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Study Resources (Statistics)

    51.Inaone-tailedhypothesistest(lowertail)theteststatisticisdeterminedtobe-2.Thep-valueforthistestisa.0.4772 b.0.0228 c.0.0056 d.0.5228     52.TheaveragemanufacturingworkweekinmetropolitanChattanoogawas40.1hourslastyear.Itisbelievedthattherecessionhasledtoareductionintheaverageworkweek.Totestthevalidityofthisbelief,thehypothesesare a.H0:μ<40.1Ha:μ≥40.1b.H0:μ≥40.1Ha:μ<40.1c.H0:μ>40.1Ha:μ≤40.1d.H0:μ=40.1Ha:μ≠40.1   53.Theaveragemonthlyrentforone-bedroomapartmentsinChattanoogahasbeen$700.Becauseofthedownturnintherealestatemarket,itisbelievedthattherehasbeenadecreaseintheaveragerental.Thecorrecthypothesestobetestedare a.H0:μ≥ 700Ha:μ< 700b.H0:μ=700Ha:μ≠ 700c.H0:μ>700Ha:μ≤700d.H0:μ<700Ha:μ≥ 700     54.Inhypothesestesting, a.thesumofTypeIandTypeIIerrorsmustaddupto1 b.TypeIIisalwaystwiceaslargeasTypeIerror c.theprobabilityofTypeIerrorisα d.theprobabilityofTypeIIerrorisβ     55.Amachineisdesignedtofilltoothpastetubeswith5.8ouncesoftoothpaste.Themanufacturerdoesnotwantanyunderfillingoroverfilling.Thecorrecthypothesestobetestedare a.H0:μ≠5.8 Ha:μ= 5.8b.H0:μ=5.8 Ha:μ≠ 5.8c.H0:μ>5.8 Ha:μ≤5.8d.H0:μ≥5.8   Ha:μ<5.8     56.Theaveragehourlywageofcomputerprogrammerswith2yearsofexperiencehasbeen$21.80.Becauseofhighdemandforcomputerprogrammers,itisbelievedtherehasbeenasignificantincreaseintheaveragewageofcomputerprogrammers.Totestwhetherornottherehasbeenanincrease,thecorrecthypothesestobetestedarea.H0:μ<21.80              Ha:μ≥21.80 b.H0:μ=21.80Ha:μ≠21.80c.H0:μ>21.80Ha:μ≤21.80d.H0:μ≤21.80Ha:μ> 21.80   57.Astudentbelievesthattheaveragegradeonthefinalexaminationinstatisticsisatleast85.Sheplansontakingasampletotestherbelief.Thecorrectsetofhypothesesis a.H0:μ<85   Ha:μ≥ 85b.H0:μ≤ 85Ha:μ> 85c.H0:μ≥85   Ha:μ<85d.H0:μ>85    Ha:μ ≤ 85   58.Inthepast,75%ofthetouristswhovisitedChattanoogawenttoseeRockCity.ThemanagementofRockCityrecentlyundertookanextensivepromotionalcampaign.TheyareinterestedindeterminingwhetherthepromotionalcampaignactuallyincreasedtheproportionoftouristsvisitingRockCity.Thecorrectsetofhypothesesis a.H0:P>0.75Ha: P ≤ 0.75b.H0:P<0.75Ha: P≥ 0.75c.H0:P≥0.75  Ha:P<0.75d.H0:P≤0.75    Ha:P>0.75     59.TheaveragelifeexpectancyoftiresproducedbytheWhitneyTireCompanyhasbeen40,000miles.Managementbelievesthatduetoanewproductionprocess,thelifeexpectancyoftheirtireshasincreased.Inordertotestthevalidityoftheirbelief,thecorrectsetofhypothesesis a.H0:μ<40,000Ha:μ≥40,000b.H0:μ≤ 40,000Ha:μ>40,000c.H0:μ>40,000Ha:μ≤40,000d.H0:μ≥ 40,000Ha:μ<40,000     60.Asoftdrinkfillingmachine,wheninperfectadjustment,fillsthebottleswith12ouncesofsoftdrink.Anyoverfillingorunderfillingresultsintheshutdownandreadjustmentofthemachine.Todeterminewhetherornotthemachineisproperlyadjusted,thecorrectsetofhypothesesis a.H0:μ<12   Ha:μ≤ 12b.H0:μ≤ 12  Ha:μ> 12c.H0:μ≠12   Ha:μ=12d.H0:μ=12    Ha:μ≠ 12     .
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    61.Apopulationhasameanof84andastandarddeviationof12.Asampleof36observationswillbetaken.Theprobabilitythatthesamplemeanwillbebetween80.54and88.9is a.0.0347 b.0.7200 c.0.9511 d.8.3600     62.Apopulationhasameanof53andastandarddeviationof21.Asampleof49observationswillbetaken.Theprobabilitythatthesamplemeanwillbegreaterthan57.95is a.0 b..0495 c..4505 d..9505     63.Randomsamplesofsize100aretakenfromaninfinitepopulationwhosepopulationproportionis0.2.Themeanandstandarddeviationofthesampleproportionare a.0.2and.04 b.0.2and0.2 c.20and.04 d.20and0.2       64.Apopulationofsize1,000hasaproportionof0.5.Therefore,theproportionandthestandarddeviationofthesampleproportionforsamplesofsize100are a.500and0.047 b.500and0.050 c.0.5and0.047 d.0.5and0.050     65.Asampleof25observationsistakenfromaninfinitepopulation.Thesamplingdistributionofis a.notnormalsincen<30 b.approximatelynormalbecauseisalwaysnormallydistributed c.approximatelynormal if np≥5andn(1-P)≥5 d.approximatelynormalifnp>30andn(1-P)>30       66.Asampleof66observationswillbetakenfromaninfinitepopulation.Thepopulationproportionequals0.12.Theprobabilitythatthesampleproportionwillbelessthan0.1768is a.0.0568 b.0.0778 c.0.4222 d.0.9222     67.Asampleof51observationswillbetakenfromaninfinitepopulation.Thepopulationproportionequals0.85.Theprobabilitythatthesampleproportionwillbebetween0.9115and0.946is a.0.8633 b.0.6900 c.0.0819 d.0.0345     68.Asubsetofapopulationselectedtorepresentthepopulationis a.asubset b.asample c.asmallpopulation d.aparameter       69.Afinitepopulationcorrectionfactorisneededincomputingthestandarddeviationofthesamplingdistributionofsamplemeans a.wheneverthepopulationisinfinite b.wheneverthesamplesizeismorethan5%ofthepopulationsize c.wheneverthesamplesizeislessthan5%ofthepopulationsize d.Thecorrectionfactorisnotnecessaryifthepopulationhasanormaldistribution     70.Doublingthesizeofthesamplewill a.reducethestandarderrorofthemeantoone-halfitscurrentvalue b.reducethestandarderrorofthemeantoapproximately70%ofitscurrentvalue c.havenoeffectonthestandarderrorofthemean d.doublethestandarderrorofthemean         .
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    11.Inhypothesistestingifthenullhypothesisisrejected, a.noconclusionscanbedrawnfromthetest b.thealternativehypothesisistrue c.thedatamusthavebeenaccumulatedincorrectly d.thesamplesizehasbeentoosmall         12.Thelevelofsignificanceisthe a.maximumallowableprobabilityofTypeIIerror b.maximumallowableprobabilityofTypeIerror c.sameastheconfidencecoefficient 13.Thepowercurveprovidestheprobabilityof a.correctlyacceptingthenullhypothesis b.incorrectlyacceptingthenullhypothesis c.correctlyrejectingthealternativehypothesis d.correctlyrejectingthenullhypothesis     14.ATypeIIerroriscommittedwhen a.atruealternativehypothesisismistakenlyrejected b.atruenullhypothesisismistakenlyrejected c.thesamplesizehasbeentoosmall d.notenoughinformationhasbeenavailable     15.Theerrorofrejectingatruenullhypothesisis a.aTypeIerror b.aTypeIIerror c.isthesameasβ d.committedwhennotenoughinformationisavailable     16.Thelevelofsignificanceinhypothesistestingistheprobabilityof a.acceptingatruenullhypothesis b.acceptingafalsenullhypothesis c.rejectingatruenullhypothesis d.Noneofthesealternativesiscorrect.     17.Thelevelofsignificance a.canbeanypositivevalue b.canbeanyvalue c.is(1-confidencelevel) d.canbeanyvaluebetween-1.96to1.96         18.Inhypothesistestingifthenullhypothesishasbeenrejectedwhenthealternativehypothesishasbeentrue, a.aTypeIerrorhasbeencommitted b.aTypeIIerrorhasbeencommitted c.eitheraTypeIorTypeIIerrorhasbeencommitted d.thecorrectdecisionhasbeenmade     19.TheprobabilityofmakingaTypeIerrorisdenotedby a.α b.β c.1-α d.1-β     20.TheprobabilityofmakingaTypeIIerrorisdenotedby a.α b.β c.1-α d.1-β       .
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    21.Ifweconsiderthesimplerandomsamplingprocessasanexperiment,thesamplemeanis a.alwayszero b.alwayssmallerthanthepopulationmean c.arandomvariable d.exactlyequaltothepopulationmean     22.Theprobabilitydistributionofthesamplemeaniscalledthe a.centralprobabilitydistribution b.samplingdistributionofthemean c.randomvariation d.standarderror     23.Theexpectedvalueoftherandomvariableis a.thestandarderror b.thesamplesize c.thesizeofthepopulation d.Noneofthesealternativesiscorrect.     24.Thestandarddeviationofallpossiblevaluesiscalledthe a.standarderrorofproportion b.standarderrorofthemean c.meandeviation d.centralvariation     25.Apopulationhasameanof75andastandarddeviationof8.Arandomsampleof800isselected.Theexpectedvalue ofis a.8 b.75c.800 d.Noneofthesealternativesiscorrect.       26.Asthesamplesizebecomeslarger,thesamplingdistributionofthesamplemeanapproachesa a.binomialdistribution b.Poissondistribution c.normaldistribution d.chi-squaredistribution     27.Wheneverthepopulationhasa normalprobabilitydistribution,thesamplingdistributionofisanormalprobabilitydistributionfor a.onlylargesamplesizes b.onlysmallsamplesizes c.anysamplesize d.onlysamplesofsizethirtyorgreater       28.Thesamplingerroristhe a.sameasthestandarderrorofthemean b.differencebetweenthevalueofthesamplemeanandthevalueofthepopulationmean c.errorcausedbyselectingabadsample d.standarddeviationmultipliedbythesamplesize     29.Thestandarddeviationofasampleof100elementstakenfromaverylargepopulationisdeterminedtobe60.Thevarianceofthepopulation a.cannotbelargerthan60 b.cannotbelargerthan3600 c.mustbeatleast100 d.canbeanyvaluegreaterorequaltozero     30.Fromapopulationof200elements,asampleof49elementsisselected.Itisdeterminedthatthesamplemeanis56andthesamplestandarddeviationis14.Thestandarderrorofthemeanis a.3 b.2 c.greaterthan2 d.lessthan2         .
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  123.Aqualitycontroltechnicianischeckingtheweightsofaproduct.Shetakesarandomsampleof8unitsandweighseachunit.Theobservedweightsareshownbelow.Assumethepopulationhasanormaldistribution.       Weight 50 48 55 52 53 46 54 50   Providea95%confidenceintervalforthemeanweightoftheunits.     124.Astatisticianemployedbyaconsumertestingorganizationreportsthatat95%confidencehehasdeterminedthatthetrueaveragecontentoftheUncolasoftdrinksisbetween11.7to12.3ounces.Hefurtherreportsthathissamplerevealedanaveragecontentof12ounces,butheforgottoreportthesizeofthesamplehehadselected.Assumingthestandarddeviationofthepopulationis1.28,determinethesizeofthesample.   125.Asimplerandomsampleof144itemsresultedinasamplemeanof1257.85andastandarddeviationof480.Developa95%confidenceintervalforthepopulationmean.   126.Asimplerandomsampleof36itemsresultedinasamplemeanof40andastandarddeviationof12.Constructa95%confidenceintervalforthepopulationmean.   127.Sixhundredconsumerswereaskedwhethertheywouldliketopurchaseadomesticoraforeignautomobile.Theirresponsesaregivenbelow.       PreferenceFrequency Domestic240 Foreign360   Developa95%confidenceintervalfortheproportionofallconsumerswhoprefertopurchasedomesticautomobiles.   128.AnExcelprintoutofthedescriptivemeasuresofdailycheckingaccountbalances(indollars)ofcustomersofFirstDaisyBankisshownbelow.Developa95%confidenceintervalestimateforthemeanofthepopulationofthecheckingbalances.       AccountBalanceInformation Mean4828.29 Median5115.25 Mode4976.50 StandardDeviation1143.57 SampleVariance1307763.49 Kurtosis8.63 Skewness-3.06 Range4968.50 Minimum600.00 Maximum5568.50 Sum173818.50 Count36.00       129.Informationregardingthepriceofarollofcamerafilm(35mm,24exposure)forasampleof12citiesworldwideisshownbelow.Determinea95%confidenceintervalforthepopulationmean.       PriceofFilmInformation Mean5.3667 StandardError0.7409 Median4.8700 StandardDeviation2.5666 SampleVariance6.5873 Kurtosis4.0201 Skewness1.8041 Range9.4100 Minimum2.7300 Maximum12.1400 Sum64.4000 Count12.0000   130.Inordertodeterminetheaverageweightofcarry-onluggagebypassengersinairplanes,asampleof25piecesofcarry-onluggagewascollectedandweighed.Theaverageweightwas18pounds.Assumethatweknowthestandarddeviationofthepopulationtobe7.5pounds.   a.Determinea97%confidenceintervalestimateforthemeanweightofthecarry-onluggage. b.Determinea95%confidenceintervalestimateforthemeanweightofthecarry-onluggage. b.15.06to20.94   131.Alocalelectronicsfirmwantstodeterminetheiraveragedailysales(indollars.)Asampleofthesalesfor36daysrevealedaveragesalesof$139,000.Assumethatthestandarddeviationofthepopulationisknowntobe $12,000.   a.Providea95%confidenceintervalestimatefortheaveragedailysales. b.Providea97%confidenceintervalestimatefortheaveragedailysales. b.$134,660to$143,340   132.TheHighwaySafetyDepartmentwantstostudythedrivinghabitsofindividuals.Asampleof81carstravelingonthehighwayrevealedanaveragespeedof67milesperhourwithastandarddeviationof9milesperhour.     a.Computethestandarderrorofthemean. b.Determinea99%confidenceintervalestimateforthespeedofallcars.       133.Inordertodeterminethesummerunemploymentrateamongcollegestudents,apilotsamplewastaken;anditwasdeterminedthattenpercentoftheindividualsinthesamplewereunemployed.Usingtheresultsofthepilotstudyanda95%confidence,whatsizesamplewouldberequiredtoestimatetheproportionofunemployedcollegestudentsifwewantthemarginoferrornottoexceed3percent?       .
