Economics Chapter 11 Test Hypotheses Regarding Two Proportions From Independent

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Ch.11 InferencesonTwoSamples

11.1 InferenceaboutTwoPopulationProportions

1 Distinguishbetweenindependentanddependentsampling.

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

Provideanappropriateresponse.

1) Classifythetwogivensamplesasindependentordependent.

Sample1:Pre–trainingbloodpressureof15people

Sample2:Post–trainingbloodpressureof15people

A) dependent B) independent

2) Classifythetwogivensamplesasindependentordependent.

Sample1:Theheightsininchesof27newbornfemales

Sample2:Theheightsininchesof27newbornmales

A) independent B) dependent

3) Classifythetwogivensamplesasindependentordependent.

Sample1:Thescoresof16studentswhotookastatisticsfinal

Sample2:Thescoresof16differentstudentswhotookaphysicsfinal

A) independent B) dependent

4) Iftheindividualsselectedforasamplehavenoinfluenceuponwhichindividualsareselectedforasecond

sample,thenthesamplesaresaidtobe

A) independent B) dependent C) inconsistent D) consistent

5) Twosamplesaresaidtobedependentif

A) theindividualsinonesampleareusedtodeterminetheindividualsinasecondsample.

B) theindividualsinonesamplehavenoinfluenceovertheselectionoftheindividualsinasecondsample.

C) someindividuals,butnotall,inonesampleexertinfluenceoverwhoisselectedforinclusioninasecond

ample.

D) samplingforinclusioninthetwosamplesisdonewithreplacement.

Determinewhetherthesamplingisdependentorindependent.Indicatewhethertheresponsevariableisqualitativeor

quantitative.

6) Apsychologistwantstomeasuretheeffectofmusiconmemory.Herandomlyselects80studentsand

measurestheirscoresonamemorytestconductedinsilence.Thenextdayhemeasurestheirscoresona

similartestconductedwhileclassicalmusicisplaying.Themeanscorewithoutmusiciscomparedtothe

meanscorewithmusic.

A) quantitative,dependent B) qualitative,dependent

C) quantitative,independent D) qualitative,independent

7) Acitycouncilrandomlyselects1000marriedcouplesfromacertaincityandrecordsthenumberofwomen

whoareinfavorofanewfootballstadiumandthenumberofmenwhoareinfavor.

A) qualitative,dependent B) quantitative,dependent

C) qualitative,independent D) quantitative,independent

8) Aresearcherrandomlyselected100adultsaged18–25and100adultsaged50–60.Withineachagegroup,she

recordedthenumberofsmokers.

A) qualitative,independent B) quantitative,independent

C) qualitative,dependent D) quantitative,dependent

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9) Onehundredmensufferingfromhighcholesterolwererandomlyassignedtoreceiveplaceboora

cholesterol–loweringmedication.Afterthreemonths,themeancholesterollevelofthosereceivingplacebowas

comparedwiththemeancholesterollevelofthosereceivingthemedication.

A) quantitative,independent B) quantitative,dependent

C) qualitative,dependent D) qualitative,independent

10) AgroupofwinetastersratedChardonnaywinesfromtwodifferentwineriesaspoor,acceptable,goodor

excellent.

A) qualitative,dependent B) quantitative,independent

C) quantitative,dependent D) qualitative,independent

11) Auniversitycomparedthemeansalaryofitssciencegraduatestenyearsaftergraduationwiththemean

salaryofitssocialsciencegraduatestenyearsaftergraduation.

A) quantitative,independent B) qualitative,dependent

C) quantitative,dependent D) qualitative,independent

2 Testhypothesesregardingtwoproportionsfromindependentsamples.

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

Provideanappropriateresponse.

1) Findthestandardizedteststatistic,ztotestthehypothesisthatp1=p2.Useα =0.05.Thesamplestatistics

listedbelowarefromindependentsamples.

Samplestatistics:n1=50,x1=35,andn2=60,x2=40

A) 0.374 B) 0.982 C) 1.328 D) 2.361

2) Findthestandardizedteststatisticestimate,z,totestthehypothesisthatp1>p2.Useα=0.01.Thesample

statisticslistedbelowarefromindependentsamples.

Samplestatistics:n1=100,x1=38,andn2=140,x2=50

A) 0.362 B) 2.116 C) 1.324 D) 0.638

3) Findthestandardizedteststatistic,z,totestthehypothesisthatp1<p2.Useα =0.10.Thesamplestatistics

listedbelowarefromindependentsamples.

Samplestatistics:n1=550,x1=121,andn2=690,x2=195

A) –2.513 B) –2.132 C) –0.985 D) 1.116

4) Findthestandardizedteststatistic,z,totestthehypothesisthatp1≠p2.Useα =0.02.Thesamplestatistics

listedbelowarefromindependentsamples.

Samplestatistics:n1=1000,x1=250,andn2=1200,x2=195

A) 5.087 B) 2.798 C) 4.761 D) 3.212

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

5) Testthehypothesisthatp1=p2.Useα =0.05.Thesamplestatisticslistedbelowarefromindependent

samples.

Samplestatistics:n1=50,x1=35,andn2=60,x2=40

6) Testthehypothesisthatp1>p2.Useα =0.01.Thesamplestatisticslistedbelowarefromindependent

samples.

Samplestatistics:n1=100,x1=38,andn2=140,x2=50

Page287

7) Testthehypothesisthatp1<p2.Useα =0.10.Thesamplestatisticslistedbelowarefromindependent

samples.

Samplestatistics:n1=550,x1=121,andn2=690,x2=195

8) Testthehypothesisthatp1≠p2.Useα =0.02.Thesamplestatisticslistedbelowarefromindependentsamples.

Samplestatistics:n1=1000,x1=250,andn2=1200,x2=195.

9) Inarecentsurveyofdrinkinglaws,arandomsampleof1000womenshowedthat65%wereinfavorof

increasingthelegaldrinkingage.Inarandomsampleof1000men,60%favoredincreasingthelegaldrinking

age.Testthehypothesisthatthepercentageofmenandwomenfavoringahigherlegaldrinkingageisthe

same.Useα=0.05.

10) Arecentsurveyshowedthatinasampleof100elementaryschoolteachers,15weresingle.Inasampleof180

highschoolteachers,36weresingle.Istheproportionofhighschoolteacherswhoweresinglegreaterthanthe

proportionofelementaryteacherswhoweresingle?Useα=0.01.

11) Totesttheeffectivenessofanewdrugdesignedtorelieveflusymptoms,200patientswererandomlyselected

anddividedintotwoequalgroups.Onegroupof100patientswasgivenapillcontainingthedrugwhilethe

othergroupof100wasgivenaplacebo.Whatcanweconcludeabouttheeffectivenessofthedrugif62ofthose

actuallytakingthedrugfeltabeneficialeffectwhile41ofthepatientstakingtheplacebofeltabeneficialeffect?

Useα=0.05.

