Chapter 08 Assume The Two Samples Are Random And

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Ch.8 HypothesisTestingwithTwoSamples

8.1 TestingtheDifferenceBetweenMeans(IndependentSamples,σ1andσ2Known)

1 DeterminetheDifferenceBetweenDependentandIndependentSamples

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weightsof18people

Sample2:Post–trainingweightsof18people

A) dependent B) independent

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

Sample1:Theweightsinpoundsof21newbornfemales

Sample2:Theweightsinpoundsof21newbornmales

A) independent B) dependent

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

Sample1:Thescoresof22studentswhotooktheACT

Sample2:Thescoresof22differentstudentswhotooktheSAT

A) independent B) dependent

4) Aspartofamarketingexperiment,adepartmentstoreregularlymaileddiscountcouponsto25ofitscredit

cardholders.Theirtotalcreditcardpurchasesoverthenextthreemonthswerecomparedtotheirpriorcredit

cardpurchasesduringthepreviousthreemonths.Determinewhetherthesamplesaredependentor

independent.

A) dependent B) independent

5) Aspartofamarketingexperiment,adepartmentstoreregularlymaileddiscountcouponsto25ofitscredit

cardholders.Theirtotalcreditcardpurchasesoverthenextthreemonthswerecomparedtothecreditcard

purchasesoverthenextthreemonthsfor25creditcardholderswhowerenotsentdiscountcoupons.

Determinewhetherthesamplesaredependentorindependent.

A) independent B) dependent

6) AspartofaMasterʹsthesisproject,amathematicsteacherisinterestedintheeffectsoftwodifferentteaching

methodsonmathematicsachievement.Sherandomlychoosesoneclassofstudentstolearnanalgebraic

conceptusingtraditionalmethodsandanotherclassofstudentstolearnthesamealgebraicconceptusing

manipulatives.Theteacherthencomparestheirtestscores.Determinewhetherthesamplesaredependentor

independent.

A) independent B) dependent

7) AspartofaMasterʹsthesisproject,amathematicsteacherisinterestedintheeffectsoftwodifferentteaching

methodsonmathematicsachievement.Sherandomlychoosesaclassofstudentstolearnonealgebraicconcept

usingtraditionalmethods.Thenonanotherday,thesamestudentslearnasimilaralgebraicconceptusing

manipulatives.Theteacherthencomparestheirtestscores.Determinewhetherthesamplesaredependentor

independent.

A) dependent B) independent

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2 TestaClaimAbouttheDifferenceBetweenTwoPopulation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totesttheclaimthatμ1=μ2.Assumethetwosamplesarerandomand

independent.

Populationstatistics:σ1=1.5andσ2=1.9

Samplestatistics:x1=24,n1=50andx2=22,n2=60

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

2) Findthestandardizedteststatistictotesttheclaimthatμ1=μ2.Assumethetwosamplesarerandomand

independent.

Populationstatistics:σ1=2.5andσ2=2.8

Samplestatistics:x1=3,n1=40andx2=4,n2=35

A) –1.6 B) –0.8 C) –2.6 D) –1.0

3) Findthestandardizedteststatistictotesttheclaimthatμ1>μ2.Assumethetwosamplesarerandomand

independent.

Populationstatistics:σ1=45andσ2=25

Samplestatistics:x1=480,n1=100andx2=465,n2=125

A) 2.99 B) 2.81 C) 1.86 D) 0.91

4) Findthestandardizedteststatistictotesttheclaimthatμ1<μ2.Assumethetwosamplesarerandomand

independent.

Populationstatistics:σ1=2.9andσ2=2.8

Samplestatistics:x1=20.16,n1=35andx2=22.71,n2=42

A) –3.90 B) –3.16 C) –2.63 D) –1.66

5) Findthestandardizedteststatistictotesttheclaimthatμ1≠μ2.Assumethetwosamplesarerandomand

independent.

Populationstatistics:σ1=0.76andσ2=0.51

Samplestatistics:x1=4.1,n1=51andx2=4.5,n2=38

A) –2.97 B) –1.82 C) –2.12 D) –2.32

6) Supposeyouwanttotesttheclaimthatμ1≠μ2.Assumethetwosamplesarerandomandindependent.Ata

levelofsignificanceofα=0.05,whenshouldyourejectH0?

Populationstatistics:σ1=1.5andσ2=1.9

Samplestatistics:x1=19,n1=50andx2=17,n2=60

A) RejectH0ifthestandardizedteststatisticislessthan–1.96orgreaterthan1.96.

B) RejectH0ifthestandardizedteststatisticislessthan–2.33orgreaterthan2.33.

C) RejectH0ifthestandardizedteststatisticislessthan–1.645orgreaterthan1.645.