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  11) Organizations that utilize the file processing approach spend as much as ________ of their IS development budget on maintenance. A) 40 percent B) 25 percent C) 60 percent D) 80 percent 12) A graphical system used to capture the nature and relationships among data is called a(n): A) logical data.
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  112.Astudentbelievesthattheaveragegradeonthestatisticsfinalexaminationwas87.Asampleof36finalexaminationswastaken.Theaveragegradeinthesamplewas83.96withastandarddeviationof12.   a.Statethenullandalternativehypotheses. b.Usingthecriticalvalueapproach,testthehypothesesatthe5%levelofsignificance. c.Usingthep-valueapproach,testthehypothesesatthe5%levelofsignificance.   113.Acarpetcompanyadvertisesthatitwilldeliveryourcarpetwithin15daysofpurchase.Asampleof49pastcustomersistaken.Theaveragedeliverytimeinthesamplewas16.2days.Thestandarddeviationofthepopulation(σ)isknowntobe5.6days.     a.Statethenullandalternativehypotheses. b.Usingthecriticalvalueapproach,testtodetermineiftheiradvertisementislegitimate.Letα=.05. c.Usingthep-valueapproach,testthehypothesesatthe5%levelofsignificance.   114.Asampleof30cookiesistakentotesttheclaimthateachcookiecontainsatleast9chocolatechips.Theaveragenumberofchocolatechipspercookieinthesamplewas7.8withastandarddeviationof3.   a.Statethenullandalternativehypotheses. b.Usingthecriticalvalueapproach,testthehypothesesatthe5%levelofsignificance. c.Usingthep-valueapproach,testthehypothesisatthe5%levelofsignificance. d.ComputetheprobabilityofaTypeIIerrorifthetruenumberofchocolatechipspercookieis8.   115.Agroupofyoungbusinesswomenwishtoopenahighfashionboutiqueinavacantstorebutonlyiftheaverageincomeofhouseholdsintheareaisatleast$25,000.Arandomsampleof9householdsshowedthefollowingresults.     $28,000 $24,000 $26,000 $25,000 $23,000 $27,000 $26,000 $22,000 $24,000         Assumethepopulationofincomesisnormallydistributed.       a.Computethesamplemeanandthestandarddeviation. b.Statethehypothesesforthisproblem. c.Computetheteststatistic. d.At95%confidenceusingthep-valueapproach,whatisyourconclusion?         116.Nancybelievesthattheaveragerunningtimeofmoviesisequalto140minutes.Asampleof4movieswastakenandthefollowingrunningtimeswereobtained.Assumethepopulationoftherunningtimesisnormallydistributed.     150150180170       a.Computethesamplemeanandthestandarddeviation. b.Statethenullandalternativehypotheses. c.Usingthecriticalvalueapproach,testthehypothesesatthe10%levelofsignificance. d.Usingthep-valueapproach,testthehypothesesatthe10%levelofsignificance.       .
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    21.Whenthefollowinghypothesesarebeingtestedatalevelofsignificanceofα     thenullhypothesiswillberejectedifthep-valueis a.≤α b.>α c.>α/2 d.≤1-α/2     22.Whenthep-valueisusedforhypothesistesting,thenullhypothesisisrejectedif a.p­value≤α b.α<p-value c.p­value≥α d.p-value=1-α         23.Inordertotestthefollowinghypothesesatanαlevelofsignificance     thenullhypothesiswillberejectediftheteststatisticZis a.≥Zα b.<Zα c.<-Zα d.=α     24.Whichofthefollowingdoesnotneedtobeknowninordertocomputethep-value? a.knowledgeofwhetherthetestisone-tailedortwo-tailed b.thevalueoftheteststatistic c.thelevelofsignificance d.Noneofthesealternativesiscorrect.     25.Inthehypothesistestingprocedure,αis a.thelevelofsignificance b.thecriticalvalue c.theconfidencelevel d.1-levelofsignificance     26.Ifahypothesistestleadstotherejectionofthenullhypothesis, a.aTypeIIerrormusthavebeencommitted b.aTypeIIerrormayhavebeencommitted c.aTypeIerrormusthavebeencommitted d.aTypeIerrormayhavebeencommitted     27.Astheteststatisticbecomeslarger,thep-value a.getssmaller b.becomeslarger c.staysthesame,sincethesamplesizehasnotbeenchanged d.becomesnegative         28.Thep-valuerangesbetween a.zeroandinfinity b.minusinfinitytoplusinfinity c.zerotoone d.-1to+1     29.Foralowerboundsone-tailedtest,theteststatisticzisdeterminedtobezero.Thep-valueforthistestis a.zerob.-0.5c.+0.5d.1.00   30.Inatwo-tailedhypothesistestsituation,theteststatisticisdeterminedtobet=-2.692.Thesamplesizehasbeen 45.Thep-valueforthistestisa.-0.005 b.+0.005 c.-0.01 d.+0.01       .
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    11.Stratifiedrandomsamplingisamethodofselectingasampleinwhich a.thesampleisfirstdividedintostrata,andthenrandomsamplesaretakenfromeachstratum b.variousstrataareselectedfromthesample c.thepopulationisfirstdividedintostrata,andthenrandomsamplesaredrawnfromeachstratum d.Noneofthesealternativesiscorrect.     12.Apopulationconsistsof500elements.Wewanttodrawasimplerandomsampleof50elementsfromthispopulation.Onthefirstselection,theprobabilityofanelementbeingselectedis a.0.100 b.0.010 c.0.001 d.0.002     13.Thecloserthesamplemeanistothepopulationmean, a.thelargerthesamplingerror b.thesmallerthesamplingerror c.thesamplingerrorequals1 d.Noneofthesealternativesiscorrect.     14.Sincethesamplesizeisalwayssmallerthanthesizeofthepopulation,thesamplemean a.mustalwaysbesmallerthanthepopulationmean b.mustbelargerthanthepopulationmean c.mustbeequaltothepopulationmean d.canbesmaller,larger,orequaltothepopulationmean     15.Asthesamplesizeincreases,the a.standarddeviationofthepopulationdecreases b.populationmeanincreases c.standarderrorofthemeandecreases d.standarderrorofthemeanincreases       16.Asimplerandomsamplefromaninfinitepopulationisasampleselectedsuchthat a.eachelementisselectedindependentlyandfromthesamepopulation b.eachelementhasa0.5probabilityofbeingselected c.eachelementhasaprobabilityofatleast0.5ofbeingselected d.theprobabilityofbeingselectedchanges       17.Apopulationconsistsof8items.Thenumberofdifferentsimplerandomsamplesofsize3thatcanbeselectedfromthispopulationis a.24 b.56c.512d.128   18.Inpointestimation a.datafromthepopulationisusedtoestimatethepopulationparameter b.datafromthesampleisusedtoestimatethepopulationparameter c.datafromthesampleisusedtoestimatethesamplestatistic d.themeanofthepopulationequalsthemeanofthesample     19.Thesamplestatisticsisthepointestimatorof a.μ b.σc. d.   20.Thesamplemeanisthepointestimatorof a.μ b.σc. d.       .
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  122.Anautomobilemanufacturerstatedthatitwillbewillingtomassproduceelectric-poweredcarsifmorethan30%ofpotentialbuyersindicatetheywillpurchasethenewlydesignedelectriccars.Inasampleof500potentialbuyers,160indicatedthattheywouldbuysuchaproduct.   a.Statethehypothesesforthisproblem b.Computethestandarderrorof. c.Computetheteststatistic. d.At95%confidence,whatisyourconclusion?Shouldthemanufacturerproducethenewelectricpoweredcar?     123.Itissaidthatmoremalesregistertovoteinanationalelectionthanfemales.Aresearchorganizationselectedarandomsampleof300registeredvotersandreportedthat165oftheregisteredvotersweremale.   a.Formulatethehypothesesforthisproblem. b.Computethestandarderrorof. c.Computetheteststatistic. d.Usingthep-valueapproach,canyouconcludethatmoremalesregisteredtovotethanfemales?Letα=.05.     124.Considerthefollowinghypothesistest:   Ho:μ=10 Ha:μ≠10   Asampleof81providesasamplemeanof9.5andasamplestandarddeviationof1.8.   a.Determinethestandarderrorofthemean. b.Computethevalueoftheteststatistic. c.Determinethep-value;andat95%confidence,testtheabovehypotheses.   125.Considerthefollowinghypothesistest:   Ho:μ≥ 14 Ha:μ<14   Asampleof64providesasamplemeanof13andasamplestandarddeviationof4.     a.Determinethestandarderrorofthemean. b.Computethevalueoftheteststatistic. c.Determinethep-value;andat95%confidence,testtheabovehypotheses.   Ho:μ≥ 40 Ha:μ<40   Asampleof49providesasamplemeanof38andasamplestandarddeviationof7.     a.Determinethestandarderrorofthemean. b.Computethevalueoftheteststatistic. c.Determinethep-value;andat95%confidence,testtheabovehypotheses.         .
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  115.Arandomsampleoftenexaminationpapersinacoursethatwasgivenonapassorfailbasisshowedthefollowingscores.     PaperNumber 1Grade 65Status Pass 287Pass 392Pass 435Fail 579Pass 6100Pass 748Fail 874Pass 979Pass 1091Pass     a.Whatisthepointestimateforthemeanofthepopulation? b.Whatisthepointestimateforthestandarddeviationofthepopulation? c.Whatisthepointestimatefortheproportionofallstudentswhopassedthecourse? 116.Considerapopulationoffiveweightsidenticalinappearancebutweighing1,3,5,7,and9ounces.   a.Determinethemeanandthevarianceofthepopulation. b.Samplingwithoutreplacementfromtheabovepopulationwithasamplesizeof2producestenpossiblesamples.Usingthetensamplemeanvalues,determinethemeanofthepopulationandthevarianceof. c.Computethestandarderrorofthemean.         117.Considerapopulationoffivefamilieswiththefollowingdatarepresentingthenumberofpetsineachfamily.     FamilyNumberofPets A2 B6 C4 D3 E1     a.Determinethemeanandthevarianceofthepopulation. b.Therearetenpossiblesamplesofsize2(samplingwithoutreplacement).Listthe10possiblesamplesofsize2,anddeterminethemeanofeachsample. c.Usingthetensamplemeanvalues,computethemeanandthestandarderrorofthemean.   118.Theaverageweeklyearningsofbusdriversinacityare$950(thatisμ)withastandarddeviationof$45(thatis σ).Assumethatweselectarandomsampleof81busdrivers.   a.Computethestandarderrorofthemean. b.Whatistheprobabilitythatthesamplemeanwillbegreaterthan$960? c.Ifthepopulationofbusdriversconsistedof400drivers,whatwouldbethestandarderrorofthemean?       119.Anautomotiverepairshophasdeterminedthattheaverageservicetimeonanautomobileis2hourswithastandarddeviationof32minutes.Arandomsampleof64servicesisselected.     a.Whatistheprobabilitythatthesampleof64willhaveameanservicetimegreaterthan114minutes? b.Assumethepopulationconsistsof400services.Determinethestandarderrorofthemean.     .
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    21.Asthesamplesizeincreases,themarginoferror a.increases b.decreases c.staysthesame d.increasesordecreasesdependingonthesizeofthemean     22.ForwhichofthefollowingvaluesofPisthevalueofP(1-P)maximized?a.P=0.99 b.P=0.90c.P=0.01d.P=0.50   23.A95%confidenceintervalforapopulationmeanisdeterminedtobe100to120.Iftheconfidencecoefficientisreducedto0.90,theintervalforμ a.becomesnarrower b.becomeswider c.doesnotchange d.becomes0.1     24.Usinganα=0.04aconfidenceintervalforapopulationproportionisdeterminedtobe0.65to0.75.Ifthelevelofsignificanceisdecreased,theintervalforthepopulationproportion a.becomesnarrower b.becomeswider c.doesnotchange d.remainsthesame     25.Theabilityofanintervalestimatetocontainthevalueofthepopulationparameterisdescribedbythe a.confidencelevel b.degreesoffreedom c.precisevalueofthepopulationmeanμ d.degreesoffreedomminus1         26.Aftercomputingaconfidenceinterval,theuserbelievestheresultsaremeaninglessbecausethewidthoftheintervalistoolarge.Whichoneofthefollowingisthebestrecommendation? a.Increasethelevelofconfidencefortheinterval. b.Decreasethesamplesize. c.Increasethesamplesize. d.Reducethepopulationvariance.     27.Ifwechangea95%confidenceintervalestimatetoa99%confidenceintervalestimate,wecanexpect a.thesizeoftheconfidenceintervaltoincrease b.thesizeoftheconfidenceintervaltodecrease c.thesizeoftheconfidenceintervaltoremainthesame d.thesamplesizetoincrease     28.Ingeneral,higherconfidencelevelsprovide a.widerconfidenceintervals b.narrowerconfidenceintervals c.asmallerstandarderror d.unbiasedestimates     29.Anintervalestimateisarangeofvaluesusedtoestimate a.theshapeofthepopulation'sdistribution b.thesamplingdistribution c.asamplestatistic d.apopulationparameter     30.Indeterminingthesamplesizenecessarytoestimateapopulationproportion,whichofthefollowinginformationis notneeded? a.themaximummarginoferrorthatcanbetolerated b.theconfidencelevelrequired c.apreliminaryestimateofthetruepopulationproportionP d.themeanofthepopulation           .
