Chapter 06 Confidence Interval For The Population

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Ch.6 ConfidenceIntervals

6.1 ConfidenceIntervalsfortheMean(LargeSamples)

1 FindaCriticalValue

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Findthecriticalvaluezcthatcorrespondstoa95%confidencelevel.

A) ±1.96 B) ±2.575 C) ±2.33 D) ±1.645

2 FindtheMarginofError

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

2) Determinethesamplingerrorifthegradepointaveragesfor10randomlyselectedstudentsfromaclassof125

studentshasameanofx=1.8.Assumethegradepointaverageofthe125studentshasameanof

μ=2.4.

A) 0.6 B) 2.1 C) –0.6 D) 1.5

3) Arandomsampleof120studentshasatestscoreaveragewithastandarddeviationof9.2.Findthemarginof

errorifc=0.98.

A) 1.96 B) 0.18 C) 0.84 D) 0.82

4) Arandomsampleof150studentshasagradepointaveragewithastandarddeviationof0.78.Findthemargin

oferrorifc=0.98.

A) 0.15 B) 0.08 C) 0.11 D) 0.12

5) Arandomsampleof40studentshasameanannualearningsof$3120andastandarddeviationof$677.Find

themarginoferrorifc=0.95.

A) $210 B) $77 C) $2891 D) $7

3 ConstructandInterpretConfidenceIntervalsforthePopulationMean

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

6) Arandomsampleof150studentshasagradepointaveragewithameanof2.86andwithastandarddeviation

of0.78.Constructtheconfidenceintervalforthepopulationmean,μ,ifc=0.98.

A) (2.71,3.01) B) (2.51,3.53) C) (2.43,3.79) D) (2.31,3.88)

7) Arandomsampleof40studentshasatestscorewithx=81.5ands=10.2.Constructtheconfidenceinterval

forthepopulationmean,μifc=0.90.

A) (78.8,84.2) B) (51.8,92.3) C) (66.3,89.1) D) (71.8,93.5)

8) Arandomsampleof40studentshasameanannualearningsof$3120andastandarddeviationof$677.

Constructtheconfidenceintervalforthepopulationmean,μifc=0.95.

A) ($2910,$3330) B) ($210,$110) C) ($4812,$5342) D) ($1987,$2346)

9) Arandomsampleof56fluorescentlightbulbshasameanlifeof645hourswithastandarddeviationof31

hours.Constructa95%confidenceintervalforthepopulationmean.

A) (636.9,653.1) B) (539.6,551.2) C) (112.0,118.9) D) (712.0,768.0)

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10) Agroupof49randomlyselectedstudentshasameanageof22.4yearswithastandarddeviationof3.8.

Constructa98%confidenceintervalforthepopulationmean.

A) (21.1,23.7) B) (20.3,24.5) C) (19.8,25.1) D) (18.8,26.3)

11) Agroupof40bowlersshowedthattheiraveragescorewas192withastandarddeviationof8.Findthe95%

confidenceintervalofthemeanscoreofallbowlers.

A) (189.5,194.5) B) (186.5,197.5) C) (188.5,195.6) D) (187.3,196.1)

12) Inarandomsampleof60computers,themeanrepaircostwas$150withastandarddeviationof$36.

Constructa90%confidenceintervalforthepopulationmean.

A) ($142,$158) B) ($138,$162) C) ($141,$159) D) ($537,$654)

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

13) Inarandomsampleof60computers,themeanrepaircostwas$150withastandarddeviationof$36.

a)Constructthe99%confidenceintervalforthepopulationmeanrepaircost.

b)Ifthelevelofconfidencewasloweredto95%,whatwillbetheeffectontheconfidenceinterval?

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

14) Inarecentstudyof42eighthgraders,themeannumberofhoursperweekthattheywatchedtelevisionwas

19.6withastandarddeviationof5.8hours.Findthe98%confidenceintervalforthepopulationmean.

A) (17.5,21.7) B) (14.1,23.2) C) (18.3,20.9) D) (19.1,20.4)

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

15) Inarecentstudyof54eighthgraders,themeannumberofhoursperweekthattheywatchedtelevisionwas

19.5withastandarddeviationof5.1hours.

a)Findthe98%confidenceintervalofthemean.

b)Ifthestandarddeviationisdoubledto10.2,whatwillbetheeffectontheconfidenceinterval?

