustryfallsintheinterval$2,181,260to$5,836,180.ANSWER:dTYPE:MCDIFFICULTY:DifficultKEYWORDS:confidenceinterval,interpretationConfidenceIntervalEstimation227Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHall9.ItisdesiredtoestimatetheaveragetotalcompensationofCEOsintheServiceindustry.Datawererandomlycollectedfrom18CEOsandthe97%confidenceintervalwascalculatedtobe($2,181,260,$5,836,180).Basedontheintervalabove,doyoubelievetheaveragetotalcompensationofCEOsintheServiceindustryismorethan$3,000,000?a)Yes,andIam97%confidentofit.b)Yes,andIam78%confidentofit.c)Iam97%confidentthattheaveragecompensationis$3,000,000.d)Icannotconcludethattheaverageexceeds$3,000,000atthe97%confidencelevel.ANSWER:dTYPE:MCDIFFICULTY:DifficultKEYWORDS:confidenceinterval,interpretation10.Aconfidenceintervalwasusedtoestimatetheproportionofstatisticsstudentsthatarefemales.Arandomsampleof72statisticsstudentsgeneratedthefollowing90%confidenceinterval:(0.438,0.642).Basedontheintervalabove,isthepopulationproportionoffemalesequalto0.60?a)No,andweare90%sureofit.b)No.Theproportionis54.17%.c)Maybe.0.60isabelievablevalueofthepopulationproportionbasedontheinformationabove.d)Yes,andweare90%sureofit.ANSWER:cTYPE:MCDIFFICULTY:ModerateKEYWORDS:confidenceinterval,proportion,testing11.Aconfidenceintervalwasusedtoestimatetheproportionofstatisticsstudentsthatarefemale.Arandomsampleof72statisticsstudentsgeneratedthefollowing90%confidenceinterval:(0.438,0.642).Usingtheinformationabove,whattotalsizesamplewouldbenecessaryifwewantedtoestimatethetrueproportiontowithin0.08using95%confidence?a)105b)150c)420d)597ANSWER:bTYPE:MCDIFFICULTY:ModerateKEYWORDS:proportion,samplesizedetermination228ConfidenceIntervalEstimationCopyright©2010PearsonEducation,Inc.PublishingasPrenticeHall12.Whendeterminingthesamplesizenecessaryforestimatingthetruepopulationmean,whichfactorisnotconsideredwhensamplingwithreplacement?a)Thepopulationsize.b)Thepopulationstandarddeviation.c)Thelevelofconfidencedesiredintheestimate.d)Theallowableortol