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  96.Themakersofasoftdrinkwanttoidentifytheaverageageofitsconsumers.Asampleof55consumerswastaken.Theaverageageinthesamplewas21yearswithastandarddeviationof4years.   a.Constructa95%confidenceintervalforthetrueaverageageoftheconsumers. b.Constructan80%confidenceintervalforthetrueaverageageoftheconsumers. c.Discusswhythe95%and80%confidenceintervalsaredifferent.       97.Arandomsampleof53observationswastaken.Theaverageinthesamplewas90withavarianceof400.   a.Constructa98%confidenceintervalforμ. b.Constructa99%confidenceintervalforμ. c.Discusswhythe98%and99%confidenceintervalsaredifferent. d.WhatwouldyouexpecttohappentotheconfidenceintervalinPartaifthesamplesizewasincreased?Besuretoexplainyouranswer.     98.Youaregiventhefollowinginformationobtainedfromarandomsampleof6observations.Assumethepopulationhasanormaldistribution.   142021161819   a.Whatisthepointestimateofμ? b.Constructan80%confidenceintervalforμ. c.Constructa98%confidenceintervalforμ. d.Discusswhythe80%and98%confidenceintervalsaredifferent.   99.Belowyouaregivenagesthatwereobtainedbytakingarandomsampleof9undergraduatestudents.Assumethepopulationhasanormaldistribution.   404243393739   a.Whatisthepointestimateofμ? b.Determinethestandarddeviation. c.Constructa90%confidenceintervalfortheaverageageofundergraduatestudents. d.Constructa99%confidenceintervalfortheaverageageofundergraduatestudents. e.Discusswhythe99%and90%confidenceintervalsaredifferent.       100.Auniversityplannerisinterestedindeterminingthepercentageofspringsemesterstudentswhowillattendsummerschool.Shetakesapilotsampleof160springsemesterstudentsdiscoveringthat56willreturntosummerschool.     a.Constructa95%confidenceintervalestimateforthepercentageofspringsemesterstudentswhowillreturntosummerschool. b.Usingtheresultsofthepilotstudywitha0.95probability,howlargeofasamplewouldhavetobetakentoprovideamarginoferrorof3%orless?         .
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  115.ThemonthlystartingsalariesofstudentswhoreceiveanMBAdegreehaveapopulationstandarddeviationof $110.Whatsizesampleshouldbeselectedtoobtaina0.95probabilityofestimatingthemeanmonthlyincomewithin$20orless?   116.Acoalcompanywantstodeterminea95%confidenceintervalestimatefortheaveragedailytonnageofcoalthattheymine.Assumingthatthecompanyreportsthatthestandarddeviationofdailyoutputis200tons,howmanydaysshouldtheysamplesothatthemarginoferrorwillbe39.2tonsorless?   117.Ifthestandarddeviationofthelifetimeofavacuumcleanerisestimatedtobe300hours,howlargeofasamplemustbetakeninordertobe97%confidentthatthemarginoferrorwillnotexceed40hours?       118.Alocalhealthcenternotedthatinasampleof400patients80werereferredtothembythelocalhospital.     a.Providea95%confidenceintervalforallthepatientswhoarereferredtothehealthcenterbythehospital. b.Whatsizesamplewouldberequiredtoestimatetheproportionofhospitalreferralswithamarginoferrorof0.04orlessat95%confidence?     119.Inarandomsampleof400residentsofChattanooga,320residentsindicatedthattheyvotedfortheDemocraticcandidateinthelastpresidentialelection.Developa95%confidenceintervalestimatefortheproportionofallChattanoogaresidentswhovotedfortheDemocraticcandidate.   120.Themanagerofagrocerystorewantstodeterminewhatproportionofpeoplewhoenterhisstorearehisregularcustomers.Whatsizesampleshouldhetakesothatat97%confidencethemarginoferrorwillnotbemorethan0.1?   121.Theaveragescoreofasampleof87seniorbusinessmajorsatUTCwhotooktheGraduateManagementAdmissionTestwas510withastandarddeviationof36.Providea98%confidenceintervalforthemeanofthepopulation.   122.Inapollof600votersinacampaigntoeliminatenon-returnablebeveragecontainers,210ofthevoterswereopposed.Developa92%confidenceintervalestimatefortheproportionofallthevoterswhoopposedthecontainercontrolbill.       .
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    71.RefertoExhibit9-2.Ifthetestisdoneat95%confidence,thenullhypothesisshould a.notberejected b.berejected c.Notenoughinformationisgiventoanswerthisquestion. d.Noneofthesealternativesiscorrect.       Exhibit9-3     n=49=54.8s=28H0:μ≤ 50 Ha:μ>50 72.RefertoExhibit9-3.Theteststatisticisa.0.1714 b.0.3849 c.-1.2 d.1.2         73.RefertoExhibit9-3.Thep-valueisbetweena.0.01to0.025 b.0.025to0.05 c..05to0.1 d.0.1to0.2     74.RefertoExhibit9-3.Ifthetestisdoneatthe5%levelofsignificance,thenullhypothesisshould a.notberejected b.berejected c.Notenoughinformationgiventoanswerthisquestion. d.Noneofthesealternativesiscorrect.     Exhibit9-4 Themanagerofagrocerystorehastakenarandomsampleof100customers.Theaveragelengthoftimeittookthecustomersinthesampletocheckoutwas3.1minuteswithastandarddeviationof0.5minutes.Wewanttotesttodeterminewhetherornotthemeanwaitingtimeofallcustomersissignificantlymorethan3minutes. 75.RefertoExhibit9-4.Theteststatisticisa.1.96 b.1.64 c.2.00 d.0.056       76.RefertoExhibit9-4.Thep-valueisbetweena..005to.01 b..01to.025 c..025to.05 d..05to.10     77.RefertoExhibit9-4.At95%confidence,itcanbeconcludedthatthemeanofthepopulationis a.significantlygreaterthan3 b.notsignificantlygreaterthan3 c.significantlylessthan3 d.significantlygreaterthen3.18       Exhibit9-5 Arandomsampleof100peoplewastaken.Eighty-fiveofthepeopleinthesamplefavoredCandidateA.WeareinterestedindeterminingwhetherornottheproportionofthepopulationinfavorofCandidateAissignificantlymorethan80%. 78.RefertoExhibit9-5.Theteststatisticisa.0.80 b.0.05 c.1.25 d.2.00       79.RefertoExhibit9-5.Thep-valueisa.0.2112 b.0.05 c.0.025 d.0.1056     80.RefertoExhibit9-5.At95%confidence,itcanbeconcludedthattheproportionofthepopulationinfavorofcandidateA a.issignificantlygreaterthan80% b.isnotsignificantlygreaterthan80% c.issignificantlygreaterthan85% d.isnotsignificantlygreaterthan85%       Exhibit9-6 Arandomsampleof16studentsselectedfromthestudentbodyofalargeuniversityhadanaverageageof25yearsandastandarddeviationof2years.Wewanttodetermineiftheaverageageofallthestudentsattheuniversityissignificantlymorethan24.Assumethedistributionofthepopulationofagesisnormal.   .
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  102.Theaveragegasolinepriceofoneofthemajoroilcompanieshasbeen$2.20pergallon.Becauseofcostreductionmeasures,itisbelievedthattherehasbeenasignificantreductionintheaverageprice.Inordertotestthisbelief,werandomlyselectedasampleof36ofthecompany'sgasstationsanddeterminedthattheaveragepriceforthestationsinthesamplewas$2.14.Assumethatthestandarddeviationofthepopulation(σ)is$0.12.   a.Statethenullandthealternativehypotheses. b.Computetheteststatistic. c.Whatisthep-valueassociatedwiththeabovesampleresults? d.At95%confidence,testthecompany'sclaim. 103.Asampleof81accountbalancesofacreditcompanyshowedanaveragebalanceof$1,200withastandarddeviationof$126.     a.Formulatethehypothesesthatcanbeusedtodeterminewhetherthemeanofallaccountbalancesissignificantlydifferentfrom$1,150. b.Computetheteststatistic. c.Usingthep-valueapproach,whatisyourconclusion?Letα=.05. 104.Fromapopulationofcansofcoffeemarked"12ounces,"asampleof50canswasselectedandthecontentsofeachcanwereweighed.Thesamplerevealedameanof11.8ounceswithastandarddeviationof0.5ounces.     a.Formulatethehypothesestotesttoseeifthemeanofthepopulationisatleast12ounces. b.Computetheteststatistic. c.Usingthep-valueapproach,whatisyourconclusion?Letα=.05.     105.Alatheissettocutbarsofsteelintolengthsof6centimeters.Thelatheisconsideredtobeinperfectadjustmentiftheaveragelengthofthebarsitcutsis6centimeters.Asampleof121barsisselectedrandomlyandmeasured.Itisdeterminedthattheaveragelengthofthebarsinthesampleis6.08centimeterswithastandarddeviationof0.44centimeters.   a.Formulatethehypothesestodeterminewhetherornotthelatheisinperfectadjustment. b.Computetheteststatistic. c.Usingthep-valueapproach,whatisyourconclusion?Letα=.05. 106.Ahmadi,Inc.hasbeenmanufacturingsmallautomobilesthathaveaveraged50milespergallonofgasolineinhighwaydriving.Thecompanyhasdevelopedamoreefficientengineforitssmallcarsandnowadvertisesthatitsnewsmallcarsaveragemorethan50milespergalloninhighwaydriving.Anindependenttestingserviceroad-tested64oftheautomobiles.Thesampleshowedanaverageof51.5milespergallonwithastandarddeviationof4milespergallon.     a.Formulatethehypothesestodeterminewhetherornotthemanufacturer'sadvertisingcampaignislegitimate. b.Computetheteststatistic. c.Whatisthep-valueassociatedwiththesampleresultsandwhatisyourconclusion?Letα= .05.         .
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    51.AsimplerandomsampleofsizenfromaninfinitepopulationofsizeNistobeselected.Eachpossiblesampleshouldhave a.thesameprobabilityofbeingselected b.aprobabilityof1/nofbeingselected c.aprobabilityof1/Nofbeingselected d.aprobabilityofN/nofbeingselected     52.Arandomsampleof150peoplewastakenfromaverylargepopulation.Ninetyofthepeopleinthesamplewerefemale.Thestandarderroroftheproportionis a.0.0016 b.0.2400 c.0.1600 d.0.0400     53.Forapopulationwithanydistribution,theformofthesamplingdistributionofthesamplemeanis a.sometimesnormalforallsamplesizes b.sometimesnormalforlargesamplesizes c.alwaysnormalforallsamplesizes d.alwaysnormalforlargesamplesizes       54.Asimplerandomsampleof28observationswastakenfromalargepopulation.Thesamplemeanequaled50.Fiftyisa a.populationparameter b.biasedestimateofthepopulationmean c.sampleparameter d.pointestimate     55.Thereare6childreninafamily.Thenumberofchildrendefinesapopulation.Thenumberofsimplerandomsamplesofsize2(withoutreplacement)whicharepossibleequals a.12 b.15 c.3 d.16       56.Asimplerandomsampleof5observationsfromapopulationcontaining400elementswastaken,andthefollowingvalueswereobtained.   1218192021   Apointestimateofthemeanisa.400 b.18 c.20 d.10     57.Randomsamplesofsize49aretakenfromapopulationthathas200elements,ameanof180,andavarianceof 196.Thedistributionofthepopulationisunknown.Themeanandthestandarderrorofthemeanarea.180and24.39 b.180and28 c.180and2 d.180and1.74     58.Randomsamplesofsize36aretakenfromaninfinitepopulationwhosemeanandstandarddeviationare20and15,respectively.Thedistributionofthepopulationisunknown.Themeanandthestandarderrorofthemeanare a.36and15 b.20and15 c.20and0.417 d.20and2.5     59.Asampleof24observationsistakenfromapopulationthathas150elements.Thesamplingdistributionofis a.approximatelynormalbecauseisalwaysapproximatelynormallydistributed b.approximatelynormalbecausethesamplesizeislargeincomparisontothepopulationsize c.approximatelynormalbecauseofthecentrallimittheorem d.normalifthepopulationisnormallydistributed     60.Asampleof92observationsistakenfromaninfinitepopulation.Thesamplingdistributionof isapproximately a.normalbecauseisalwaysapproximatelynormallydistributed b.normalbecausethesamplesizeissmallincomparisontothepopulationsize c.normalbecauseofthecentrallimittheorem d.Noneofthesealternativesiscorrect.         .