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

16) Inasampleof10randomlyselectedwomen,itwasfoundthattheirmeanheightwas63.4inches.From

previousstudies,itisassumedthatthestandarddeviationσis2.4andthatthepopulationofheight

measurementsisnormallydistributed.Constructthe95%confidenceintervalforthepopulationmean.

A) (61.9,64.9) B) (58.1,67.3) C) (59.7,66.5) D) (60.8,65.4)

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

17) Inasampleof10randomlyselectedwomen,itwasfoundthattheirmeanheightwas63.4inches.From

previousstudies,itisassumedthatthestandarddeviation,σ,is2.4inchesandthatthepopulationofheight

measurementsisnormallydistributed.

a)Constructthe99%confidenceintervalforthepopulationmeanheightofwomen.

b)Ifthesamplesizewasdoubledto20women,whatwillbetheeffectontheconfidenceinterval?

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18) Thenumbersofadvertisementsseenorheardinoneweekfor30randomlyselectedpeopleintheUnitedStates

arelistedbelow.Constructa95%confidenceintervalforthetruemeannumberofadvertisements.

598 494 441 595 728 690 684 486 735 808

481 298 135 846 764 317 649 732 582 677

734 588 590 540 673 727 545 486 702 703

19) Thenumberofwinsinaseasonfor32randomlyselectedprofessionalfootballteamsarelistedbelow.

Constructa90%confidenceintervalforthetruemeannumberofwinsinaseason.

999810972

11106411988

12107512643

1299710775

4 DeterminetheMinimumSampleSize

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

20) ThestandardIQtesthasameanof101 andastandarddeviationof16.Wewanttobe98%certainthatweare

within4IQpointsofthetruemean.Determinetherequiredsamplesize.

A) 87 B) 10 C) 188 D) 1

21) Anurseatalocalhospitalisinterestedinestimatingthebirthweightofinfants.Howlargeasamplemustshe

selectifshedesirestobe99%confidentthatthetruemeaniswithin2ouncesofthesamplemean?The

standarddeviationofthebirthweightsisknowntobe7ounces.

A) 82 B) 81 C) 10 D) 9

22) Inordertosetrates,aninsurancecompanyistryingtoestimatethenumberofsickdaysthatfulltimeworkers

atanautorepairshoptakeperyear.Apreviousstudyindicatedthatthestandarddeviationwas2.8days.How

largeasamplemustbeselectedifthecompanywantstobe95%confidentthatthetruemeandiffersfromthe

samplemeanbynomorethan1day?

A) 31 B) 141 C) 512 D) 1024

23) Inordertoefficientlybidonacontract,acontractorwantstobe95%confidentthathiserrorislessthantwo

hoursinestimatingtheaveragetimeittakestoinstalltileflooring.Previouscontractsindicatethatthe

standarddeviationis4.5hours.Howlargeasamplemustbeselected?

A) 20 B) 4 C) 5 D) 19

24) Inordertofairlysetflatratesforautomechanics,ashopforemanneedstoestimatetheaveragetimeittakesto

replaceafuelpumpinacar.Howlargeasamplemustheselectifhewantstobe99%confidentthatthetrue

averagetimeiswithin15minutesofthesampleaverage?Assumethestandarddeviationofalltimesis30

minutes.

A) 27 B) 26 C) 6 D) 5

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SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

25) Inordertosetrates,aninsurancecompanyistryingtoestimatethenumberofsickdaysthatfulltimeworkers

atanautorepairshoptakeperyear.Apreviousstudyindicatedthatthestandarddeviationwas2.8days.a)

Howlargeasamplemustbeselectedifthecompanywantstobe90%confidentthatthetruemeandiffersfrom

thesamplemeanbynomorethan1day?b)Repeatpart(a)usinga95%confidenceinterval.Whichlevelof

confidencerequiresalargersamplesize?Explain.

5 DeterminetheFinitePopulationCorrectionFactor

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Provideanappropriateresponse.