12) Arandomsampleof100studentsatahighschoolwasaskedwhethertheywouldasktheirfatherormotherfor

helpwithafinancialproblem.Asecondsampleof100differentstudentswasaskedthesamequestion

regardingadatingproblem.If43studentsinthefirstsampleand47studentsinthesecondsamplerepliedthat

theyturnedtotheirmotherratherthantheirfatherforhelp,testthehypothesisofnodifferenceinthe

proportions.Useα=0.02.

13) IntheinitialtestoftheSalkvaccineforpolio,400,000childrenwereselectedanddividedintotwogroupsof

200,000.OnegroupwasvaccinatedwiththeSalkvaccinewhilethesecondgroupwasvaccinatedwitha

placebo.OfthosevaccinatedwiththeSalkvaccine,33laterdevelopedpolio.Ofthosereceivingtheplacebo,115

laterdevelopedpolio.TestthehypothesisthattheSalkvaccineiseffectiveinloweringthepoliorate.Use

α=0.01.

14) Awell–knownstudyof22,000malephysicianswasconductedtodetermineiftakingaspirindailyreducesthe

chancesofaheartattack.Halfofthephysiciansweregivenaregulardoseofaspirinwhiletheotherhalfwas

givenplacebos.Sixyearslater,amongthosewhotookaspirin,104sufferedheartattackswhileamongthose

whotookplacebos,189sufferedheartattacks.Doesitappearthattheaspirincanreducethenumberofheart

attacksamongthesamplegroupthattookaspirin?Useα

=0.01.

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

15) Toperformahypothesistestoftwopopulationproportions,thepooledestimateofpmustbedetermined.The

pooledestimate,p

^,is

A) p

^=x1+x2

n1+n2B) p

^= x1

n1+x2

n2C) p

^=n2x1+n1x2

n1+n2D) p

^=x1+x2

n1n2

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3 Constructandinterpretconfidenceintervalsforthedifferencebetweentwopopulationproportions.

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

Provideanappropriateresponse.

1) Constructa95%confidenceintervalforp1–p2.Thesamplestatisticslistedbelowarefromindependent

samples.

Samplestatistics:n1=50,x1=35,andn2=60,x2=40

A) (–0.141,0.208) B) (–0.871,0.872) C) (–1.341,1.781) D) (–2.391,3.112)

2) Constructa98%confidenceintervalforp1–p2.Thesamplestatisticslistedbelowarefromindependent

samples.

Samplestatistics:n1=1000,x1=250,andn2=1200,x2=195

A) (0.047,0.128) B) (–0.621,0.781) C) (0.581,1.819) D) (1.516,3.021)

3) Inarecentsurveyofdrinkinglaws,arandomsampleof1000womenshowedthat65%wereinfavorof

increasingthelegaldrinkingage.Inarandomsampleof1000men,60%favoredincreasingthelegaldrinking

age.Constructa95%confidenceintervalforp1–p2.

A) (0.008,0.092) B) (0.587,0.912) C) (–1.423,1.432) D) (–2.153,1.679)

4) Constructa95%confidenceintervalforp1–p2forasurveythatfinds30%of240malesand41%of200

femalesareopposedtothedeathpenalty.

A) (–0.200,–0.021) B) (–1.532,1.342) C) (–0.561,0.651) D) (–1.324,1.512)

5) Arandomsampleof100studentsatahighschoolwasaskedwhethertheywouldasktheirfatherormotherfor

helpwithafinancialproblem.Asecondsampleof100differentstudentswasaskedthesamequestion

regardingadatingproblem.Forty–threestudentsinthefirstsampleand47studentsinthesecondsample

repliedthattheyturnedtotheirmotherratherthantheirfatherforhelp.Constructa98%confidenceinterval

forp1–p2.

A) (–0.204,0.124) B) (–1.324,1.521) C) (–0.591,0.762) D) (–1.113,1.311)

6) TrueorFalse:Whenconstructingaconfidenceintervalforthedifferenceoftwopopulationproportions,a

pooledestimateofpisnotrequired.

A) True B) False

7) Toconstructaconfidenceintervalforthedifferenceoftwopopulationproportionsthesamplesmustbe

independentlyobtainedrandomsamples,bothmustconsistoflessthan5%ofthepopulation,and

A) bothnp

1(1–p

1)≥10andnp

2(1–p

2)≥10mustbetrue.

B) onlyoneofnp

1(1–p

1)≥10ornp

2(1–p

2)≥10mustbetrue.

C) np

1(1–p

1)+np

2(1–p

2)≥20.

D) np

1(1–p

1)np

2(1–p

2)≥100.

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4 Testhypothesesregardingtwoproportionsfromdependentsamples.

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

Performtheindicatedhypothesistest.

1) Testwhetherthepopulationproportionsdifferattheα=0.05levelofsignificancebydeterminingthenulland

alternativehypotheses,theteststatistic,andthecriticalvalue.Assumethatthesamplesaredependentandthat

theywereobtainedrandomly.

TreatmentA

TreatmentB

Success Failure

Success 87 32

Failure 12 59

2) Testwhetherthepopulationproportionsdifferattheα=0.05levelofsignificancebydeterminingthenulland

alternativehypotheses,theteststatistic,andtheP–value.Assumethatthesamplesaredependentandthat

theywereobtainedrandomly.

TreatmentA

TreatmentB

Success Failure

Success 368 120

Failure 130 437

3) Aresearcherwantstodeterminewhetherthereisadifferencebetweentwosunscreenlotions.Participantsina

marathonraceonahot,sunnydayappliedlotionAtoonearmandlotionBtotheotherarm.Theresultsare

showninthetable.

LotionA

LotionB

Noburn(Success) Burn(Failure)

Noburn(Success) 720 41

Burn(Failure) 51 74

Isthereadifferenceintheeffectivenessofthetwolotionsinpreventingsunburn?Usethecritical –value

methodandtheα=0.05levelofsignificance.

4) Inasurvey,studentswereselectedatrandomfromacertaincollegeandwereaskedtwoquestions.Thefirst

questionwasʺDoyoubelieveitiswrongtohunt?ʺThesecondquestionwasʺDoyoubelieveitiswrongtoeat

meat?ʺTheresultsareshowninthetable.Successforthefirstquestionisidentifyingsomeonewhofeelsthatit

iswrongtohuntandforthesecondquestionisidentifyingsomeonewhofeelsthatitiswrongtoeatmeat.

Hunt

EatMeat

Wrong(Success) Notwrong(Failure)

Wrong(Success) 48 56

Notwrong(Failure) 85 259

Isthereasignificantdifferenceintheproportionofstudentsatthiscollegewhofeelitiswrongtohuntandthe

proportionwhofeelthatitiswrongtoeatmeat?UsetheP–valuemethodandtheα=0.05levelofsignificance.

Page290

5 Determinethesamplesizeneededforestimatingthedifferencebetweentwopopulationproportions.

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

Provideanappropriateresponse.