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    81.RefertoExhibit9-6.Theteststatisticisa.1.96 b.2.00 c.1.645 d.0.05         82.RefertoExhibit9-6.Thep-valueisbetweena..005to.01 b..01to.025 c..025to.05 d..05to.10     83.RefertoExhibit9-6.At95%confidence,itcanbeconcludedthatthemeanageis a.notsignificantlydifferentfrom24 b.significantlydifferentfrom24 c.significantlylessthan24 d.significantlymorethan24     Exhibit9-7 Arandomsampleof16statisticsexaminationsfromalargepopulationwastaken.Theaveragescoreinthesamplewas78.6withavarianceof64.Weareinterestedindeterminingwhethertheaveragegradeofthepopulationissignificantlymorethan75.Assumethedistributionofthepopulationofgradesisnormal. 84.RefertoExhibit9-7.Theteststatisticisa.0.45 b.1.80 c.3.6 d.8       85.RefertoExhibit9-7.Thep-valueisbetweena..005to.01 b..01to.025 c..025to.05 d..05to0.1     86.RefertoExhibit9-7.At95%confidence,itcanbeconcludedthattheaveragegradeofthepopulation a.isnotsignificantlygreaterthan75 b.issignificantlygreaterthan75 c.isnotsignificantlygreaterthan78.6 d.issignificantlygreaterthan78.6       Exhibit9-8 TheaveragegasolinepriceofoneofthemajoroilcompaniesinEuropehasbeen$1.25perliter.Recently,thecompanyhasundertakenseveralefficiencymeasuresinordertoreduceprices.Managementisinterestedindeterminingwhethertheirefficiencymeasureshaveactuallyreducedprices.Arandomsampleof49oftheirgasstationsisselectedandtheaveragepriceisdeterminedtobe$1.20perliter.Furthermore,assumethatthestandarddeviationofthepopulation(σ)is$0.14. 87.RefertoExhibit9-8.Thestandarderrorhasavalueofa.0.14 b.7c.2.5 d.0.02       88.RefertoExhibit9-8.Thevalueoftheteststatisticforthishypothesistestisa.1.96 b.1.645 c.-2.5 d.-1.645     89.RefertoExhibit9-8.Thep-valueforthisproblemisa.0.4938 b.0.0062 c.0.0124 d.0.05       Exhibit9-9 Thesalesofagrocerystorehadanaverageof$8,000perday.Thestoreintroducedseveraladvertisingcampaignsinordertoincreasesales.Todeterminewhetherornottheadvertisingcampaignshavebeeneffectiveinincreasingsales,asampleof64daysofsaleswasselected.Itwasfoundthattheaveragewas$8,300perday. Frompastinformation,itisknownthatthestandarddeviationofthepopulationis$1,200. 90.RefertoExhibit9-9.Thecorrectnullhypothesisforthisproblemisa.μ≤8000 b.μ>8000c.μ=8000d.μ>8250       91.RefertoExhibit9-9.Thevalueoftheteststatisticisa.250 b.8000 c.8250 d.2.0     92.RefertoExhibit9-9.Thep-valueisa.2.00 b.0.9772 c.0.0228 d.0.5475           .
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    31.Inalowerone-tailhypothesistestsituation,thep-valueisdeterminedtobe0.2.Ifthesamplesizeforthistestis51,thetstatistichasavalueof a.0.849 b.-0.849 c.1.299 d.-1.299     32.Ifahypothesisisrejectedatthe5%levelofsignificance,it a.willalwaysberejectedatthe1%level b.willalwaysbeacceptedatthe1%level c.willneverbetestedatthe1%level d.mayberejectedornotrejectedatthe1%level         33.Ifahypothesisisnotrejectedatthe5%levelofsignificance,it a.willalsonotberejectedatthe1%level b.willalwaysberejectedatthe1%level c.willsometimesberejectedatthe1%level d.Noneofthesealternativesiscorrect.     34.IftheprobabilityofaTypeIerror(α)is0.05,thentheprobabilityofaTypeIIerror(β)mustbea.0.05 b.0.95 c.0.025 d.Noneofthesealternativesiscorrect.     35.Ifthelevelofsignificanceofahypothesistestisraisedfrom.01to.05,theprobabilityofaTypeIIerror a.willalsoincreasefrom.01to.05 b.willnotchange c.willdecrease d.willincrease     36.Ifahypothesisisrejectedat95%confidence,it a.willalwaysbeacceptedat90%confidence b.willalwaysberejectedat90%confidence c.willsometimesberejectedat90%confidence d.Noneofthesealternativesiscorrect.     37.Foratwo-tailedtestat86.12%confidence,Z=a.1.96 b.1.48 c.1.09 d.0.86     38.Foraone-tailedtest(lowertail)at93.7%confidence,Z=a.-1.86 b.-1.53 c.-1.96 d.-1.645         39.ReadtheZstatisticfromthenormaldistributiontableandcirclethecorrectanswer.Aone-tailedtest(uppertail)at87.7%confidence;Z= a.1.54 b.1.96 c.1.645 d.1.16     40.Foratwo-tailedtest,asampleof20at80%confidence,t=a.1.328 b.2.539 c.1.325 d.2.528       .
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    41.Foraone-tailedtest(uppertail),asamplesizeof18at95%confidence,t=a.2.12 b.-2.12 c.-1.740 d.1.740     42.Foraone-tailedtest(lowertail),asamplesizeof10at90%confidence,t=a.1.383 b.2.821 c.-1.383 d.-2.821     43.Atwo-tailedtestisperformedat95%confidence.Thep-valueisdeterminedtobe0.09.Thenullhypothesis a.mustberejected b.shouldnotberejected c.couldberejected,dependingonthesamplesize d.hasbeendesignedincorrectly       44.Foratwo-tailedtestat98.4%confidence,Z=a.1.96 b.1.14 c.2.41 d.0.8612     45.Foraone-tailedtest(lowertail)at89.8%confidence,Z=a.-1.27 b.-1.53 c.-1.96 d.-1.64     46.Foraone-tailedtest(uppertail)at93.7%confidence,Z=a.1.50 b.1.96 c.1.645 d.1.53     47.Foraone-tailedtest(uppertail),asamplesizeof26at90%confidence,t=a.1.316 b.-1.316 c.-1.740 d.1.740     48.Foraone-tailedtest(lowertail)with22degreesoffreedomat95%confidence,thevalueoft=a.-1.383 b.1.383 c.-1.717 d.-1.721       49.Foraone-tailedhypothesistest(uppertail)thep-valueiscomputedtobe0.034.Ifthetestisbeingconductedat95%confidence,thenullhypothesis a.couldberejectedornotrejecteddependingonthesamplesize b.couldberejectedornotrejecteddependingonthevalueofthemeanofthesample c.isnotrejected d.isrejected     50.Inatwo-tailedhypothesistesttheteststatisticisdeterminedtobeZ=-2.5.Thep-valueforthistestisa.-1.25 b.0.4938 c.0.0062 d.0.0124       .
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  127.Considerthefollowinghypothesistest:   Ho:μ≤ 38 Ha:μ>38   Youaregiventhefollowinginformationobtainedfromarandomsampleofsixobservations.Assumethepopulationhasanormaldistribution.     X 38 40 42 32 46 42       a.Computethemeanofthesample b.Determinethestandarddeviationofthesample. c.Determinethestandarderrorofthemean. d.Computethevalueoftheteststatistic. e.At95%confidenceusingthep-valueapproach,testtheabovehypotheses. 128.Considerthefollowinghypothesistest:   Ho:P≤0.8 Ha:P>0.8   Asampleof400providedasampleproportionof0.853.     a.Determinethestandarderroroftheproportion. b.Computethevalueoftheteststatistic. c.Determinethep-value;andat95%confidence,testtheabovehypotheses.     129.Youaregiventhefollowinginformationobtainedfromarandomsampleof5observations.Assumethepopulationhasanormaldistribution.   2018172218   Youwanttodeterminewhetherornotthemeanofthepopulationfromwhichthissamplewastakenissignificantlylessthan21.     a.Statethenullandthealternativehypotheses. b.Computethestandarderrorofthemean. c.Determinetheteststatistic. d.Determinethep-valueandat90%confidence,testwhetherornotthemeanofthepopulationissignificantlylessthan21.     a.Ho:μ≥ 21 Ha:μ<21 b.0.8944 c.t=-2.236 d.p-valueisbetween.025and.05;rejectHo,themeanissignificantlylessthan21.   130.Considerthefollowinghypothesistest:   Ho:p=0.5 Ha:p ≠ 0.5   Asampleof800providedasampleproportionof0.58.   a.Determinethestandarderroroftheproportion. b.Computethevalueoftheteststatistic. c.Determinethep-value,andat95%confidence,testthehypotheses.   131.Youaregiventhefollowinginformationobtainedfromarandomsampleof4observations.2547              32              56 Youwanttodeterminewhetherornotthemeanofthepopulationfromwhichthissamplewastakenissignificantlydifferentfrom48.(Assumethepopulationisnormallydistributed.)   a.Statethenullandthealternativehypotheses. b.Determinetheteststatistic. c.Determinethep-value;andat95%confidencetesttodeterminewhetherornotthemeanofthepopulationissignificantlydifferentfrom48.         .
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  125.Anewsoftdrinkisbeingmarkettested.Itisestimatedthat60%ofconsumerswilllikethenewdrink.Asampleof96tastetestedthenewdrink.   a.Determinethestandarderroroftheproportion b.Whatistheprobabilitythatmorethan70.4%ofconsumerswillindicatetheylikethedrink? c.Whatistheprobabilitythatmorethan30%ofconsumerswillindicatetheydonotlikethedrink?   126.Abankhaskeptrecordsofthecheckingbalancesofitscustomersanddeterminedthattheaveragedailybalanceofitscustomersis$300withastandarddeviationof$48.Arandomsampleof144checkingaccountsisselected.   a.Whatistheprobabilitythatthesamplemeanwillbemorethan$306.60? b.Whatistheprobabilitythatthesamplemeanwillbelessthan$308? c.Whatistheprobabilitythatthesamplemeanwillbebetween$302and$308? d.Whatistheprobabilitythatthesamplemeanwillbeatleast$296?   127.Inalargeuniversity,20%ofthestudentsarebusinessmajors.Arandomsampleof100studentsisselected,andtheirmajorsarerecorded.   a.Computethestandarderroroftheproportion. b.Whatistheprobabilitythatthesamplecontainsatleast12businessmajors? c.Whatistheprobabilitythatthesamplecontainslessthan15businessmajors? d.Whatistheprobabilitythatthesamplecontainsbetween12and14businessmajors? 128.Asimplerandomsampleof6computerprogrammersinHouston,Texasrevealedthesexoftheprogrammersandthefollowinginformationabouttheirweeklyincomes.     ProgrammerWeeklyIncomeSex A$250M B270M C285F D240M E255M F290F     a.WhatisthepointestimatefortheaverageweeklyincomeofallthecomputerprogrammersinHouston? b.Whatisthepointestimateforthestandarddeviationofthepopulation? c.DetermineapointestimatefortheproportionofallprogrammersinHoustonwhoarefemale.     129.Themilkprices(inquarts)fromasampleof9conveniencestoresinChattanooga,Tennesseeareshownbelow.     Store#PricePerQuart(x) 1$1.14 2$1.19 3$1.25 4$1.21 5$1.17 6$1.19 7$1.22 8$1.24 9$1.19     a.WhatisthepointestimateforthepricesofallconveniencestoresinChattanooga? b.Whatisthepointestimateforthestandarddeviationofthepopulation?             .
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  31) A centralized knowledge base of all data definitions, data relationships, screen and report formats, and other system components is called a(n): A) index. B) data warehouse. C) repository. D) database management system. 32) CASE is a class of tools that: A) assists the database administrator in maintaining a database..
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MultipleChoice 1.Thesumofthevaluesofαandβ a.alwaysaddupto1.0 b.alwaysaddupto0.5 c.istheprobabilityofTypeIIerror d.noneofthesealternativesiscorrect       2.WhattypeoferroroccursifyoufailtorejectH0when,infact,itisnottrue? a.TypeII b.TypeI c.eitherTypeIorTypeII,dependingonthelevelofsignificance d.eitherTypeIorTypeII,dependingonwhetherthetestisonetailortwotail     3.Anassumptionmadeaboutthevalueofapopulationparameteriscalleda a.hypothesis b.conclusion c.confidence d.significance     4.TheprobabilityofcommittingaTypeIerrorwhenthenullhypothesisistrueis a.theconfidencelevel b.β c.greaterthan1 d.theLevelofSignificance     5.Inhypothesistesting, a.thesmallertheTypeIerror,thesmallertheTypeIIerrorwillbe b.thesmallertheTypeIerror,thelargertheTypeIIerrorwillbe c.TypeIIerrorwillnotbeeffectedbyTypeIerror d.thesumofTypeIandTtypeIIerrorsmustequalto1         6.Inhypothesistesting,thetentativeassumptionaboutthepopulationparameteris a.thealternativehypothesis b.thenullhypothesis c.eitherthenullorthealternative d.Noneofthesealternativesiscorrect.     7.Foralowertailtest,thep-valueistheprobabilityofobtainingavaluefortheteststatistic a.atleastassmallasthatprovidedbythesample b.atleastaslargeasthatprovidedbythesample c.atleastassmallasthatprovidedbythepopulation d.atleastaslargeasthatprovidedbythepopulation.     8.Thep-valueisaprobabilitythatmeasuresthesupport(orlackofsupport)forthe a.nullhypothesis b.alternativehypothesis c.eitherthenullorthealternativehypothesis d.samplestatistic     9.Thep-value a.isthesameastheZstatistic b.measuresthenumberofstandarddeviationsfromthemean c.isadistance d.isaprobability     10.Foratwo-tailtest,thep-valueistheprobabilityofobtainingavaluefortheteststatisticas a.likelyasthatprovidedbythesample b.unlikelyasthatprovidedbythesample c.likelyasthatprovidedbythepopulation d.unlikelyasthatprovidedbythepopulation       .