26) Therewere800mathinstructorsatamathematicsconvention.Fortyinstructorswererandomlyselectedand

givenanIQtest.Thescoresproducedameanof130withastandarddeviationof10.Finda95%confidence

intervalforthemeanofthe800instructors.Usethefinitepopulationcorrectionfactor.

6 Concepts

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Provideanappropriateresponse.

27) Arandomsampleof200highschoolseniorsisgiventheSAT–Vtest.Themeanscoreforthissampleisx=493.

Whatcanyousayaboutthemeanscoreμofallhighschoolseniors?

28) Thegradepointaveragesfor10randomlyselectedstudentsinastatisticsclasswith125studentsarelisted

below.Whatcanyousayaboutthemeanscoreμofall125students?

2.13.12.03.93.53.72.81.92.52.2

29) Acertainconfidenceinintervalis9.75<μ<11.05.FindthesamplemeanxandtheerrorofestimateE.

30) Giventhesamesamplestatistics,whichlevelofconfidencewillproducethenarrowestconfidenceinterval:

75%,85%,90%,or95%?Explainyourreasoning.

31) Thegradepointaveragesfor10randomlyselectedstudentsinastatisticsclasswith125studentsarelisted

below.

2.03.21.82.90.94.03.32.93.60.8

Whatistheeffectonthewidthoftheconfidenceintervalifthesamplesizeisincreasedto20?Explainyour

reasoning.

6.2 ConfidenceIntervalsfortheMean(SmallSamples)

1 FindaCriticalValue

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Findthecriticalvalue,tcforc=0.99andn=10.

A) 3.250 B) 3.169 C) 2.262 D) 1.833

2) Findthecriticalvalue,tc

forc=0.95andn=16.

A) 2.131 B) 2.120 C) 2.602 D) 2.947

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3) Findthecriticalvalue,tc

forc=0.90andn=15.

A) 1.761 B) 1.753 C) 2.145 D) 2.624

2 ConstructandInterpretConfidenceIntervalsforthePopulationMean

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

4) FindthevalueofE,themarginoferror,forc=0.90

n=16ands=2.5.

A) 1.1 B) 0.27 C) 0.84 D) 0.21

5) FindthevalueofE,themarginoferror,forc=0.99

n=10ands=3.2.

A) 3.29 B) 2.85 C) 1.04 D) 3.21

6) FindthevalueofE,themarginoferror,forc=0.95

n=15ands=5.2.

A) 2.88 B) 2.96 C) 2.36 D) 0.74

7) Inarandomsampleof28families,theaverageweeklyfoodexpensewas$95.60withastandarddeviationof

$22.50.Determinewhetheranormaldistributionorat–distributionshouldbeusedorwhetherneitherofthese

canbeusedtoconstructaconfidenceinterval.Assumethedistributionofweeklyfoodexpensesisnormally

shaped.

A) Usethet–distribution.

B) Usenormaldistribution.

C) Cannotusenormaldistributionort–distribution.

8) Forasampleof20IQscoresthemeanscoreis105.8.Thestandarddeviation,σ

is15.Determinewhethera

normaldistributionorat–distributionshouldbeusedorwhetherneitherofthesecanbeusedtoconstructa

confidenceinterval.AssumethatIQscoresarenormallydistributed.

A) Usenormaldistribution.

B) Usethet–distribution.

C) Cannotusenormaldistributionort–distribution.

9) Arandomsampleof40collegestudentshasameanearningsof$3120withastandarddeviationof$677over

thesummermonths.Determinewhetheranormaldistributionorat–distributionshouldbeusedorwhether

neitherofthesecanbeusedtoconstructaconfidenceinterval.

A) Usenormaldistribution.

B) Usethet–distribution.

C) Cannotusenormaldistributionort–distribution.

10) Arandomsampleof15statisticstextbookshasameanpriceof$105withastandarddeviationof$30.25.

Determinewhetheranormaldistributionorat–distributionshouldbeusedorwhetherneitherofthesecanbe

usedtoconstructaconfidenceinterval.Assumethedistributionofstatisticstextbookpricesisnotnormally

distributed.

A) Cannotusenormaldistributionort–distribution.

B) Usenormaldistribution.