1) Twosurgicalproceduresarewidelyusedtotreatacertaintypeofcancer.Tocomparethesuccessratesofthe

twoprocedures,randomsamplesofthetwotypesofsurgicalpatientswereobtainedandthenumbersof

patientswhoshowednorecurrenceofthediseaseaftera1–yearperiodwererecorded.Thedataareshownin

thetable.Howlargeasamplewouldbenecessaryinordertoestimatethedifferenceinthetruesuccessrates

towithin0.10with95%reliability?

n NumberofSuccesses

ProcedureA 100 73

ProcedureB 100 92

A) n1=n2=104 B) n1=n2=73 C) n1=n2=53 D) n1=n2=192

2) Acontroversialbillisbeingdebatedinthestatelegislature.RepresentativeWilliamswantstoestimatewithin2

percentagepointsandwith95%confidencethedifferenceintheproportionofhermaleandfemale

constituentswhofavorthebill.Whatsamplesizeshouldsheobtain?

A) n1=n2=4802 B) n1=n2=3383 C) n1=n2=97 D) n1=n2=2401

11.2 InferenceaboutTwoMeans:DependentSamples

1 Testhypothesesregardingmatched–pairsdata.

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

Provideanappropriateresponse.

1) DatasetsAandBaredependent.Findd.

A31 29 48 44 32

B29 25 2636 23

Assumethatthepaireddatacamefromapopulationthatisnormallydistributed.

A) 9.0 B) –5.1 C) 33.1 D) 25.2

2) DatasetsAandBaredependent.Findd.

A6.1 7.1 9.0 6.0 6.1

B 8.5 7.4 7.3 7.2 8.6

Assumethatthepaireddatacamefromapopulationthatisnormallydistributed.

A) –0.94 B) –0.76 C) 0.58 D) 0.89

3) DatasetsAandBaredependent.Findsd.

A13 11 30 26 14

B11 7 8 18 5

Assumethatthepaireddatacamefromapopulationthatisnormallydistributed.

A) 7.8 B) 5.6 C) 6.8 D) 8.9

4) DatasetsAandBaredependent.Findsd.

A5.3 6.3 8.2 5.2 5.3

B 7.7 6.6 6.5 6.4 7.8

Assumethatthepaireddatacamefromapopulationthatisnormallydistributed.

A) 1.73 B) 1.21 C) 1.32 D) 1.89

Page291

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

5) DatasetsAandBaredependent.Testtheclaimthatμ

d=0.Useα =0.05.

A47 45 64 60 48

B45 41 4252 39

Assumethatthepaireddatacamefromapopulationthatisnormallydistributed.

6) DatasetsAandBaredependent.Testtheclaimthatμ

d=0.Useα =0.01.

A6.7 7.7 9.6 6.6 6.7

B 9.1 8.0 7.9 7.8 9.2

Assumethatthepaireddatacamefromapopulationthatisnormallydistributed.

7) NinestudentstooktheSAT.Theirscoresarelistedbelow.Lateron,theyreadabookontestpreparationand

retooktheSAT.Theirnewscoresarelistedbelow.Testtheclaimthatthebookhadnoeffectontheirscores.

Useα=0.05.Assumethatthedistributionisnormallydistributed.

Student 123456789

Scoresbeforereadingbook 720 860 850 880 860 710 850 1200 950

Scoresafterreadingbook 740 860 840 920 890 720 840 1240 970

8) Afootballcoachclaimsthatplayerscanincreasetheirstrengthbytakingacertainsupplement.Totestthe

theory,thecoachrandomlyselects9athletesandgivesthemastrengthtestusingabenchpress.Theresultsare

listedbelow.Thirtydayslater,afterregulartrainingusingthesupplement,theyaretestedagain.Thenew

resultsarelistedbelow.Testtheclaimthatthesupplementiseffectiveinincreasingtheathletesʹstrength.Useα

=0.05.Assumethatthedistributionisnormallydistributed.

Athlete 123456789

Before 215 240 188 212 275 260 225 200 185

After 225 245 188 210 282 275 230 195 190

9) Apharmaceuticalcompanywishestotestanewdrugwiththeexpectationofloweringcholesterollevels.Ten

subjectsarerandomlyselectedandpretested.Theresultsarelistedbelow.Thesubjectswereplacedonthe

drugforaperiodof6months,afterwhichtheircholesterollevelsweretestedagain.Theresultsarelisted

below.(Allunitsaremilligramsperdeciliter.)Testthecompanyʹsclaimthatthedruglowerscholesterollevels.

Useα=0.01.Assumethatthedistributionisnormallydistributed.

Subject

Before

After

1

195

180

2

225

220

3

202

210

4

195

175

5

175

170

6

250

7

235

205

8

268

250

9

190

10

240

225

10) Inastudyoftheeffectivenessofdietonweightloss,20peoplewererandomlyselectedtoparticipateinadiet

programfor30days.Testtheclaimthatdiethadnobearingonweightloss.Useα

=0.02..Assumethatthe

distributionisnormallydistributed.

WeightbeforeProgram

(inpounds)

Weightafterprogram

(inpounds)

178

182

210

205

156

188

190

193

183

225

220

190

195

165

155

168

165

200

WeightbeforeProgram

(inpounds)Cont.

Weightafterprogram

(inpounds)Cont.

186

180

172

173

166

165

184

186

225

240

145

138

208

203

214

203

148

142

174

Page292

11) Alocalcompanyisconcernedaboutthenumberofdaysmissedbyitsemployeesduetoillness.Arandom

sampleof10employeesisselected.Thenumberofdaysabsentinoneyearislistedbelow.Anincentive

programisofferedinanattempttodecreasethenumberofdaysabsent.Thenumberofdaysabsentinoneyear

aftertheincentiveprogramislistedbelow.Testtheclaimthattheincentiveprogramcutsdownonthenumber

ofdaysmissedbyemployees.Useα=0.05.Assumethatthedistributionisnormallydistributed.

Employee

Daysabsentbefore

incentive

Daysabsentafter

incentive

A

B

C

D

E

F

G

H

I

J

12) Aphysicianclaimsthatapersonʹsdiastolicbloodpressurecanbeloweredif,insteadoftakingadrug,the

personmeditateseachevening.Tensubjectsarerandomlyselectedandpretested.Theirbloodpressures,

measuredinmillimetersofmercury,arelistedbelow.The10patientsareinstructedinbasicmeditationand

toldtopracticeiteacheveningforonemonth.Attheendofthemonth,theirbloodpressuresaretakenagain.

Thedataarelistedbelow.Testthephysicianʹsclaim.Useα=0.01.

Patient

Before

After

1

2

3

4

5

6

7

8

9

10

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

13) Whenperformingahypothesistestupontwodependentsamples,thevariableofinterestis

A) thedifferencesthatexistbetweenthematched–pairdata.

B) allofthecombineddata.