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    31.Theprobabilitydistributionofallpossiblevaluesofthesamplemeanis a.theprobabilitydensityfunctionof b.thesamplingdistributionof c.thegrandmean,sinceitconsidersallpossiblevaluesofthesamplemean d.one,sinceitconsidersallpossiblevaluesofthesamplemean     32.Whichofthefollowingsamplingmethodsdoesnotleadtoprobabilitysamples? a.stratifiedsampling b.clustersampling c.systematicsampling d.conveniencesampling       33.Whichofthefollowingis(are)pointestimator(s)? a.σ b.μ c.s d.α     34.Aprobabilitydistributionforallpossiblevaluesofasamplestatisticisknownas a.asamplestatistic b.aparameter c.simplerandomsampling d.asamplingdistribution     35.Apopulationcharacteristic,suchasapopulationmean,iscalled a.astatistic b.aparameter c.asample d.themeandeviation       36.Apopulationhasameanof300andastandarddeviationof18.Asampleof144observationswillbetaken.Theprobabilitythatthesamplemeanwillbebetween297to303is a.0.4332 b.0.8664 c.0.9332 d.0.0668     37.Asamplestatistic,suchasasamplemean,isknownas a.astatistic b.aparameter c.themeandeviation d.thecentrallimittheorem     38.Thestandarddeviationofapointestimatoriscalledthe a.standarddeviation b.standarderror c.pointestimator d.varianceofestimation     39.Asinglenumericalvalueusedasanestimateofapopulationparameterisknownas a.aparameter b.apopulationparameter c.ameanestimator d.apointestimate     40.Thesamplestatistic,suchas, s,or,thatprovidesthepointestimateofthepopulationparameterisknownas a.apointestimator b.aparameter c.apopulationparameter d.apopulationstatistic         .
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  SubjectiveShortAnswer 75.AlocaluniversityadministersacomprehensiveexaminationtothecandidatesforB.S.degreesinBusinessAdministration.Fiveexaminationsareselectedatrandomandscored.Thescoresareshownbelow.       Grades 80 90 91 62 77       a.Computethemeanandthestandarddeviationofthesample. b.Computethemarginoferrorat95%confidence. c.Developa95%confidenceintervalestimateforthemeanofthepopulation.Assumethepopulationisnormallydistributed.       76.Arandomsampleof87airlinepilotshadanaverageyearlyincomeof$99,400withastandarddeviationof$12,000.     a.Ifwewanttodeterminea95%confidenceintervalfortheaverageyearlyincome,whatisthevalueoft? b.Developa95%confidenceintervalfortheaverageyearlyincomeofallpilots.   77.Arandomsampleof81creditsalesinadepartmentstoreshowedanaveragesaleof$68.00.Frompastdata,itisknownthatthestandarddeviationofthepopulationis$27.00.   a.Determinethestandarderrorofthemean. b.Witha0.95probability,whatcanbesaidaboutthesizeofthemarginoferror? c.Whatisthe95%confidenceintervalofthepopulationmean?   78.Youaregiventhefollowinginformationobtainedfromasampleof5observationstakenfromapopulationthathasanormaldistribution.   9472935477   Developa98%confidenceintervalestimateforthemeanofthepopulation.       79.ManypeoplewhoboughtX-Gamegamingsystemsovertheholidayshavecomplainedthatthesystemstheypurchasedweredefective.Inasampleof1200unitssold,18unitsweredefective.   a.Determinea95%confidenceintervalforthepercentageofdefectivesystems. b.If1.5millionX-Gamesweresoldovertheholidays,determineanintervalforthenumberofdefectivesinsales.   a.0.00812to0.02188(rounded) b.12,184to32,816   80.ChooChooPaperCompanyproducespapersofvariousthickness.Arandomsampleof256cutshadameanthicknessof30.3milswithastandarddeviationof4mils.Developa95%confidenceintervalforthemeanthicknessofthepopulation.       .
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    41.Atheoremthatallowsustousethenormalprobabilitydistributiontoapproximatethesamplingdistributionofsamplemeansandsampleproportionswheneverthesamplesizeislargeisknownasthe a.approximationtheorem b.normalprobabilitytheorem c.centrallimittheorem d.centralnormalitytheorem     42.Thepurposeofstatisticalinferenceistoprovideinformationaboutthe a.samplebaseduponinformationcontainedinthepopulation b.populationbaseduponinformationcontainedinthesample c.populationbaseduponinformationcontainedinthepopulation d.meanofthesamplebaseduponthemeanofthepopulation     43.Asimplerandomsampleof64observationswastakenfromalargepopulation.Thesamplemeanandthestandarddeviationweredeterminedtobe320and120respectively.Thestandarderrorofthemeanis a.1.875 b.40 c.5 d.15       44.Thenumberofrandomsamples(withoutreplacement)ofsize3thatcanbedrawnfromapopulationofsize5is a.15 b.10 c.20d.125   45.Randomsamplesofsize81aretakenfromaninfinitepopulationwhosemeanandstandarddeviationare200and18,respectively.Thedistributionofthepopulationisunknown.Themeanandthestandarderrorofthemeanare a.200and18 b.81and18 c.9 and 2 d.200and2       46.Apopulationhasameanof80andastandarddeviationof7.Asampleof49observationswillbetaken.Theprobabilitythatthesamplemeanwillbelargerthan82is a.0.5228 b.0.9772 c.0.4772 d.0.0228     47.Apopulationhasameanof180andastandarddeviationof24.Asampleof64observationswillbetaken.Theprobabilitythatthesamplemeanwillbebetween183and186is a.0.1359 b.0.8185 c.0.3413 d.0.4772     48.Randomsamplesofsize525aretakenfromaninfinitepopulationwhosepopulationproportionis0.3.Thestandarddeviationofthesampleproportions(i.e.,thestandarderroroftheproportion)is a.0.0004 b.0.2100 c.0.3000 d.0.0200       49.Asampleof400observationswillbetakenfromaninfinitepopulation.Thepopulationproportionequals0.8.Theprobabilitythatthesampleproportionwillbegreaterthan0.83is a.0.4332 b.0.9332 c.0.0668 d.0.5668     50.Fromapopulationof500elements,asampleof225elementsisselected.Itisknownthatthevarianceofthepopulationis900.Thestandarderrorofthemeanisapproximately a.1.1022 b.2 c.30 d.1.4847         .
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    61.RefertoExhibit8-3.Thestandarderrorofthemeanequalsa.0.001 b.0.010 c.0.100 d.1.000       62.RefertoExhibit8-3.Witha.95probability,thesamplemeanwillprovideamarginoferrorofa.1.96 b.0.10 c.0.196 d.1.64     b.1.36to4.64 c.1.00to5.00 d.2.804to3.196     Exhibit8-4 Inordertoestimatetheaverageelectricusagepermonth,asampleof81houseswasselected,andtheelectricusagewasdetermined.Assumeapopulationstandarddeviationof450-kilowatthours. 64.RefertoExhibit8-4.Thestandarderrorofthemeanisa.450 b.81c.500 d.50       65.RefertoExhibit8-4.At95%confidence,thesizeofthemarginoferrorisa.1.96 b.50 c.98 d.42       66.RefertoExhibit8-4.Ifthesamplemeanis1,858KWH,the95%confidenceintervalestimateofthepopulationmeanis a.1,760to1,956KWH b.1,858to1,956KWH c.1,760to1,858KWH d.noneofthesealternativesiscorrect     Exhibit8-5 Arandomsampleof64SATscoresofstudentsapplyingformeritscholarshipsshowedanaverageof1400withastandarddeviationof240. 67.RefertoExhibit8-5.Ifwewanttoprovidea95%confidenceintervalfortheSATscores,thedegreesoffreedom forreadingthecriticalvaluesof“t”statisticis a.60 b.61 c.62 d.63       68.RefertoExhibit8-5.The“t”valueforthisintervalestimationis a.1.96 b.1.998 c.1.64 d.1.28     69.RefertoExhibit8-5.Themarginoferrorat95%confidenceisa.1.998 b.1400 c.240 d.59.95       70.RefertoExhibit8-5.The95%confidenceintervalfortheSATscoresisa.1340.05to1459.95 b.1400to1459.95 c.1340.05to1400 d.1400to 1600       Exhibit8-6 Asampleof75informationsystemmanagershadanaveragehourlyincomeof$40.75withastandarddeviationof $7.00. 71.RefertoExhibit8-6.Ifwewanttodeterminea95%confidenceintervalfortheaveragehourlyincome,thevalue of“t”statisticsis a.1.96 b.1.64 c.1.28 d.1.993       72.RefertoExhibit8-6.Thestandarderrorofthemeanisa.80.83 b.7 c.0.8083 d.1.611     73.RefertoExhibit8-6.Thevalueofthemarginoferrorat95%confidenceisa.80.83 b.7 c.0.8083 d.1.611     74.RefertoExhibit8-6.The95%confidenceintervalfortheaveragehourlywageofallinformationsystemmanagersis a.40.75to42.36 b.39.14to40.75 c.39.14to42.36 d.30to50             .
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  101.Anewbrandofchocolatebarisbeingmarkettested.Fourhundredofthenewchocolatebarsweregiventoconsumerstotry.Theconsumerswereaskedwhethertheylikedordislikedthechocolatebar.Youaregiventheirresponsesbelow.     ResponseFrequency Liked300 Disliked100 400     a.Whatisthepointestimatefortheproportionofpeoplewholikedthechocolatebar? b.Constructa95%confidenceintervalforthetrueproportionofpeoplewholikedthechocolatebar. c.Witha.95probability,howlargeofasampleneedstobetakentoprovideamarginoferrorof3%orless?         102.AlocaluniversityadministersacomprehensiveexaminationtotherecipientsofaB.S.degreeinBusinessAdministration.Asampleof5examinationsisselectedatrandomandscored.Thescoresareshownbelow.       Grade 54 68 75 80 98       a.Computethesamplemeanandthestandarddeviation. b.Determinethemarginoferrorat95%confidence. c.At95%confidence,determineanintervalforthemeanofthepopulation.   At98%confidence,determineanintervalforthemeanofthepopulation. 103.Ifthepopulationstandarddeviationofthelifetimeofwashingmachinesisestimatedtobe900hours,howlargeasamplemustbetakeninordertobe97%confidentthatthemarginoferrorwillnotexceed100hours?   104.Themanagerofadepartmentstorewantstodeterminewhatproportionofpeoplewhoenterthestoreusethestore'screditcardsfortheirpurchases.Whatsizesampleshouldhetakesothatat95%confidencetheerrorwillnotbemorethan6%?   105.Inordertoestimatetheaverageelectricusagepermonth,asampleof196houseswasselected,andtheirelectricusagedetermined.     a.Assumeapopulationstandarddeviationof350-kilowatthours.Determinethestandarderrorofthemean. b.Witha0.95probability,determinethemarginoferror. c.Ifthesamplemeanis2,000KWH,whatisthe95%confidenceintervalestimateofthepopulationmean?       106.Arandomsampleof100creditsalesinadepartmentstoreshowedanaveragesaleof$120.00.Frompastdata,itisknownthatthestandarddeviationofthepopulationis$40.00.   a.Determinethestandarderrorofthemean. b.Witha0.95probability,determinethemarginoferror. c.Whatisthe95%confidenceintervalofthepopulationmean?       .
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  81.Theaveragemonthlyelectricbillofarandomsampleof256residentsofacityis$90withastandarddeviationof $24.   a.Constructa90%confidenceintervalforthemeanmonthlyelectricbillsofallresidents. b.Constructa95%confidenceintervalforthemeanmonthlyelectricbillsofallresidents. 82.Inarandomsampleof400registeredvoters,120indicatedtheyplantovoteforCandidateA.Determinea95%confidenceintervalfortheproportionofalltheregisteredvoterswhowillvoteforCandidateA.   83.TwohundredstudentsareenrolledinanEconomicsclass.Afterthefirstexamination,arandomsampleof6paperswasselected.Thegradeswere65,75,89,71,70and80.   a.Determinethestandarderrorofthemean. b.Whatassumptionmustbemadebeforewecandetermineanintervalforthemeangradeofallthestudentsintheclass?Explainwhy. c.AssumetheassumptionofPartbismet.Providea95%confidenceintervalforthemeangradeofallthestudentsintheclass.   84.Astatisticianselectedasampleof16accountsreceivableanddeterminedthemeanofthesampletobe$5,000withastandarddeviationof$400.Hereportedthatthesampleinformationindicatedthemeanofthepopulationrangesfrom$4,739.80to$5,260.20.Heneglectedtoreportwhatconfidencecoefficienthehadused.Basedontheaboveinformation,determinetheconfidencecoefficientthatwasused.Assumethepopulationhasanormaldistribution.     85.Aresearcherisinterestedindeterminingtheaveragenumberofyearsemployeesofacompanystaywiththecompany.Ifpastinformationshowsastandarddeviationof7months,whatsizesampleshouldbetakensothatat95%confidencethemarginoferrorwillbe2monthsorless?   86.Asampleof144cansofcoffeeshowedanaverageweightof16ounces.Thestandarddeviationofthepopulationisknowntobe1.4ounces.   a.Constructa68.26%confidenceintervalforthemeanofthepopulation. b.Constructa97%confidenceintervalforthemeanofthepopulation. c.DiscusswhytheanswersinPartsaandbaredifferent.   87.Youaregiventhefollowinginformationobtainedfromarandomsampleof5observationstakenfromalargepopulation.   3234323032   Constructa95%confidenceintervalforthemeanofthepopulation,assumingthepopulationhasanormaldistribution.       .