C) Usethet–distribution.

11) Constructa95%confidenceintervalforthepopulationmean,μ.Assumethepopulationhasanormal

distribution.Asampleof20collegestudentshadmeanannualearningsof$3120withastandarddeviationof

$677.

A) ($2803,$3437) B) ($1324,$1567) C) ($2135,$2567) D) ($2657,$2891)

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12) Constructa90%confidenceintervalforthepopulationmean,μ.Assumethepopulationhasanormal

distribution.Asampleof15randomlyselectedstudentshasagradepointaverageof2.86withastandard

deviationof0.78.

A) (2.51,3.21) B) (2.41,3.42) C) (2.37,3.56) D) (2.28,3.66)

13) Constructa95%confidenceintervalforthepopulationmean,μ.Assumethepopulationhasanormal

distribution.Asampleof25randomlyselectedstudentshasameantestscoreof81.5withastandarddeviation

of10.2.

A) (77.29,85.71) B) (56.12,78.34) C) (66.35,69.89) D) (87.12,98.32)

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

14) Constructa98%confidenceintervalforthepopulationmean,μ.Assumethepopulationhasanormal

distribution.Arandomsampleof20collegestudentshasmeanannualearningsof$3180withastandard

deviationof$673.

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

15) Constructa95%confidenceintervalforthepopulationmean,μ.Assumethepopulationhasanormal

distribution.Arandomsampleof16fluorescentlightbulbshasameanlifeof645hourswithastandard

deviationof31hours.

A) (628.5,661.5) B) (876.2,981.5) C) (531.2,612.9) D) (321.7,365.8)

16) Constructa99%confidenceintervalforthepopulationmean,μ.Assumethepopulationhasanormal

distribution.Agroupof19randomlyselectedstudentshasameanageof22.4yearswithastandarddeviation

of3.8years.

A) (19.9,24.9) B) (16.3,26.9) C) (17.2,23.6) D) (18.7,24.1)

17) Constructa98%confidenceintervalforthepopulationmean,μ.Assumethepopulationhasanormal

distribution.Astudyof14bowlersshowedthattheiraveragescorewas192withastandarddeviationof8.

A) (186.3,197.7) B) (222.3,256.1) C) (328.3,386.9) D) (115.4,158.8)

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

18) Constructa95%confidenceintervalforthepopulationmean,μ.Assumethepopulationhasanormal

distribution.Inarandomsampleof26computers,themeanrepaircostwas$149withastandarddeviationof

$39.

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

19) Constructa90%confidenceintervalforthepopulationmean,μ.Assumethepopulationhasanormal

distribution.Inarecentstudyof22eighthgraders,themeannumberofhoursperweekthattheywatched

televisionwas19.6withastandarddeviationof5.8hours.

A) (17.47,21.73) B) (18.63,20.89) C) (5.87,7.98) D) (19.62,23.12)

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

20) a)Constructa95%confidenceintervalforthepopulationmean,μ

.Assumethepopulationhasanormal

distribution.Inarandomsampleof26computers,themeanrepaircostwas$129withastandarddeviationof

$37.

b)Supposeyoudidsomeresearchonrepaircostsforcomputersandfoundthatthestandarddeviationis

σ=37.Usethenormaldistributiontoconstructa95%confidenceintervalforthepopulationmean,μ.Compare

theresults.

Page123

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

21) Arandomsampleof10parkingmetersinabeachcommunityshowedthefollowingincomesforaday.

Assumetheincomesarenormallydistributed.

$3.60$4.50$2.80$6.30$2.60$5.20$6.75$4.25$8.00$3.00

Findthe95%confidenceintervalforthetruemean.

A) ($3.39,$6.01) B) ($2.11,$5.34) C) ($4.81,$6.31) D) ($1.35,$2.85)

22) Thegradepointaveragesfor10randomlyselectedhighschoolstudentsarelistedbelow.Assumethegrade

pointaveragesarenormallydistributed.

2.03.21.82.90.94.03.32.93.60.8

Finda98%confidenceintervalforthetruemean.