C) theabsolutevalueofthedifferencesthatexistbetweenthematched–pairdata.

D) thedatathatisthesameinbothsamples.

14) Robustnessinhypothesistestingmeans

A) departuresfromnormalitydonotadverselyaffecttheresults.

B) therearenodeparturesfromnormality.

C) thedataiseffectedbyoutliers.

D) allprocessescanbeexactlyduplicatedbyselectinganotherpairofsamples.

2 Constructconfidenceintervalsaboutthepopulationmeandifferenceofmatched –pairsdata.

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

Provideanappropriateresponse.

1) Constructa95%confidenceintervalfordatasetsAandB.DatasetsAandBaredependent.

A30 28 47 43 31

B2824253522

Assumethatthepaireddatacamefromapopulationthatisnormallydistributed.

A) (–0.696,18.700) B) (–1.324,8.981) C) (–0.113,12.761) D) (–15.341,15.431)

2) Constructa99%confidenceintervalfordatasetsAandB.DatasetsAandBaredependent.

A5.8 6.8 8.7 5.7 5.8

B 8.2 7.1 7.0 6.9 8.3

Assumethatthepaireddatacamefromapopulationthatisnormallydistributed.

A) (–4.502,2.622) B) (–25.123,5.761) C) (–21.342,18.982) D) (–15.123,15.123)

Page293

3) NinestudentstooktheSAT.Theirscoresarelistedbelow.Lateron,theyreadabookontestpreparationand

retooktheSAT.Theirnewscoresarelistedbelow.Constructa95%confidenceintervalforμ

d.Assumethatthe

distributionisnormallydistributed.

Student 123456789

Scoresbeforereadingbook 720 860 850 880 860 710 850 1200 950

Scoresafterreadingbook 740 860 840 920 890 720 840 1240 970

A) (–30.503,–0.617) B) (–20.341,4.852) C) (–10.321,15.436) D) (1.651,30.590)

4) WeareinterestedincomparingtheaveragesupermarketpricesoftwoleadingcolasintheTampaarea.Our

samplewastakenbyrandomlygoingtoeachofeightsupermarketsandrecordingthepriceofasix –packof

colaofeachbrand.Thedataareshowninthefollowingtable.Finda98%confidenceintervalforthedifference

inmeanpriceofbrand1andbrand2.Assumethatthepaireddatacamefromapopulationthatisnormally

distributed.

Price

Supermarket Brand1 Brand2 Difference

1 $2.25 $2.30 $–0.05

22.47 2.45 0.02

32.38 2.44 –0.06

42.27 2.29 –0.02

52.15 2.25 –0.10

62.25 2.25 0.00

72.36 2.42 –0.06

82.37 2.40 –0.03

x1=2.3125

s1=0.1007

x2=2.3500

s2=0.0859

d=–0.0375

sd=0.0381

A) (–0.0779,0.0029) B) (–0.1768,0.1018) C) (–0.0846,0.0096) D) (–0.0722,–0.0028)

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

5) Anewweight–reducingtechnique,consistingofaliquidproteindiet,iscurrentlyundergoingtestsbeforeits

introductionintothemarket.Atypicaltestperformedisthefollowing:Theweightsofarandomsampleoffive

peoplearerecordedbeforetheyareintroducedtotheliquidproteindiet.Thefiveindividualsarethen

instructedtofollowtheliquidproteindietfor3weeks.Attheendofthisperiod,theirweights(inpounds)are

againrecorded.Theresultsarelistedinthetable.Letμ1bethetruemeanweightofindividualsbeforestarting

thedietandletμ2bethetruemeanweightofindividualsafter3weeksonthediet.Calculatea90%confidence

intervalforthedifferencebetweenthemeanweightsbeforeandafterthedietisused.Assumethatthepaired

datacamefromapopulationthatisnormallydistributed.

Person WeightBeforeDiet WeightAfterDiet

1 152 145

2 197 192

3 190 187

4 199 193

5 206 202

Summaryinformationisasfollows:d=5,sd=1.58.

Page294

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

6) Sevenrandomlyselectedplantsthatbottlethesamebeverageimplementedatimemanagementprogramin

hopesofimprovingproductivity.Theaveragetime,inminutes,thatittookthecompaniestoproducethesame

quantityofbottlesbeforeandaftertheprogramarelistedbelow.Assumethetwopopulationdistributionsare

normal.Constructa90%confidenceintervalforμd.Assumethatthepaireddatacamefromapopulationthat

isnormallydistributed.

Plant 1234567

Before 75 89 31 90 120 50 40

After 70 80 30 85 100 49 42

A) (0.21,10.93) B) (1.60,9.54) C) (–0.22,11.36) D) (–22,33.3)

7) Whenformingaconfidenceintervalformatched–pairdatathepointestimateisthe

A) meanofthedifferences. B) differenceofthemeans.

C) standarddeviationofthedifferences. D) differencesofthestandarddeviations.

11.3 InferenceaboutTwoMeans:IndependentSamples

1 Testhypothesesregardingthedifferenceoftwoindependentmeans.

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

Provideanappropriateresponse.

1) Findthestandardizedteststatistic,t,totestthehypothesisthatμ

1=μ2.Twosamplesarerandomlyselected

andcomefrompopulationsthatarenormal.Thesamplestatisticsaregivenbelow.

n1=25 n2=30

x1=16 x2=14

s1=1.5 s2=1.9

A) 4.361 B) 3.287 C) 2.892 D) 1.986

2) Findthestandardizedteststatistic,t,totestthehypothesisthatμ

1=μ2.Twosamplesarerandomlyselected

andcomefrompopulationsthatarenormal.Thesamplestatisticsaregivenbelow.

n1=14 n2=12

x1=5x

2=6

s1=2.5 s2=2.8

A) –0.954 B) –0.915 C) –1.558 D) –0.909

3) Findthestandardizedteststatistic,t,totestthehypothesisthatμ

1>μ2.Twosamplesarerandomlyselected

andcomefrompopulationsthatarenormal.Thesamplestatisticsaregivenbelow.

n1=18 n2=13

x1=425 x2=410

s1=40 s2=25

A) 1.282 B) 3.271 C) 2.819 D) 1.865

4) Findthestandardizedteststatistic,t,totestthehypothesisthatμ

1<μ2.Twosamplesarerandomlyselected

andcomefrompopulationsthatarenormal.Thesamplestatisticsaregivenbelow.

n1=15 n2=15

x1=27.44 x2=29.99

s1=2.9 s2=2.8

A) –2.450 B) –3.165 C) –1.667 D) –0.669

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5) Findthestandardizedteststatistic,t,totestthehypothesisthatμ

1≠μ2.Twosamplesarerandomlyselected

andcomefrompopulationsthatarenormal.Thesamplestatisticsaregivenbelow.