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  SubjectiveShortAnswer 93.TheDepartmentofEconomicandCommunityDevelopment(DECD)reportedthatin2009theaveragenumberofnewjobscreatedpercountywas450.Thedepartmentalsoprovidedthefollowinginformationregardingasampleof5countiesin2010.       CountyNewJobsCreatedIn2010 Bradley410 Rhea 480 Marion407 Grundy428 Sequatchie400       a.Computethesampleaverageandthestandarddeviationfor2010. b.Wewanttodeterminewhethertherehasbeenasignificantdecreaseintheaveragenumberofjobscreated.Providethenullandthealternativehypotheses. c.Computetheteststatistic. d.Computethep-value;andat95%confidence,testthehypotheses.Assumethepopulationisnormallydistributed.         94.TheBureauofLaborStatisticsreportedthattheaverageyearlyincomeofdentistsintheyear2009was$110,000.Asampleof81dentists,whichwastakenin2010,showedanaverageyearlyincomeof$120,000.Assumethestandarddeviationofthepopulationofdentistsin2010is$36,000.     a.Wewanttotesttodetermineiftherehasbeenasignificantincreaseintheaverageyearlyincomeofdentists.Providethenullandthealternativehypotheses. b.Computetheteststatistic. c.Determinethep-value;andat95%confidence,testthehypotheses.   95.Atiremanufacturerhasbeenproducingtireswithanaveragelifeexpectancyof26,000miles.Nowthecompanyisadvertisingthatitsnewtires'lifeexpectancyhasincreased.Inordertotestthelegitimacyoftheadvertisingcampaign,anindependenttestingagencytestedasampleof6oftheirtiresandhasprovidedthefollowingdata.     LifeExpectancy (InThousandsofMiles) 28 27 25 28 29 25       a.Determinethemeanandthestandarddeviation. b.At99%confidenceusingthecriticalvalueapproach,testtodeterminewhetherornotthetirecompanyisusinglegitimateadvertising.Assumethepopulationisnormallydistributed. c.Repeatthetestusingthep-valueapproach.     96.Aproducerofvariouskindsofbatterieshasbeenproducing"D"sizebatterieswithalifeexpectancyof87hours.Duetoanimprovedproductionprocess,managementbelievesthattherehasbeenanincreaseinthelifeexpectancyoftheir"D"sizebatteries.Asampleof36batteriesshowedanaveragelifeof88.5hours.Assumefrompastinformationthatitisknownthatthestandarddeviationofthepopulationis9hours.   a.Givethenullandthealternativehypotheses. b.Computetheteststatistic. c.At99%confidenceusingthecriticalvalueapproach,testmanagement'sbelief. d.Whatisthep-valueassociatedwiththesampleresults?Whatisyourconclusionbasedonthe p-value?             .
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    31.Wheneverusingthetdistributionforintervalestimation(whenthesamplesizeisverysmall),wemustassumethat a.thesamplehasameanofatleast30 b.thesamplingdistributionisnotnormal c.thepopulationisapproximatelynormal d.thefinitepopulationcorrectionfactorisnecessary     32.Asampleof20itemsfromapopulationwithanunknownσisselectedinordertodevelopanintervalestimateofμ.Whichofthefollowingisnotnecessary? a.Wemustassumethepopulationhasanormaldistribution. b.Wemustuseatdistribution. c.Samplestandarddeviationmustbeusedtoestimateσ. d.Thesamplemusthaveanormaldistribution.     33.Asampleof225elementsfromapopulationwithastandarddeviationof75isselected.Thesamplemeanis180. The95%confidenceintervalforμisa.105.0to225.0 b.175.0to185.0 c.100.0to200.0 d.170.2to189.8     34.Itisknownthatthevarianceofapopulationequals1,936.Arandomsampleof121hasbeentakenfromthepopulation.Thereisa.95probabilitythatthesamplemeanwillprovideamarginoferrorof a.7.84 b.31.36 c.344.96 d.1,936     35.Arandomsampleof144observationshasameanof20,amedianof21,andamodeof22.Thepopulationstandarddeviationisknowntoequal4.8.The95.44%confidenceintervalforthepopulationmeanis a.15.2to24.8 b.19.200to20.800 c.19.216to20.784 d.21.2to22.8         36.Whenthelevelofconfidencedecreases,themarginoferror a.staysthesame b.becomessmaller c.becomeslarger d.becomessmallerorlarger,dependingonthesamplesize     37.Arandomsampleof64studentsatauniversityshowedanaverageageof25yearsandasamplestandarddeviationof2years.The98%confidenceintervalforthetrueaverageageofallstudentsintheuniversityisa.20.5to26.5 b.24.4to25.6 c.23.0to27.0 d.20.0to30.0     38.Arandomsampleof49statisticsexaminationswastaken.Theaveragescore,inthesample,was84withavarianceof12.25.The95%confidenceintervalfortheaverageexaminationscoreofthepopulationoftheexaminationsis a.76.00to84.00 b.77.40to86.60 c.83.00to85.00 d.68.00to100.00     39.Thesamplesizeneededtoprovideamarginoferrorof2orlesswitha.95probabilitywhenthepopulationstandarddeviationequals11is a.10 b.11c.116d.117   40.Itisknownthatthepopulationvarianceequals484.Witha0.95probability,thesamplesizethatneedstobetakenifthedesiredmarginoferroris5orlessis a.25 b.74c.189 d.75           .
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  97.SomepeoplewhoboughtX-Gamegamingsystemscomplainedabouthavingreceiveddefectivesystems.Theindustrystandardforsuchsystemshasbeenninety-eightpercentnon-defectivesystems.Inasampleof120unitssold,6unitsweredefective.   a.Computetheproportionofdefectiveitemsinthesample. b.Computethestandarderrorof  . c.At95%confidenceusingthecriticalvalueapproach,testtoseeifthepercentageofdefectivesystemsproducedbyX-Gamehasexceededtheindustrystandard. d.Showthatthep-valueapproachresultsinthesameconclusionasthatofpartb.   98.ChooChooPaperCompanymakesvarioustypesofpaperproducts.Oneoftheirproductsisa30milsthickpaper.Inordertoensurethatthethicknessofthepapermeetsthe30milsspecification,randomcutsofpaperareselectedandthethicknessofeachcutismeasured.Asampleof256cutshadameanthicknessof30.3milswithastandarddeviationof 4 mils.   a.Computethestandarderrorofthemean. b.At95%confidenceusingthecriticalvalueapproach,testtoseeifthemeanthicknessissignificantlymorethan30mils. c.Showthatthep-valueapproachresultsinthesameconclusionasthatofpartb. 99.Lastyear,50%ofMNM,Inc.employeeswerefemale.Itisbelievedthattherehasbeenareductioninthepercentageoffemalesinthecompany.Thisyear,inarandomsampleof400employees,180werefemale.   a.Givethenullandthealternativehypotheses. b.At95%confidenceusingthecriticalvalueapproach,determineiftherehasbeenasignificantreductionintheproportionoffemales. c.Showthatthep-valueapproachresultsinthesameconclusionasthatofPartb.   100.Lastyear,asoftdrinkmanufacturerhad21%ofthemarket.Inordertoincreasetheirportionofthemarket,themanufacturerhasintroducedanewflavorintheirsoftdrinks.Asampleof400individualsparticipatedinthetastetestand100indicatedthattheylikethetaste.Weareinterestedindeterminingifmorethan21%ofthepopulationwilllikethenewsoftdrink.   a.Setupthenullandthealternativehypotheses. b.Determinetheteststatistic. c.Determinethep-value. d.At95%confidence,testtodetermineifmorethan21%ofthepopulationwilllikethenewsoftdrink.   101.Inthepast,theaverageageofemployeesofalargecorporationhasbeen40years.Recently,thecompanyhasbeenhiringolderindividuals.Inordertodeterminewhethertherehasbeenanincreaseintheaverageageofalltheemployees,asampleof64employeeswasselected.Theaverageageinthesamplewas45yearswithastandarddeviationof16years.Letα=.05.   a.Statethenullandthealternativehypotheses. b.Computetheteststatistic. c.Usingthep-valueapproach,testtodeterminewhetherornotthemeanageofallemployeesissignificantlymorethan40years.           .
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  117.Astudentbelievesthatnomorethan20%(i.e.,≤20%)ofthestudentswhofinishastatisticscoursegetanA.A randomsampleof100studentswastaken.Twenty-fourpercentofthestudentsinthesamplereceivedA's.       a.Statethenullandalternativehypotheses. b.Usingthecriticalvalueapproach,testthehypothesesatthe1%levelofsignificance. c.Usingthep-valueapproach,testthehypothesesatthe1%levelofsignificance. 118.Anofficialofalargenationalunionclaimsthatthefractionofwomenintheunionisnotsignificantlydifferentfromone-half.Usingthecriticalvalueapproachandthesampleinformationreportedbelow,carryoutatestofthisstatement.Letα=0.05.   samplesize400 women168 men232     119.Alawenforcementagentbelievesthatatleast88%ofthedriversstoppedonSaturdaynightsforspeedingareundertheinfluenceofalcohol.Asampleof66driverswhowerestoppedforspeedingonaSaturdaynightwastaken.Eightypercentofthedriversinthesamplewereundertheinfluenceofalcohol.   a.Statethenullandalternativehypotheses. b.Computetheteststatistic. c.Usingthep-valueapproach,testthehypothesesatthe.05levelofsignificance.   120.Twothousandnumbersareselectedrandomly;960wereevennumbers.     a.Statethehypothesestodeterminewhethertheproportionofoddnumbersissignificantlydifferentfrom50%. b.Computetheteststatistic. c.At90%confidenceusingthep-valueapproach,testthehypotheses. 121.Inthelastpresidentialelection,anationalsurveycompanyclaimedthatnomorethan50%(i.e.,≤ 50%)ofallregisteredvotersvotedfortheRepublicancandidate.Inarandomsampleof400registeredvoters,208votedfortheRepublicancandidate.   a.Statethenullandthealternativehypotheses. b.Computetheteststatistic. c.At95%confidence,computethep-valueandtestthehypotheses.           .
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  120.Thereare8,000studentsattheUniversityofTennesseeatChattanooga.Theaverageageofallthestudentsis24yearswithastandarddeviationof9years.Arandomsampleof36studentsisselected.   a.Determinethestandarderrorofthemean. b.Whatistheprobabilitythatthesamplemeanwillbelargerthan19.5? c.Whatistheprobabilitythatthesamplemeanwillbebetween25.5and27years?   121.Inalocaluniversity,10%ofthestudentsliveinthedormitories.Arandomsampleof100studentsisselectedforaparticularstudy.     a.Whatistheprobabilitythatthesampleproportion(theproportionlivinginthedormitories)isbetween0.172and0.178? b.Whatistheprobabilitythatthesampleproportion(theproportionlivinginthedormitories)isgreaterthan0.025?     122.Adepartmentstorehasdeterminedthat25%ofalltheirsalesarecreditsales.Arandomsampleof75salesisselected.   a.Whatistheprobabilitythatthesampleproportionwillbegreaterthan0.34? b.Whatistheprobabilitythatthesampleproportionwillbebetween0.196and0.354? c.Whatistheprobabilitythatthesampleproportionwillbelessthan0.25? d.Whatistheprobabilitythatthesampleproportionwillbelessthan0.10?     123.Tenpercentoftheitemsproducedbyamachinearedefective.Arandomsampleof100itemsisselectedandcheckedfordefects.   a.Determinethestandarderroroftheproportion. b.Whatistheprobabilitythatthesamplewillcontainmorethan2.5%defectiveunits? c.Whatistheprobabilitythatthesamplewillcontainmorethan13%defectiveunits? 124.Thereare500employeesinafirm,45%arefemale.Asampleof60employeesisselectedrandomly.   a.Determinethestandarderroroftheproportion. b.Whatistheprobabilitythatthesampleproportion(proportionoffemales)isbetween0.40and0.55?         .
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  130.Arandomsampleof15telephonecallsinanofficeshowedthedurationofeachcallandwhetheritwasalocaloralongdistancecall.       CallNumberDuration(InMinutes)   TypeofCall 12local 212longdistance 310local 43local 55longdistance 66local 73local 85local 98local 104local 115local 124local 135local 144local 159longdistance     a.Whatisthepointestimatefortheaveragedurationofallcalls? b.Whatisthepointestimateforthestandarddeviationofthepopulation? c.Whatisthepointestimatefortheproportionofallcallsthatwerelongdistance?   131.Anautomotiverepairshophasdeterminedthattheaverageservicetimeonanautomobileis130minuteswithastandarddeviationof26minutes.Arandomsampleof40automotiveservicesisselected.   a.Computethestandarderrorofthemean. b.Whatistheprobabilitythatthesampleof40automotiveserviceswillhaveameanservicetimegreaterthan136minutes? c.Assumethepopulationconsistsof400automotiveservices.Determinethestandarderrorofthemean.       132.Adepartmentstorehasdeterminedthat25%ofalltheirsalesarecreditsales.Arandomsampleof60salesisselected.   a.What isthesamplingdistributionof? b.Whatistheprobabilitythatthesampleproportionwillbegreaterthan0.30? c.Whatistheprobabilitythatthesampleproportionwillbebetween0.20to0.30?       .