A) (1.55,3.53) B) (0.67,1.81) C) (2.12,3.14) D) (3.11,4.35)

23) Alocalbankneedsinformationconcerningthecheckingaccountbalancesofitscustomers.Arandomsample

of15accountswaschecked.Themeanbalancewas$686.75withastandarddeviationof$256.20.Finda98%

confidenceintervalforthetruemean.Assumethattheaccountbalancesarenormallydistributed.

A) ($513.17,$860.33) B) ($238.23,$326.41) C) ($326.21,$437.90) D) ($487.31,$563.80)

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

24) Amanufacturerreceivesanorderforfluorescentlightbulbs.Theorderrequiresthatthebulbshaveameanlife

spanof500hours.Themanufacturerselectsarandomsampleof25fluorescentlightbulbsandfindsthatthey

haveameanlifespanof495hourswithastandarddeviationof15hours.Testtoseeifthemanufactureris

makingacceptablelightbulbs.Usea95%confidencelevel.Assumethedataarenormallydistributed.

25) Acoffeemachineissupposedtodispense12ouncesofcoffeeineachcup.Aninspectorselectsarandom

sampleof40cupsofcoffeeandfindstheyhaveanaverageamountof12.2ounceswithastandarddeviationof

0.3ounce.Usea99%confidenceintervaltotestwhetherthemachineisdispensingacceptableamountsof

coffee.

6.3 ConfidenceIntervalsforPopulationProportions

1 FindaPointEstimate

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) When435collegestudentsweresurveyed,120 saidtheyowntheircar.Findapointestimateforp,the

populationproportionofstudentswhoowntheircars.

A) 0.276 B) 0.724 C) 0.381 D) 0.216

2) Asurveyof100fatalaccidentsshowedthat12 werealcoholrelated.Findapointestimateforp,thepopulation

proportionofaccidentsthatwerealcoholrelated.

A) 0.12 B) 0.88 C) 0.136 D) 0.107

3) Asurveyof400non–fatalaccidentsshowedthat189 involvedtheuseofacellphone.Findapointestimatefor

p,thepopulationproportionofnon–fatalaccidentsthatinvolvedtheuseofacellphone.

A) 0.472 B) 0.527 C) 0.896 D) 0.321

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4) Asurveyof250homelesspersonsshowedthat17 wereveterans.Findapointestimatep,forthepopulation

proportionofhomelesspersonswhoareveterans.

A) 0.068 B) 0.932 C) 0.073 D) 0.064

5) Asurveyof2650golfersshowedthat379 ofthemareleft–handed.Findapointestimateforp,thepopulation

proportionofgolfersthatareleft–handed.

A) 0.143 B) 0.857 C) 0.167 D) 0.125

2 ConstructandInterpretConfidenceIntervalsforthePopulationProportion

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

6) Inasurveyof2480golfers,15%saidtheywereleft–handed.Thesurveyʹsmarginoferrorwas3%.Constructa

confidenceintervalfortheproportionofleft–handedgolfers.

A) (0.12,0.18) B) (0.18,0.21) C) (0.12,0.15) D) (0.11,0.19)

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

7) TheFederalBureauofLaborStatisticssurveyed50,000peopleandfoundtheunemploymentratetobe5.8%.

Themarginoferrorwas0.2%.Constructaconfidenceintervalfortheunemploymentrate.

8) When495collegestudentsweresurveyed,150 saidtheyowntheircar.Constructa95%confidenceintervalfor

theproportionofcollegestudentswhosaytheyowntheircars.

9) Asurveyof300fatalaccidentsshowedthat123werealcoholrelated.Constructa98%confidenceintervalfor

theproportionoffatalaccidentsthatwerealcoholrelated.

10) Asurveyof400non–fatalaccidentsshowedthat197 involvedtheuseofacellphone.Constructa99%

confidenceintervalfortheproportionoffatalaccidentsthatinvolvedtheuseofacellphone.

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

11) Asurveyof280homelesspersonsshowedthat63wereveterans.Constructa90%confidenceintervalforthe

proportionofhomelesspersonswhoareveterans.

A) (0.184,0.266) B) (0.176,0.274) C) (0.167,0.283) D) (0.161,0.289)

12) Asurveyof2450golfersshowedthat281ofthemareleft–handed.Constructa98%confidenceintervalforthe

proportionofgolfersthatareleft–handed.