n1=11 n2=18

x1=2.8 x2=3.2

s1=0.76 s2=0.51

A) –1.546 B) –1.821 C) –2.123 D) –1.326

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

6) Testthehypothesisthatμ1=μ2.Twosamplesarerandomlyselectedfromnormalpopulations.Thesample

statisticsaregivenbelow.

n1=25 n2=30

x1=22 x2=20

s1=1.5 s2=1.9

7) Testthehypothesisthatμ1=μ2.Twosamplesarerandomlyselectedfromnormalpopulations.Thesample

statisticsaregivenbelow.

n1=14 n2=12

x1=11 x2=12

s1=2.5 s2=2.8

8) Testthehypothesisthatμ1>μ2.Twosamplesarerandomlyselectedfromnormalpopulations.Thesample

statisticsaregivenbelow.

n1=18 n2=13

x1=530 x2=515

s1=40 s2=25

9) Testthehypothesisthatμ1<μ2.Twosamplesarerandomlyselectedfromnormalpopulations.Thesample

statisticsaregivenbelow.

n1=15 n2=15

x1=24.73 x2=27.28

s1=2.9 s2=2.8

10) Testthehypothesisthatμ1≠μ2.Twosamplesarerandomlyselectedfromnormalpopulations.Thesample

statisticsaregivenbelow.

n1=11 n2=18

x1=7.8 x2=8.2

s1=0.76 s2=0.51

11) Alocalsupermarketclaimsthatthewaitingtimeforitscustomerstobeservedisthelowestinthearea.A

competitorʹssupermarketchecksthewaitingtimesatbothsupermarkets.Thesamplestatisticsarelistedbelow.

Testthelocalsupermarketʹshypothesis.Useα=0.05.

LocalSupermarket CompetitorSupermarket

n1=15 n2=16

x1=5.3minutes x2=5.6minutes

s1=1.1minutes s2=1.0minutes

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12) Astudywasconductedtodetermineifthesalariesoflibrariansfromtwoneighboringcitieswereequal.A

sampleof15librariansfromeachcitywasrandomlyselected.Themeanfromthefirstcitywas$28,900witha

standarddeviationof$2300.Themeanfromthesecondcitywas$30,300withastandarddeviationof$2100.

Testthehypothesisthatthesalariesfrombothcitiesareequal.

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

13) Findthestandardizedteststatistictotestthehypothesisthatμ

1=μ2.Twosamplesarerandomlyselectedfrom

eachpopulation.Thesamplestatisticsaregivenbelow.Useα

=0.05.

n1=50 n2=60

x1=21 x2=19

s1=1.5 s2=1.9

A) 6.2 B) 8.1 C) 4.2 D) 3.8

14) Findthestandardizedteststatistictotestthehypothesisthatμ

1=μ2.Twosamplesarerandomlyselectedfrom

eachpopulation.Thesamplestatisticsaregivenbelow.Useα

=0.05.

n1=40 n2=35

x1=18 x2=19

s1=2.5 s2=2.8

A) –1.6 B) –0.8 C) –2.6 D) –1.0

15) Findthestandardizedteststatistictotestthehypothesisthatμ

1>μ2.Twosamplesarerandomlyselectedfrom

eachpopulation.Thesamplestatisticsaregivenbelow.Useα

=0.05.

n1=100 n2=125

x1=505 x2=490

s1=45 s2=25

A) 2.98 B) 2.81 C) 1.86 D) 0.91

16) Findthestandardizedteststatistictotestthehypothesisthatμ

1<μ2.Twosamplesarerandomlyselectedfrom

eachpopulation.Thesamplestatisticsaregivenbelow.Useα

=0.05.

n1=35 n2=42

x1=21.94 x2=24.49

s1=2.9 s2=2.8

A) –3.90 B) –3.16 C) –2.63 D) –1.66

17) Findthestandardizedteststatistictotestthehypothesisthatμ

1≠μ2.Twosamplesarerandomlyselectedfrom

eachpopulation.Thesamplestatisticsaregivenbelow.Useα

=0.02.

n1=51 n2=38

x1=6.3 x2=6.7

s1=0.76 s2=0.51

A) –2.97 B) –1.82 C) –2.12 D) –2.32

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

18) Testthehypothesisthatμ1=μ2.Twosamplesarerandomlyselectedfromeachpopulation.Thesample

statisticsaregivenbelow.Useα=0.05.

n1=50n2=60

x1=26 x2=24

s1=1.5s2=1.9

Page297

19) Testthehypothesisthatμ1>μ2.Twosamplesarerandomlyselectedfromeachpopulation.Thesample

statisticsaregivenbelow.Useα=0.01.

n1=100 n2=125

x1=520 x2=505

s1=45 s2=25

20) Testthehypothesisthatμ1<μ2.Twosamplesarerandomlyselectedfromeachpopulation.Thesample

statisticsaregivenbelow.Useα=0.05.

n1=35 n2=42

x1=19.44 x2=21.99

s1=2.9 s2=2.8

21) Testthehypothesisthatμ1≠μ2.Twosamplesarerandomlyselectedfromeachpopulation.Thesample

statisticsaregivenbelow.Useα=0.02.

n1=51 n2=38

x1=3.9 x2=4.3

s1=0.76 s2=0.51

22) Astudywasconductedtodetermineifthesalariesoflibrariansfromtwoneighboringstateswereequal.A

sampleof100librariansfromeachstatewasrandomlyselected.Themeanfromthefirststatewas$28,900with

astandarddeviationof$2300.Themeanfromthesecondstatewas$30,300withastandarddeviationof$2100.

Testthehypothesisthatthesalariesfrombothstatesareequal.Use α=0.05.

23) Atalocalstore,65femaleemployeeswererandomlyselectedanditwasfoundthattheirmeanmonthly

incomewas$642withastandarddeviationof$121.50.Seventy–fivemaleemployeeswerealsorandomly

selectedandtheirmeanmonthlyincomewasfoundtobe$684withastandarddeviationof$168.70.Testthe

hypothesisthatmaleemployeeshaveahighermonthlyincomethanfemaleemployees.Useα

=0.01.

24) Amedicalresearchersuspectsthatthepulserateofdrinkersishigherthanthepulserateofnon –drinkers.Use

thesamplestatisticsbelowtotesttheresearcherʹssuspicion.Useα=0.05.

Drinkers Nondrinkers

n1=100 n2=100

x1=88 x2=85

s1=4.8 s2=5.3

25) Ahistoryteacherbelievesthatstudentsinanafternoonclassscorehigherthanthestudentsinamorningclass.

Theresultsofaspecialexamareshownbelow.Cantheteacherconcludethattheafternoonstudentshavea

higherscore?Useα=0.01.

MorningStudents AfternoonStudents

n1=36 n2=41

x1=78 x2=81

s1=5.8 s2=6.3

26) Alocalrestaurantclaimsthatthewaitingtimeforitspatronstobeservedisthelowestinthearea.A

competitorrestaurantchecksthewaitingtimesatbothrestaurants.Thesamplestatisticsarelistedbelow.Test

thelocalrestaurantʹshypothesis.Useα=0.05.