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  107.Inordertodeterminetheaverageweightofcarry-onluggagebypassengersinairplanes,asampleof16piecesofcarry-onluggagewasweighed.Theaverageweightwas20pounds.Assumethatweknowthestandarddeviationofthepopulationtobe8pounds.   a.Determinea97%confidenceintervalestimateforthemeanweightofthecarry-onluggage. b.Determinea95%confidenceintervalestimateforthemeanweightofthecarry-onluggage.   108.Asmallstockbrokeragefirmwantstodeterminetheaveragedailysales(indollars)ofstockstotheirclients.Asampleofthesalesfor36daysrevealedaveragedailysalesof$200,000.Assumethatthestandarddeviationofthepopulationisknowntobe$18,000.   a.Providea95%confidenceintervalestimatefortheaveragedailysale. b.Providea97%confidenceintervalestimatefortheaveragedailysale.   109.Arandomsampleof81childrenwithworkingmothersshowedthattheywereabsentfromschoolanaverageof6dayspertermwithastandarddeviationof1.8days.Providea95%confidenceintervalfortheaveragenumberofdaysabsentpertermforallthechildren.   110.TheHighwaySafetyDepartmentwantstostudythedrivinghabitsofindividuals.Asampleof121carstravelingonthehighwayrevealedanaveragespeedof60milesperhourwithastandarddeviationof11milesperhour.Determinea95%confidenceintervalestimateforthespeedofallcars.       111.Inordertodeterminehowmanyhoursperweekfreshmencollegestudentswatchtelevision,arandomsampleof256studentswasselected.Itwasdeterminedthatthestudentsinthesamplespentanaverageof14hourswithastandarddeviationof3.2hourswatchingTVperweek.     a.Providea95%confidenceintervalestimatefortheaveragenumberofhoursthatallcollegefreshmenspendwatchingTVperweek. Assumethatasampleof62studentswasselected(withthesamemeanandthestandard b.deviation).Providea95%confidenceintervalestimatefortheaveragenumberofhoursthatallcollegefreshmenspendwatchingTVperweek.     112.ComputerServices,Inc.wantstodetermineaconfidenceintervalfortheaverageCPUtimeoftheirteleprocessingtransactions.Asampleof64transactionsyieldedameanof6secondswithastandarddeviationof0.8seconds.Determinea98%confidenceintervalfortheaverageCPUtime.   113.TheproprietorofaboutiqueinNewYorkwantedtodeterminetheaverageageofhiscustomers.Arandomsampleof53customersrevealedanaverageageof28yearswithastandarddeviationof4years.Determinea98%confidenceintervalestimatefortheaverageageofallhiscustomers.   114.Asampleof36patientsinadoctor'sofficeshowedthattheyhadtowaitanaverageof45minuteswithastandarddeviationof10minutesbeforetheycouldseethedoctor.Providea90%confidenceintervalestimatefortheaveragewaitingtimeofallthepatientswhovisitthisdoctor.       .
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    71.Thefactthatthesamplingdistributionofsamplemeanscanbeapproximatedbyanormalprobabilitydistributionwheneverthesamplesizeislargeisbasedonthe a.centrallimittheorem b.factthatwehavetablesofareasforthenormaldistribution c.assumptionthatthepopulationhasanormaldistribution d.Noneofthesealternativesiscorrect.     72.Asthesamplesizeincreases,thevariabilityamongthesamplemeans a.increases b.decreases c.remainsthesame d.dependsuponthespecificpopulationbeingsampled     73.Asaruleofthumb,thesamplingdistributionofthesampleproportionscanbeapproximatedbyanormalprobabilitydistributionwhenever a.np≥5 b.n(1- p)≥5and n≥30c.n≥30and(1-p)=0.5 d.Noneofthesealternativesiscorrect.       74.Randomsamplesofsize17aretakenfromapopulationthathas200elements,ameanof36,andastandarddeviationof8.Themeanandthestandarddeviationofthesamplingdistributionofthesamplemeansare a.8.7and1.94 b.36and1.94 c.36and1.86 d.36and8     75.Randomsamplesofsize17aretakenfromapopulationthathas200elements,ameanof36,andastandarddeviationof8.Whichofthefollowingbestdescribestheformofthesamplingdistributionofthesamplemeanforthissituation? a.approximatelynormalbecausethesamplesizeissmallrelativetothepopulationsize b.approximatelynormalbecauseofthecentrallimittheorem c.exactlynormal d.Noneofthesealternativesiscorrect.       76.Thesamplingdistributionofthesamplemeans a.istheprobabilitydistributionshowingallpossiblevaluesofthesamplemean b.isusedasapointestimatorofthepopulationmeanμ c.isanunbiasedestimator d.showsthedistributionofallpossiblevaluesofμ     77.Clustersamplingis a.anonprobabilitysamplingmethod b.thesameasconveniencesampling c.aprobabilitysamplingmethod d.Noneofthesealternativesiscorrect.     78.Thesetofallelementsofinterestinastudyis a.setnotation b.asetofinterest c.asample d.apopulation       79.Thenumberofdifferentsimplerandomsamplesofsize5thatcanbeselectedfromapopulationofsize8is a.40b.336 c.13 d.56   80.Thefollowingdatawascollectedfromasimplerandomsampleofapopulation.1315141612 Thepointestimateofthepopulationmean a.cannotbedetermined,sincethepopulationsizeisunknown b.is14 c.is4 d.is5         .
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MultipleChoice 1.Theabsolutevalueofthedifferencebetweenthepointestimateandthepopulationparameteritestimatesis a.thestandarderror b.thesamplingerror c.precision d.theerrorofconfidence       2.Whensisusedtoestimateσ,themarginoferroriscomputedbyusing a.normaldistribution b.tdistribution c.themeanofthesample d.themeanofthepopulation     3.Fromapopulationwithavarianceof900,asampleof225itemsisselected.At95%confidence,themarginoferroris a.15 b.2 c.3.92 d.4     4.Apopulationhasastandarddeviationof50.Arandomsampleof100itemsfromthispopulationisselected.Thesamplemeanisdeterminedtobe600.At95%confidence,themarginoferroris a.5b.9.8c.650 d.609.8     5.Inordertodetermineanintervalforthemeanofapopulationwithunknownstandarddeviationasampleof61itemsisselected.Themeanofthesampleisdeterminedtobe23.Thenumberofdegreesoffreedomforreadingthetvalueis a.22 b.23 c.60 d.61       6.Ifwewanttoprovidea95%confidenceintervalforthemeanofapopulation,theconfidencecoefficientisa.0.485 b.1.96 c.0.95 d.1.645     7.Asthenumberofdegreesoffreedomforatdistributionincreases,thedifferencebetweenthetdistributionandthestandardnormaldistribution a.becomeslarger b.becomessmaller c.staysthesame d.Noneofthesealternativesiscorrect.     8.Fortheintervalestimationofμwhenσisknownandthesampleislarge,theproperdistributiontouseis a.thenormaldistribution b.thetdistributionwithndegreesoffreedom c.thetdistributionwithn+1degreesoffreedom d.thetdistributionwithn+2degreesoffreedom     9.Anestimateofapopulationparameterthatprovidesanintervalofvaluesbelievedtocontainthevalueoftheparameterisknownasthe a.confidencelevel b.intervalestimate c.parametervalue d.populationestimate     10.Thevalueaddedandsubtractedfromapointestimateinordertodevelopanintervalestimateofthepopulationparameterisknownasthe a.confidencelevel b.marginoferror c.parameterestimate d.intervalestimate           .
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    132.ConfirmedcasesofWestNilevirusinbirdsforasampleofsixcountiesinthestateofGeorgiaareshownbelow.   County Cases Catoosa 6 Chattooga 3 Dade 3 Gordon 5 Murray 3 Walker 4   Weareinterestedintestingthefollowinghypothesesregardingthesedata:Ho:μ≤3 Ha:μ> 3     a.Computethemeanandthestandarddeviationofthesample. b.Computethestandarderrorofthemean. c.Determinetheteststatistic. d.Determinethep-valueandat95%confidence,testthehypotheses.     133.Asampleof64accountbalancesfromacreditcompanyshowedanaveragedailybalanceof$1,040.Thestandarddeviationofthepopulationisknowntobe$200.Weareinterestedindeterminingifthemeanofallaccountbalances(i.e.,populationmean)issignificantlydifferentfrom$1,000.   a.Developtheappropriatehypothesesforthisproblem. b.Computetheteststatistic. c.Computethep-value. d.Usingthep-valueapproachat95%confidence,testtheabovehypotheses. e.Usingthecriticalvalueapproachat95%confidence,testthehypotheses.   134.Considerthefollowinghypothesestest.   Ho:μ≥80Ha:μ<80   Asampleof121providedasamplemeanof77.3.Thepopulationstandarddeviationisknowntobe16.5.   a.Computethevalueoftheteststatistic. b.Determinethep-value;andat93.7%confidence,testtheabovehypotheses. c.Usingthecriticalvalueapproachat93.7%confidence,testthehypotheses.     135.AutomobilesmanufacturedbytheEfficiencyCompanyhavebeenaveraging42milespergallonofgasolineinhighwaydriving.Itisbelievedthatitsnewautomobilesaveragemorethan42milespergallon.Anindependenttestingserviceroad-tested36oftheautomobiles.Thesampleshowedanaverageof42.8milespergallonwithastandarddeviationof1.2milespergallon.   a.Witha0.05levelofsignificanceusingthecriticalvalueapproach,testtodeterminewhetherornotthenewautomobilesactuallydoaveragemorethan42milespergallon. b.Whatisthep-valueassociatedwiththesampleresults?Whatisyourconclusionbasedonthe p-value?   136.TheaveragestartingsalaryofstudentswhograduatedfromcollegesofBusinessin2009was$48,400.Asampleof100graduatesof2010showedanaveragestartingsalaryof$50,000.Assumethestandarddeviationofthepopulationisknowntobe$8,000.Wewanttodeterminewhetherornottherehasbeenasignificantincreaseinthestartingsalaries.   a.Statethenullandalternativehypothesestobetested. b.Computetheteststatistic. c.Thenullhypothesisistobetestedat95%confidence.Determinethecriticalvalueforthistest. d.Whatdoyouconclude? e.Computethep-value.   137.TheaveragepriceofhomessoldintheU.S.inthepastyearwas$220,000.Arandomsampleof81homessoldthisyearshowedanaveragepriceof$210,000.Itisknownthatthestandarddeviationofthepopulationis$36,000.At95%confidencetesttodetermineiftherehasbeenasignificantdecreaseintheaveragepricehomes.   a.Statethenullandalternativehypothesestobetested. b.Computetheteststatistic. c.Determinethecriticalvalueforthistest. d.Whatdoyouconclude? e.Computethep-value.         .
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  110.Studentsofalargeuniversityspendanaverageof$5adayonlunch.Thestandarddeviationoftheexpenditureis $3.Asimplerandomsampleof36studentsistaken.     a.Whataretheexpectedvalue,standarddeviation,andshapeofthesamplingdistributionofthesamplemean? b.Whatistheprobabilitythatthesamplemeanwillbeatleast$4? c.Whatistheprobabilitythatthesamplemeanwillbeatleast$5.90?   111.Theaveragelifetimeofalightbulbis3,000hourswithastandarddeviationof696hours.Asimplerandomsampleof36bulbsistaken.   a.Whataretheexpectedvalue,standarddeviation,andshapeofthesamplingdistributionof? b.Whatistheprobabilitythattheaveragelifeinthesamplewillbebetween2,670.56and2,809.76hours? c.Whatistheprobabilitythattheaveragelifeinthesamplewillbegreaterthan3,219.24hours? d.Whatistheprobabilitythattheaveragelifeinthesamplewillbelessthan3,180.96hours? 112.Michaelisrunningforpresident.TheproportionofvoterswhofavorMichaelis0.8.Asimplerandomsampleof100votersistaken.   a.Whataretheexpectedvalue,standarddeviation,andshapeofthesamplingdistributionof? b.WhatistheprobabilitythatthenumberofvotersinthesamplewhowillnotfavorMichaelwillbebetween26and30? c.WhatistheprobabilitythatthenumberofvotersinthesamplewhowillnotfavorMichaelwillbemorethan16?       113.Inarestaurant,theproportionofpeoplewhoordercoffeewiththeirdinneris.9.Asimplerandomsampleof144patronsoftherestaurantistaken.   a.Whataretheexpectedvalue,standarddeviation,andshapeofthesamplingdistributionof? b.Whatistheprobabilitythattheproportionofpeoplewhowillordercoffeewiththeirmealisbetween0.85and0.875? c.Whatistheprobabilitythattheproportionofpeoplewhowillordercoffeewiththeirmealisatleast0.945?   114.Arandomsampleofninetelephonecallsinanofficeprovidedthefollowinginformation.     Duration CallNumber(InMinutes)TypeofCall 13local 28longdistance 34local 43local 55longdistance 66local 73local 85local 98local       a.Determinethepointestimatefortheaveragedurationofallcalls. b.Whatisthepointestimateforthestandarddeviationofthepopulation? c.Determinethestandarderrorofthemean. d.Whatisthepointestimatefortheproportionofallcallsthatwerelongdistance? e.Determinethestandarderrorofproportion.       .
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  88.Inasampleof200individuals,120indicatedtheyareDemocrats.Developa95%confidenceintervalfortheproportionofpeopleinthepopulationwhoareDemocrats.   89.Arandomsampleof121checkingaccountsatabankshowedanaveragedailybalanceof$300andastandarddeviationof$44.Developa95%confidenceintervalestimateforthemeanofthepopulation.   90.Asampleof60studentsfromalargeuniversityistaken.Theaverageageinthesamplewas22yearswithastandarddeviationof6years.Constructa95%confidenceintervalfortheaverageageofthepopulation.       91.Arandomsampleof121checkingaccountsatabankshowedanaveragedailybalanceof$280.Thestandarddeviationofthepopulationisknowntobe$66.     a.Isitnecessarytoknowanythingabouttheshapeofthedistributionoftheaccountbalancesinordertomakeanintervalestimateofthemeanofalltheaccountbalances?Explain. b.Findthestandarderrorofthemean. c.Giveapointestimateofthepopulationmean. d.Constructa80%confidenceintervalestimatesforthemean. e.Constructa95%confidenceintervalforthemean. 92.Arandomsampleof49lunchcustomerswastakenatarestaurant.Theaverageamountoftimethecustomersinthesamplestayedintherestaurantwas45minuteswithastandarddeviationof14minutes.   a.Computethestandarderrorofthemean. b.Witha.95probability,whatstatementcanbemadeaboutthesizeofthemarginoferror? c.Constructa95%confidenceintervalforthetrueaverageamountoftimecustomersspentintherestaurant. d.Witha.95probability,howlargeofasamplewouldhavetobetakentoprovideamarginoferrorof2.5minutesorless?   93.Arandomsampleof81studentsatalocaluniversityshowedthattheyworkanaverageof60hourspermonthwithastandarddeviationof18hours.Computea95%confidenceintervalforthemeanofthepopulation.       94.Themonthlyincomesfromarandomsampleofworkersinafactoryareshownbelow.       MonthlyIncome(In$1,000) 4.0 5.0 7.0 4.0 6.0 6.0 7.0 9.0       a.Computethestandarderrorofthemean(indollars). b.Computethemarginoferror(indollars)at95%confidence. c.Computea95%confidenceintervalforthemeanofthepopulation.Assumethepopulationhasanormaldistribution.Giveyouranswerindollars.     95.Itisknownthatthevarianceofapopulationequals1296.Arandomsampleof144observationsisgoingtobetakenfromthepopulation.   a.Witha0.95probability,whatstatementcanbemadeaboutthesizeofthemarginoferror? b.Witha0.95probability,howlargeofasamplewouldhavetobetakentoprovideamarginoferrorof6orless?       .