A) (0.100,0.130) B) (0.203,0.293) C) (0.369,0.451) D) (0.683,0.712)

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

13) Inasurveyof10golfers,2werefoundtobeleft–handed.Isitpracticaltoconstructthe90%confidenceinterval

forthepopulationproportion,p?Explain.

14) TheUSATodayclaimsthat44%ofadultswhoaccesstheInternetreadtheinternationalnewsonline.You

wanttochecktheaccuracyoftheirclaimbysurveyingarandomsampleof120adultswhoaccesstheInternet

andaskingthemiftheyreadtheinternationalnewsonline.Fifty–twoadultsrespondedʺyes.ʺUsea95%

confidenceintervaltotestthenewspaperʹsclaim.

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3 DeterminetheMinimumSampleSize

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

15) AresearcheratamajorhospitalwishestoestimatetheproportionoftheadultpopulationoftheUnitedStates

thathashighbloodpressure.Howlargeasampleisneededinordertobe95%confidentthatthesample

proportionwillnotdifferfromthetrueproportionbymorethan4%?

A) 601 B) 13 C) 1201 D) 423

16) ApollsterwishestoestimatetheproportionofUnitedStatesvoterswhofavorcapitalpunishment.Howlargea

sampleisneededinordertobe95%confidentthatthesampleproportionwillnotdifferfromthetrue

proportionbymorethan5%?

A) 385 B) 271 C) 10 D) 769

17) Aprivateopinionpollisconductedforapoliticiantodeterminewhatproportionofthepopulationfavors

decriminalizingmarijuanapossession.Howlargeasampleisneededinordertobe95%confidentthatthe

sampleproportionwillnotdifferfromthetrueproportionbymorethan2%?

A) 2401 B) 1692 C) 4802 D) 25

18) Amanufacturerofgolfequipmentwishestoestimatethenumberofleft–handedgolfers.Howlargeasampleis

neededinordertobe98%confidentthatthesampleproportionwillnotdifferfromthetrueproportionby

morethan2%?Apreviousstudyindicatesthattheproportionofleft–handedgolfersis8%.

A) 999 B) 707 C) 1086 D) 17

19) Aresearcherwishestoestimatethenumberofhouseholdswithtwocars.Howlargeasampleisneededin

ordertobe98%confidentthatthesampleproportionwillnotdifferfromthetrueproportionbymorethan5%?

Apreviousstudyindicatesthattheproportionofhouseholdswithtwocarsis19%.

A) 335 B) 237 C) 413 D) 8

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

20) Astatehighwaypatrolofficialwishestoestimatethenumberofdriversthatexceedthespeedlimittravelinga

certainroad.

a)Howlargeasampleisneededinordertobe95%confidentthatthesampleproportionwillnotdifferfrom

thetrueproportionbymorethan2%?

b)Repeatpart(a)assumingpreviousstudiesfoundthat70%ofdriversonthisroadexceededthespeedlimit.

6.4 ConfidenceIntervalsforVarianceandStandardDeviatio

1 FindCriticalValues

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Findthecriticalvalues,X2

Rand X 2

L,forc=0.95andn=12.

A) 3.816and21.920 B) 3.053and24.725 C) 4.575and26.757 D) 2.603and19.675

2) Findthecriticalvalues,X2

Rand X 2

L,forc=0.90andn=15.

A) 6.571and23.685 B) 4.075and31.319 C) 4.660and29.131 D) 5.629and26.119

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3) Findthecriticalvalues,X2

Rand X 2

L,forc=0.98andn=20.

A) 7.633and36.191 B) 6.844and27.204 C) 8.907and38.582 D) 10.117and32.852

4) Findthecriticalvalues,X2

Rand X 2

L,forc=0.99andn=10.

A) 1.735and23.587 B) 2.156and25.188 C) 2.088and21.666 D) 2.558and23.209

2 ConstructConfidenceIntervalsforthePopulationVarianceandPopulationStandardDeviation

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Assumethesampleistakenfromanormallydistributedpopulationandconstructtheindicatedconfidenceinterval.