LocalRestaurant CompetitorRestaurant

n1=45 n2=50

x1=4.9minutes x2=5.2minutes

s1=1.1minutes s2=1.0minute

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27) Auniversitywantedtoseewhethertherewasasignificantdifferenceinagebetweenitsdaystaffandevening

staff.Arandomsampleof35staffmembersisselectedfromeachgroup.Thedataaregivenbelow.Testthe

hypothesisthatthereisnodifferenceinagebetweenthetwogroups.Useα=0.05.

DayStaff

22 24 24 23 19 19 23 22 18 21 21 18

18 25 29 24 23 22 22 21 20 20 20 27

17 19 18 21 20 23 26 30 25 21 25

EveningStaff

18 23 25 23 21 21 23 24 27 31 24 20

20 23 19 25 24 27 23 20 20 21 25 24

23 28 20 19 23 24 20 27 21 29 30

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

28) WhatistheH0fortestingdifferencesofthemeansoftwoindependentsamples?

A) H0:μ1–μ2=0B)H

0:μ1≠μ2C) H0:μ1>μ2D) H0:μ1<μ2

29) Thedegreesoffreedomusedwhentestingtwoindependentsampleswherethepopulationstandarddeviation

isunknownis

A) thesmallerofn1–1orn2–1. B) thelargerofn1–1orn2–1.

C) n1+n2–2. D) n1+n2–1.

2 Constructandinterpretconfidenceintervalsregardingthedifferenceoftwoindependentmeans.

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

Provideanappropriateresponse.

1) Constructa95%confidenceintervalforμ1–μ2.Twosamplesarerandomlyselectedfromnormalpopulations.

Thesamplestatisticsaregivenbelow.

n1=10 n2=12

x1=25 x2=23

s1=1.5 s2=1.9

A) (0.360,3.640) B) (1.335,3.012) C) (1.413,3.124) D) (1.554,3.651)

2) Constructa95%confidenceintervalforμ1–μ2.Twosamplesarerandomlyselectedfromnormalpopulations.

Thesamplestatisticsaregivenbelow.

n1=11 n2=18

x1=4.8 x2=5.2

s1=0.76 s2=0.51

A) (–0.977,0.177) B) (–4.152,3.981) C) (–2.762,2.762) D) (–1.762,1.762)

3) Constructa95%confidenceintervalforμ1–μ2.Twosamplesarerandomlyselectedfromnormalpopulations.

Thesamplestatisticsaregivenbelow.

n1=8n

2=7

x1=4.1 x2=5.5

s1=0.76 s2=2.51

A) (–3.813,1.013) B) (–1.132,1.543) C) (–1.679,1.987) D) (2.112,2.113)

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4) Astudywasconductedtodetermineifthesalariesoflibrariansfromtwoneighboringcitieswereequal.A

sampleof15librariansfromeachcitywasrandomlyselected.Themeanfromthefirstcitywas$28,900witha

standarddeviationof$2300.Themeanfromthesecondcitywas$30,300withastandarddeviationof$2100.

Constructa95%confidenceintervalforμ1–μ2.

A) (–3125,325) B) (–2054,238) C) (–2871,567) D) (–4081,597)

5) Constructa95%confidenceintervalforμ1–μ2.Twosamplesarerandomlyselectedfromeachpopulation.

Thesamplestatisticsaregivenbelow.

n1=50 n2=60

x1=25 x2=23

s1=1.5 s2=1.9

A) (1.364,2.636) B) (1.572,2.987) C) (1.723,3.012) D) (1.919,3.142)

6) Constructa95%confidenceintervalforμ1–μ2.Twosamplesarerandomlyselectedfromeachpopulation.

Thesamplestatisticsaregivenbelow.

n1=40 n2=35

x1=12 x2=13

s1=2.5 s2=2.8

A) (–2.209,0.209) B) (–2.001,–1.873) C) (–1.968,1.561) D) (–1.673,1.892)

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

7) Aresearcherwishestodeterminewhetherpeoplewithhighbloodpressurecanlowertheirbloodpressureby

performingyogaexercises.Atreatmentgroupandacontrolgroupareselected.Thesamplestatisticsaregiven

below.Constructa90%confidenceintervalforthedifferencebetweenthetwopopulationmeans,μ

1–μ2.

Wouldyourecommendusingyogaexercises?Explainyourreasoning.

TreatmentGroup ControlGroup

n1=100 n2=100

x1=178 x2=193

s1=35 s2=37

8) Arecentstudyof100socialworkersinasouthernstatefoundthattheirmeansalarywas$24,100 witha

standarddeviationof$2100.Asimilarstudyof100socialworkersinawesternstatefoundthattheirmean

salarywas$34,500withastandarddeviationof$3200.Testtheclaimthatthesalariesofsocialworkersinthe

westernstateismorethan$10,000greaterthanthatofsocialworkersinthesouthernstate.Useα

=0.05.

11.4 InferenceaboutTwoPopulationStandardDeviations

1 FindcriticalvaluesoftheF–distribution.

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

Provideanappropriateresponse.

1) Findtheright–handcriticalvalueF0foratwo–tailedtestusingα =0.05,degreesoffreedominthe

numerator=5,anddegreesoffreedominthedenominator=10.

A) 4.24 B) 4.07 C) 4.47 D) 6.62

2) FindthecriticalvalueF0foraright–tailedtestusingα =0.01,degreesoffreedominthenumerator=3, and

degreesoffreedominthedenominator=20.

A) 4.94 B) 25.58 C) 5.82 D) 3.09

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3) FindthecriticalvalueF0foraleft–tailedtestusingα =0.05,degreesoffreedominthenumerator=6,and

degreesoffreedominthedenominator=16.

A) 0.255 B) 2.74 C) 2.66 D) 0.365

4) Findtheleft–handcriticalvalueF0foratwo–tailedtestusingα =0.02,degreesoffreedominthenumerator=

5,anddegreesoffreedominthedenominator=10.

A) 0.099 B) 10.05 C) 5.64 D) 0.177

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

5) Findtheleft–tailedandright–tailedcriticalF–valuesforatwo–tailedtest.Letα =0.02,degreesoffreedomin

thenumerator=7,anddegreesoffreedominthedenominator=5.

6) Findtheleft–tailedandrighttailedcriticalF–valuesforatwo–tailedtest.Usethesamplestatisticsbelow.Let

α=0.05.

n1=5n

2=6

1=5.8 s 2

2=2.7

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

7) Twoconditionsarerequiredtotestaclaimabouttwopopulationstandarddeviations.Whatarethey?

A) Thesamplesareindependentandthepopulationisnormal.

B) Thesamplesaremutuallyexclusiveandthepopulationisnormal.

C) Thesamplesareindependentandthepopulationsarerandomlyselected.

D) Thesamplesaremutuallyexclusiveandthepopulationarerandomlyselected.