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    51.Asthenumberofdegreesoffreedomforatdistributionincreases,thedifferencebetweenthetdistributionandthestandardnormaldistribution a.becomeslarger b.becomessmaller c.staysthesame d.becomesnegative     52.Inordertoestimatetheaveragetimespentonthecomputerterminalsperstudent,datawerecollectedforasampleof49businessstudentsoveraoneweekperiod.Assumethepopulationstandarddeviationis1.4hours.Thestandarderrorofthemeanis a.0.20 b.0.30 c.5 d.7     Exhibit8-1 Inordertoestimatetheaveragetimespentonthecomputerterminalsperstudentatalocaluniversity,datawerecollectedforasampleof81businessstudentsoveraone-weekperiod.Assumethepopulationstandarddeviationis 1.8hours. 53.RefertoExhibit8-1.Thestandarderrorofthemeanisa.7.50 b.0.39 c.2.00 d.0.20       54.RefertoExhibit8-1.Witha0.95probability,themarginoferrorisapproximatelya.0.39 b.1.96 c.0.20 d.1.64       55.RefertoExhibit8-1.Ifthesamplemeanis9hours,thenthe95%confidenceintervalisa.7.04to110.96hours b.7.36to10.64hours c.7.80to10.20hours d.8.61to9.39hours       Exhibit8-2 Arandomsampleof121automobilestravelingonaninterstateshowedanaveragespeedof65mph.Frompastinformation,itisknownthatthestandarddeviationofthepopulationis22mph. 56.RefertoExhibit8-2.Ifweareinterestedindetermininganintervalestimateforμat96.6%confidence,theZvaluetouseis a.1.96 b.0.483 c.2.12 d.1.645       57.RefertoExhibit8-2.Thestandarderrorofthemeanisa.22.00 b.96.60 c.4.24 d.2.00     58.RefertoExhibit8-2.Iftheconfidencecoefficientisreducedto0.9,thestandarderrorofthemean a.willincrease b.willdecrease c.remainsunchanged d.becomesnegative     59.RefertoExhibit8-2.The96.6%confidenceintervalforμisa.63.00to67.00 b.60.76to69.24 c.61.08to68.92 d.60.00to80.00       60.RefertoExhibit8-2.Ifthesamplesizewas100(otherfactorsremainunchanged),theintervalforμwould a.notchange b.becomenarrower c.becomewider d.becomezero       Exhibit8-3 Themanagerofagrocerystorehastakenarandomsampleof100customers.Theaveragelengthoftimeittookthese100customerstocheckoutwas3.0minutes.Itisknownthatthestandarddeviationofthepopulationofcheckouttimesisoneminute.   .
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  107.Asoftdrinkfillingmachine,wheninperfectadjustment,fillsthebottleswith12ouncesofsoftdrink.Arandomsampleof49bottlesisselected,andthecontentsaremeasured.Thesampleyieldedameancontentof11.88ounceswithastandarddeviationof0.35ounces.   a.Formulatethehypothesestotesttodetermineifthemachineisinperfectadjustment. b.Computethevalueoftheteststatistic. c.Computethep-valueandgiveyourconclusionregardingtheadjustmentofthemachine.Letα= .05.   108."D"sizebatteriesproducedbyMNMCorporationhavehadalifeexpectancyof87hours.Becauseofanimprovedproductionprocess,itisbelievedthattherehasbeenanincreaseinthelifeexpectancyofits"D"sizebatteries.Asampleof36batteriesshowedanaveragelifeof88.5hours.Assumefrompastinformationthatitisknownthatthestandarddeviationofthepopulationis9hours.   a.Formulatethehypothesesforthisproblem. b.Computetheteststatistic. c.Whatisthep-valueassociatedwiththesampleresults?Whatisyourconclusionbasedonthep-value?Letα=.05.   109.Atalocaluniversity,asampleof49eveningstudentswasselectedinordertodeterminewhethertheaverageageoftheeveningstudentsissignificantlydifferentfrom21.Theaverageageofthestudentsinthesamplewas23withastandarddeviationof3.5.   a.Formulatethehypothesesforthisproblem. b.Computetheteststatistic. c.Determinethep-valueandtestthesehypotheses.Letα=.05. 110.InordertodeterminetheaveragepriceofhotelroomsinAtlanta,asampleof64hotelswasselected.Itwasdeterminedthattheaveragepriceoftheroomsinthesamplewas$108.50withastandarddeviationof$16.     a.Formulatethehypothesestodeterminewhetherornottheaverageroompriceissignificantlydifferentfrom$112. b.Computetheteststatistic. c.At95%confidenceusingthep-valueapproach,testthehypotheses.Letα=0.1.     111.Identifythenullandalternativehypothesesforthefollowingproblems.     a.Themanagerofarestaurantbelievesthatittakesacustomerlessthanorequalto25minutestoeatlunch. b.Economistshavestatedthatthemarginalpropensitytoconsumeisatleast90¢outofevery dollar. c.Ithasbeenstatedthat75outofevery100peoplewhogotothemoviesonSaturdaynightbuypopcorn.         .
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    61.Theacademicplannerofauniversitythinksthatatleast35%oftheentirestudentbodyattendssummerschool. b.H0:P≤0.35  Ha:P>0.35c.H0:P≥0.35  Ha:P<0.35d.H0:P>0.35Ha:P ≤ 0.35   62.Themanagerofanautomobiledealershipisconsideringanewbonusplaninordertoincreasesales.Currently,themeansalesratepersalespersonisfiveautomobilespermonth.Thecorrectsetofhypothesesfortestingtheeffectofthebonusplanis a.H0:μ<5    Ha:μ≤5 b.H0:μ≤ 5    Ha:μ >5 c.H0:μ>5    Ha:μ≤ 5 d.H0:μ≥5    Ha:μ <5     63.Yourinvestmentexecutiveclaimsthattheaverageyearlyrateofreturnonthestockssherecommendsisatleast10.0%.Youplanontakingasampletotestherclaim.Thecorrectsetofhypothesesis a.H0:μ<10.0%  Ha:μ≥10.0%b.H0:μ≤10.0%  Ha:μ>10.0%c.H0:μ>10.0%  Ha:μ≤10.0%d.H0:μ≥10.0%    Ha:μ<10.0%     64.AweathermanstatedthattheaveragetemperatureduringJulyinChattanoogais80degreesorless.Asampleof32Julysistaken.Thecorrectsetofhypothesesis a.H0:μ≥80  Ha:μ < 80b.H0:μ≤80  Ha:μ> 80c.H0:μ≠80  Ha:μ = 80d.H0:μ<80    Ha:μ > 80   65.Theschool'snewspaperreportedthattheproportionofstudentsmajoringinbusinessisatleast30%.Youplanontakingasampletotestthenewspaper'sclaim.Thecorrectsetofhypothesesis a.H0:P<0.30Ha: P ≥ 0.30b.H0:P≤0.30  Ha:P>0.30c.H0:P≥0.30  Ha:P<0.30d.H0:P>0.30Ha:P ≤ 0.30   Exhibit9-1     n=36=24.6S=12H0:μ≤20 Ha:μ>20 66.RefertoExhibit9-1.Theteststatisticisa.2.3 b.0.38 c.-2.3 d.-0.38       67.RefertoExhibit9-1.Thep-valueisbetweena.0.005to0.01 b.0.01to0.025 c.0.025to0.05 d.0.05to0.10     68.RefertoExhibit9-1.Ifthetestisdoneat95%confidence,thenullhypothesisshould a.notberejected b.berejected c.Notenoughinformationisgiventoanswerthisquestion. d.Noneofthesealternativesiscorrect.       Exhibit9-2     n=64=50s=16H0:μ≥ 54 Ha:μ<54 69.RefertoExhibit9-2.Theteststatisticequals a.-4 b.-3 c.-2 d.-1       70.RefertoExhibit9-2.Thep-valueisbetweena..005to.01 b..01to.025 c..025to.05 d..05to.01       .
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    41.Whenconstructingaconfidenceintervalforthepopulationmeanandthestandarddeviationofthesampleisused,thedegreesoffreedomforthetdistributionequals a.n-1 b.n c.29 d.30   42.Thefollowingrandomsamplefromapopulationwhosevalueswerenormallydistributedwascollected.1081111 The95%confidenceintervalforμisa.8.52to10.98 b.7.75to12.25 c.9.75to10.75 d.8.00to10.00     43.Thefollowingrandomsamplefromapopulationwhosevalueswerenormallydistributedwascollected.10121816 The80%confidenceintervalforμisa.12.054to15.946 b.10.108to17.892 c.10.321to17.679 d.11.009to16.991     44.Whichofthefollowingbestdescribestheformofthesamplingdistributionofthesampleproportion? a.Whenstandardized,itisexactlythestandardnormaldistribution. b.Whenstandardized,itisthetdistribution. c.Itisapproximatelynormalaslongasn≥30. d.Itisapproximatelynormalaslongasnp≥5andn(1­p)≥5.     45.In arandomsampleof144observations,=0.6.The95%confidenceintervalforPisa.0.52to0.68 b.0.144to0.200 c.0.60to0.70 d.0.50to0.70     46.In arandomsampleof100observations,=0.2.The95.44%confidenceintervalforPisa.0.122to0.278 b.0.164to0.236 c.0.134to0.266 d.0.120to0.280     47.Arandomsampleof1000peoplewastaken.FourhundredfiftyofthepeopleinthesamplefavoredCandidateA. The95%confidenceintervalforthetrueproportionofpeoplewhofavorsCandidateAisa.0.419to0.481 b.0.40to0.50 c.0.45to0.55 d.1.645to1.96     48.Amachinethatproducesamajorpartforanairplaneengineismonitoredclosely.Inthepast,10%ofthepartsproducedwouldbedefective.Witha.95probability,thesamplesizethatneedstobetakenifthedesiredmarginoferroris.04orlessis a.110 b.111 c.216 d.217     49.Weareinterestedinconductingastudyinordertodeterminewhatpercentageofvotersofastatewouldvotefortheincumbentgovernor.Whatistheminimumsizesampleneededtoestimatethepopulationproportionwithamarginoferrorof0.05orlessat95%confidence? a.200 b.100 c.58d.385     50.Inasampleof400voters,360indicatedtheyfavortheincumbentgovernor.The95%confidenceintervalofvoters notfavoringtheincumbentisa.0.871to0.929 b.0.120to0.280 c.0.765to0.835 d.0.071to0.129         .
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    11.Ifanintervalestimateissaidtobeconstructedatthe90%confidencelevel,theconfidencecoefficientwouldbea.0.1 b.0.95 c.0.9 d.0.05     12.Wheneverthepopulationstandarddeviationisunknownandthepopulationhasanormalornear-normaldistribution,whichdistributionisusedindevelopinganintervalestimation? a.standarddistribution b.zdistribution c.alphadistribution d.tdistribution     13.Inintervalestimation,thetdistributionisapplicableonlywhen a.thepopulationhasameanoflessthan30 b.thesamplestandarddeviationisusedtoestimatethepopulationstandarddeviation c.thevarianceofthepopulationisknown d.thestandarddeviationofthepopulationisknown     14.Indevelopinganintervalestimate,ifthepopulationstandarddeviationisunknown a.itisimpossibletodevelopanintervalestimate b.thestandarddeviationisarrivedatusingtherange c.thesamplestandarddeviationcanbeused d.itisassumedthatthepopulationstandarddeviationis1     15.Inordertousethenormaldistributionforintervalestimationofμwhenσisknownandthesampleisverysmall,thepopulation a.mustbeverylarge b.musthaveanormaldistribution c.canhaveanydistribution d.musthaveameanofatleast1         16.Fromapopulationthatisnotnormallydistributedandwhosestandarddeviationisnotknown,asampleof6itemsisselectedtodevelopanintervalestimateforthemeanofthepopulation(μ). a.Thenormaldistributioncanbeused. b.Thetdistributionwith5degreesoffreedommustbeused. c.Thetdistributionwith6degreesoffreedommustbeused. d.Thesamplesizemustbeincreased.     17.Asampleof200elementsfromapopulationwithaknownstandarddeviationisselected.Foranintervalestimationofμ,theproperdistributiontouseisthe a.normaldistribution b.tdistributionwith200degreesoffreedom c.tdistributionwith201degreesoffreedom d.tdistributionwith202degreesoffreedom     18.Fromapopulationthatisnormallydistributed,asampleof25elementsisselectedandthestandarddeviationofthesampleiscomputed.Fortheintervalestimationofμ,theproperdistributiontouseisthe a.normaldistribution b.tdistributionwith25degreesoffreedom c.tdistributionwith26degreesoffreedom d.tdistributionwith24degreesoffreedom     19.Thezvaluefora97.8%confidenceintervalestimationisa.2.02 b.1.96 c.2.00 d.2.29     20.Thetvaluefora95%confidenceintervalestimationwith24degreesoffreedomisa.1.711 b.2.064 c.2.492 d.2.069           .
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