5) Constructa95%confidenceintervalforthepopulationstandarddeviationσ ofarandomsampleof15men

whohaveameanweightof165.2poundswithastandarddeviationof13.5pounds.Assumethepopulationis

normallydistributed.

A) (9.9

21.3) B) (97.7

453.3) C) (2.7

5.8) D) (10.4

19.7)

6) Arandomsampleof16menhaveameanheightof67.5inchesandastandarddeviationof1.5inches.

Constructa99%confidenceintervalforthepopulationstandarddeviation,σ.

A) (1.0

2.7) B) (1.0

2.8) C) (0.8

2.2) D) (1.1

2.5)

7) Arandomsampleof20womenhaveameanheightof62.5inchesandastandarddeviationof3.2 inches.

Constructa98%confidenceintervalforthepopulationvariance,σ2.

A) (5.4

25.5) B) (2.3

5.0) C) (1.7

8.0) D) (5.7

26.8)

8) Theheights(ininches)of20randomlyselectedadultmalesarelistedbelow.Constructa99%confidence

intervalforthevariance,σ2.

70727170697369687071

67717074696871717172

A) (1.47,8.27) B) (21.61,69.06) C) (1.35,8.43) D) (2.16,71.06)

9) Thegradepointaveragesfor10randomlyselectedstudentsarelistedbelow.Constructa90%confidence

intervalforthepopulationstandarddeviation,σ.

2.03.21.82.90.94.03.32.93.60.8

A) (0.81,1.83) B) (0.32,0.85) C) (0.53,1.01) D) (1.10,2.01)

10) Themeanreplacementtimeforarandomsampleof12microwaveovensis8.6yearswithastandarddeviation

of4.2years.Constructthe98%confidenceintervalforthepopulationvariance,σ

A) (7.8

63.6) B) (2.8

8.0) C) (1.9

15.1) D) (7.4

54.3)

11) Astudentrandomlyselects10CDsatastore.Themeanis$13.75withastandarddeviationof$1.50.Construct

a95%confidenceintervalforthepopulationstandarddeviation,σ.

A) ($1.03,$2.74) B) ($0.99,$2.50) C) ($1.06,$7.51) D) ($0.84,$2.24)

Page127

12) Thestem–and–leafplotshowsthetestscoresof16randomlyselectedstudents.Constructa99%confidence

intervalforthepopulationstandarddeviation.



9

9

583

74429

5835

317

A) (7.61,20.33) B) (57.97,413.27) C) (62.18,363.63) D) (7.89,19.07)

13) Thedotplotshowstheweights(inpounds)of15dogsselectedrandomlyfromthoseadoptedoutbyananimal

shelterlastweek.Constructa98%confidenceintervalforthepopulationvariance.

Weights

25 30 35

Pounds

A) (3.03,18.97) B) (1.74,4.36) C) (3.38,15.70) D) (2.89,16.91)

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

14) Acontainerofcaroilissupposedtocontain1000millilitersofoil.Aqualitycontrolmanagerwantstobesure

thatthestandarddeviationoftheoilcontainersislessthan20milliliters.Herandomlyselects10cansofoil

withameanof997millilitersandastandarddeviationof32milliliters.Usethesesampleresultstoconstructa

95%confidenceintervalforthetruevalueofσ.Doesthisconfidenceintervalsuggestthatthevariationintheoil

containersisatanacceptablelevel?

Page128

Ch.6 ConfidenceIntervals

AnswerKey

6.1 ConfidenceIntervalsfortheMean(LargeSamples)

1 FindaCriticalValue

2 FindtheMarginofError

3 ConstructandInterpretConfidenceIntervalsforthePopulationMean

4 DeterminetheMinimumSampleSize

5 DeterminetheFinitePopulationCorrectionFactor

6 Concepts

6.2 ConfidenceIntervalsfortheMean(SmallSamples)

1 FindaCriticalValue

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6.3 ConfidenceIntervalsforPopulationProportions

1 FindaPointEstimate

2 ConstructandInterpretConfidenceIntervalsforthePopulationProportion

3 DeterminetheMinimumSampleSize

Page130

6.4 ConfidenceIntervalsforVarianceandStandardDeviatio

1 FindCriticalValues

Page131