2 Testhypothesesregardingtwopopulationstandarddeviations.

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

Testtheindicatedhypothesis.Assumethatthepopulationsarenormallydistributed.

1) Testthehypothesisthatσ1>σ2attheα=0.01levelofsignificanceforthegivensampledata.

Population1 Population2

n61 31

s34.4 27.6

A) Teststatistic:F=1.55.Criticalvalue=2.21.DonotrejectH0.

B) Teststatistic:F=1.55.Criticalvalue=2.03.RejectH0.

C) Teststatistic:F=42.88.Criticalvalue=2.03.RejectH0.

D) Teststatistic:F=1.25.Criticalvalue=2.21.DonotrejectH0.

2) Testthehypothesisthatσ1>σ2attheα=0.01levelofsignificanceforthegivensampledata.

Population1 Population2

n25 17

s5.23 2.5

A) Teststatistic:F=4.38.Criticalvalue:F=3.18.RejectH0.

B) Teststatistic:F=4.38.Criticalvalue:F=3.18.DonotrejectH0.

C) Teststatistic:F=2.09.Criticalvalue=1.87.RejectH0.

D) Teststatistic:F=2.09.Criticalvalue=3.18.DonotrejectH0.

Page301

3) Testthehypothesisthatσ1<σ2attheα=0.05levelofsignificanceforthegivensampledata.

Population1 Population2

n910

s0.0782 0.1955

A) Teststatistic:F=0.16Criticalvalue:0.295.RejectH0.

B) Teststatistic:F=0.16Criticalvalue:0.310.RejectH0.

C) Teststatistic:F=0.16Criticalvalue:0.318.DonotrejectH0.

D) Teststatistic:F=0.16Criticalvalue:0.295.DonotrejectH0.

4) Testthehypothesisthatσ1≠σ2attheα=0.10levelofsignificanceforthegivensampledata.

Population1 Population2

n31 25

s5.46 5.4

A) Teststatistic:F=1.02.Criticalvalues=0.529,1.94.DonotrejectH0.

B) Teststatistic:F=1.02.Criticalvalues=0.515,1.94.DonotrejectH0.

C) Teststatistic:F=1.01.Criticalvalues=0.529,1.94.DonotrejectH0.

D) Teststatistic:F=1.01.Criticalvalues=0.515,1.94.RejectH0.

5) Testthehypothesisthatσ1≠σ2attheα=0.05levelofsignificanceforthegivensampledata.

Population1 Population2

n16 13

s20.7 22.9

A) Teststatistic:F=0.82.Criticalvalues=0.338,3.18.DonotrejectH0.

B) Teststatistic:F=0.82.Criticalvalues=0.314,3.18.DonotrejectH0.

C) Teststatistic:F=0.82.Criticalvalues=0.338,3.18.RejectH0.

D) Teststatistic:F=0.82.Criticalvalues=0.403,2.62.RejectH0.

6) s1=20.4

n1=16,s2=21.9,n2=13;left–tailedtest,α=0.10

Testthehypothesisthatσ1<σ2attheα=0.10levelofsignificanceforthegivensampledata.

Population1 Population2

n16 13

s20.4 21.9



A) Teststatistic:F=0.87.Criticalvalue=0.495.DonotrejectH0.

B) Teststatistic:F=0.87.Criticalvalue=0.476.DonotrejectH0.

C) Teststatistic:F=0.87.Criticalvalue=0.495.RejectH0.

D) Teststatistic:F=0.87.Criticalvalue=0.476.RejectH0.

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

Testtheindicatedhypothesis.

7) Alocalsupermarketclaimsthatthevarianceofwaitingtimeforitscustomerstobeservedisthelowestinthe

area.Acompetitorsupermarketchecksthewaitingtimeatbothsupermarkets.Thesamplestatisticsarelisted

below.Testthelocalbankʹshypothesis.Useα=0.05.

LocalSupermarket CompetitorSupermarket

n1=13 n2=16

s1=0.99minutes s2=1.17minutes

Assumethesampleswererandomlyselectedfromnormalpopulations.

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8) Astudywasconductedtodetermineifthevariancesoflibrariansalariesfromtwoneighboringcitieswere

equal.Asampleof25librariansfromeachcitywasselected.Thefirstcityhadastandarddeviationofs1=

$3220,andthesecondcityhadastandarddeviations2=$2940.Testthehypothesisthatthevariancesofthe

salariesfrombothcitiesareequal.Useα=0.05Assumethesampleswererandomlyselectedfromnormal

populations.

9) Arandomsampleof21womenhadcholesterollevelswithavarianceof1107.2.Arandomsampleof18men

hadcholesterollevelswithavarianceof737.28.Testthehypothesisthatthecholesterollevelsforwomenhave

alargervariancethanthoseformen.Useα=0.01.Assumethesampleswererandomlyselectedfromnormal

populations.

10) Thetimespentwatchingtelevision(perday)of121womenbetweentheagesof55and64hadastandard

deviationof42minutes.Thetimespentwatchingtelevision(perday)ofarandomsampleof121women

betweentheagesof25and34hadastandarddeviationof56minutes.Testthehypothesisthattheolder

womenarefromapopulationwithavariancelessthanthatforwomeninthe25to34agegroup.

Useα=0.05.Assumethesampleswererandomlyselectedfromnormalpopulations.

11) Ataretailstore,61femaleemployeeswererandomlyselectedanditwasfoundthattheirmonthlyincomehad

astandarddeviationof$194.40.For121maleemployees,thestandarddeviationwas$269.92.Testthe

hypothesisthatvarianceofmonthlyincomesishigherformaleemployeesthanitisforfemaleemployees.Use

α=0.01.Assumethesampleswererandomlyselectedfromnormalpopulations.

12) Amedicalresearchersuspectsthatthevarianceofthepulserateofdrinkersishigherthanthevarianceofthe

pulserateofnon–drinkers.Usethesamplestatisticsbelowtotesttheresearcherʹssuspicion.Use

α=0.05.

Drinkers Non–drinkers

n1=61 n2=121

s1=5.46 s2=3.71

Assumethesampleswererandomlyselectedfromnormalpopulations.

13) Analgebrateacherbelievesthatthevariancesoftestscoresofstudentsinhereveningalgebraclassarelower

thanthevariancesoftestscoresofstudentsinhermorningclass.Theresultsofanexam,giventothemorning

andeveningstudents,areshownbelow.Cantheteacherconcludethathereveningstudentshavealower

variance?Useα=0.01.

EveningStudents MorningStudents

n1=41 n2=36

s1=18.55 s2=34.3

Assumethesampleswererandomlyselectedfromnormalpopulations.

14) Alocalrestaurantclaimsthatthevarianceofwaitingtimeforitspatronstobeservedisthelowestinthearea.

Acompetitorrestaurantchecksthewaitingtimeatbothrestaurants.Thesamplestatisticsarelistedbelow.Test

thelocalrestaurantʹshypothesis.Useα=0.05.

LocalRestaurant CompetitorRestaurant

n1=41 n2=61

s1=1.43minutes s2=2.6minutes

Assumethesampleswererandomlyselectedfromnormalpopulations.

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15) Auniversitywantstoseewhetherthereisasignificantdifferenceinthevariancesoftheagesbetweendaystaff

andnightstaff.Arandomsampleof31staffmembersisselectedfromeachgroup.Thedataaregivenbelow.

Testthehypothesisthatthereisnodifferenceinagebetweenthetwogroups.

Useα=0.05.

DayStaff

22 24 24 23 19 19 23 22 18 21 21

18 18 25 29 24 23 22 22 21 20 20

20 27 17 19 18 21 20 23 26

EveningStaff

18 23 25 23 21 21 23 24 27 31 34

20 20 23 19 25 24 27 23 20 20 21

25 24 23 28 20 19 23 24 20

Assumethesampleswererandomlyselectedfromnormalpopulations.

11.5 PuttingItTogether:WhichMethodDoIUse?

1 Determinetheappropriatehypothesistesttoperform.

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

Performtheappropriatehypothesistest.

1) Arandomsampleofn1=60individualsresultsinx1=48 successes.Anindependentsampleofn2=40

individualsresultsinx2=30successes.Doesthisrepresentsufficientevidencetoconcludethatp1>p2atthe

α=0.01levelofsignificance?

2) Arandomsampleofn1=20individualsresultsinx1=8 successes.Anindependentsampleofn2=60

individualsresultsinx2=18successes.Doesthisrepresentsufficientevidencetoconcludethatp1≠p2atthe

α=0.05levelofsignificance?

3) Ifs1=0.0782,n1=9,s2=0.1897

andn2=10;testwhetherσ1<σ2attheα=0.05levelofsignificance.Assume

thepopulationsarenormallydistributed.

4) Ifs1=5.89

n1=31,s2=5,andn2=25,testwhetherthepopulationstandarddeviationsdifferatthe

α=0.10levelofsignificance.Assumethepopulationsarenormallydistributed.

5) Conducttheappropriatetesttodetermineifthepopulationproportionsforthetwotreatmentsdifferattheα=

0.05levelofsignificance.Assumethatthesamplesaredependentandobtainedrandomly.

TreatmentA

TreatmentB

Success Failure

Success 260 32

Failure 49 180

6) Arandomsampleofsizen=50resultsinasamplemeanof21 andasamplestandarddeviationof1.5.An

independentsampleofsizen=60resultsinasamplemeanof19andasamplestandarddeviationof1.9.Does

thisconstitutesufficientevidencetoconcludethatthepopulationmeansdifferattheα=0.05levelof

significance?

Page304

7) Thetablebelowshowstheweights,inpounds,ofsevensubjectsbeforeandafterfollowingaparticulardiet

programforthreemonths.Doesthesampleevidencesuggestthatthedietprogramiseffectiveinreducing

weight?Usetheα=0.01levelofsignificance.Assumethatthedifferenceddatacomefromapopulationthatis

normallydistributedwithnooutliers.

Subject A B C D E F G

Before,Xi174 193 190 151 177 182 158

After,Yi167 184 188 156 163 184 146

8) Thedatarepresentthemeasureofavariablebeforeandafteratreatment. Doesthesampleevidencesuggest

thatthetreatmentiseffectiveinincreasingthevalueoftheresponsevariable?Usetheα =0.01levelof

significance.Assumethatthedifferenceddatacomefromapopulationthatisnormallydistributedwithno

outliers.

Subject A B C D E F G

Before,Xi9.4 9.7 9.6 9.5 9.4 9.4 9.5

After,Yi9.5 9.9 9.6 9.4 9.5 9.7 9.3

9) Arandomsampleof100maleemployeesofaretailstoreresultsinameanmonthlysalaryof$530 witha

standarddeviationof$44.Anindependentrandomsampleof125femaleemployeesofthesamestoreresultsin

ameanmonthlysalaryof$515withastandarddeviationof$25.Doesthisconstitutesufficientevidenceto

concludethatthemeanmonthlysalaryformaleemployeesofthestoreishigherthanthemeanmonthlysalary

forfemaleemployeesofthestore?Usetheα=0.01levelofsignificance.

10) Inasurvey,65of133womensaidthattheyregularlyremembertheirdreams,while58of127mensaidthat

theyregularlyremembertheirdreams.Doesthisconstitutesufficientevidencetoconcludethatwomenare

morelikelytoremembertheirdreamsthanmen?Usetheα=0.05levelofsignificance.

11) Asurveyfoundthat26of79peoplewhodonʹtdrinkcoffeeoftenhavetroublesleepingand28of82 coffee

drinkersoftenhavetroublesleeping.Constructa95%confidenceintervaltodeterminewhetherthereisa

differencebetweentheproportionofnoncoffeedrinkerswhohavetroublesleepingandtheproportionof

coffeedrinkerswhohavetroublesleeping.

12) Arandomsamplesof8applesofvarietyAandanindependentrandomsampleof13applesofvarietyB

yieldedthefollowingweightsinounces.Dothedataprovidesufficientevidencetoconcludethatthemean

weightofapplesofvarietyAdiffersfromthemeanweightofapplesofvarietyB?Usetheα=0.10levelof

significance.Assumethatthesampledatacomefromnormallydistributedpopulationswithnooutliers.

VarietyAVarietyB

3.73.2 3.82.83.2

3.02.5 4.03.03.6

2.73.6 3.92.63.8

2.83.4 4.02.53.6

3.9

Page305

Ch.11 InferencesonTwoSamples

AnswerKey

11.1 InferenceaboutTwoPopulationProportions

1 Distinguishbetweenindependentanddependentsampling.

2 Testhypothesesregardingtwoproportionsfromindependentsamples.

3 Constructandinterpretconfidenceintervalsforthedifferencebetweentwopopulationproportions.

Page306

4 Testhypothesesregardingtwoproportionsfromdependentsamples.

5 Determinethesamplesizeneededforestimatingthedifferencebetweentwopopulationproportions.

11.2 InferenceaboutTwoMeans:DependentSamples

1 Testhypothesesregardingmatched–pairsdata.

Page307

2 Constructconfidenceintervalsaboutthepopulationmeandifferenceofmatched –pairsdata.

11.3 InferenceaboutTwoMeans:IndependentSamples

1 Testhypothesesregardingthedifferenceoftwoindependentmeans.

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2 Constructandinterpretconfidenceintervalsregardingthedifferenceoftwoindependentmeans.

11.4 InferenceaboutTwoPopulationStandardDeviations

1 FindcriticalvaluesoftheF–distribution.

2 Testhypothesesregardingtwopopulationstandarddeviations.

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11.5 PuttingItTogether:WhichMethodDoIUse?

1 Determinetheappropriatehypothesistesttoperform.

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