D) RejectH0ifthestandardizedteststatisticislessthan–2.575orgreaterthan2.575.

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7) Supposeyouwanttotesttheclaimthatμ1=μ2.Assumethetwosamplesarerandomandindependent.Ifa

hypothesistestisperformed,howshouldyouinterpretadecisionthatrejectsthenullhypothesis?

A) Thereissufficientevidencetorejecttheclaimμ1=μ2.

B) Thereisnotsufficientevidencetorejecttheclaimμ1=μ2.

C) Thereissufficientevidencetosupporttheclaimμ1=μ2.

D) Thereisnotsufficientevidencetosupporttheclaimμ1=μ2.

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

8) Testtheclaimthatμ1=μ2.Assumethetwosamplesarerandomandindependent.Useα



=0.05.

Populationstatistics:σ1=1.5andσ2=1.9

Samplestatistics:x1=17,n1=50andx2=15,n2=60

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

9) Supposeyouwanttotesttheclaimthatμ1>μ2.Assumethetwosamplesarerandomandindependent.Ata

levelofsignificanceofα=0.01,whenshouldyourejectH0?

Populationstatistics:σ1=45andσ2=25

Samplestatistics:x1=805,n1=100andx2=790,n2=125

A) RejectH0ifthestandardizedteststatisticisgreaterthan2.33.

B) RejectH0ifthestandardizedteststatisticisgreaterthan1.96.

C) RejectH0ifthestandardizedteststatisticisgreaterthan1.645.

D) RejectH0ifthestandardizedteststatisticisgreaterthan2.575.

10) Supposeyouwanttotesttheclaimthatμ1>μ2.Assumethetwosamplesarerandomandindependent.Ifa

hypothesistestisperformed,howshouldyouinterpretadecisionthatrejectsthenullhypothesis?

A) Thereissufficientevidencetosupporttheclaimμ1>μ2.

B) Thereissufficientevidencetorejecttheclaimμ1>μ2.

C) Thereisnotsufficientevidencetorejecttheclaimμ1>μ2.

D) Thereisnotsufficientevidencetosupporttheclaimμ1>μ2.

11) Supposeyouwanttotesttheclaimthatμ1<μ2.Assumethetwosamplesarerandomandindependent.Ata

levelofsignificanceofα=0.05,whenshouldyourejectH0?

Populationstatistics:σ1=2.9andσ2=2.8

Samplestatistics:x1=28.85,n1=35andx2=31.4,n2=42

A) RejectH0ifthestandardizedteststatisticislessthan–1.645.

B) RejectH0ifthestandardizedteststatisticislessthan–1.96.

C) RejectH0ifthestandardizedteststatisticislessthan–2.33.

D) RejectH0ifthestandardizedteststatisticislessthan–2.575.

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12) Supposeyouwanttotesttheclaimthatμ1<μ2.Assumethetwosamplesarerandomandindependent.Ifa

hypothesistestisperformed,howshouldyouinterpretadecisionthatfailstorejectthenullhypothesis?

A) Thereisnotsufficientevidencetosupporttheclaimμ1<μ2.

B) Thereissufficientevidencetorejecttheclaimμ1<μ2.

C) Thereisnotsufficientevidencetorejecttheclaimμ1<μ2.

D) Thereissufficientevidencetosupporttheclaimμ1<μ2.

13) Supposeyouwanttotesttheclaimthatμ1≠μ2.Assumethetwosamplesarerandomandindependent.Ata

levelofsignificanceofα=0.02,whenshouldyourejectH0?

Populationstatistics:σ1=0.76andσ2=0.51

Samplestatistics:x1=1.8,n1=51andx2=2.2,n2=38

A) RejectH0ifthestandardizedteststatisticislessthan–2.33orgreaterthan2.33.

B) RejectH0ifthestandardizedteststatisticislessthan–1.96orgreaterthan1.96.

C) RejectH0ifthestandardizedteststatisticislessthan–1.645orgreaterthan1.645.

D) RejectH0ifthestandardizedteststatisticislessthan–2.575orgreaterthan2.575.

14) Supposeyouwanttotesttheclaimthatμ1≠μ2.Assumethetwosamplesarerandomandindependent.Ifa

hypothesistestisperformed,howshouldyouinterpretadecisionthatfailstorejectthenullhypothesis?

A) Thereisnotsufficientevidencetosupporttheclaimμ1≠μ2.

B) Thereissufficientevidencetorejecttheclaimμ1≠μ2.

C) Thereisnotsufficientevidencetorejecttheclaimμ1≠μ2.

D) Thereissufficientevidencetosupporttheclaimμ1≠μ2.

15) Twosamplesarerandomandindependent.FindtheP–valueusedtotesttheclaimthatμ1=μ2.Useα =0.05.

Populationstatistics:σ1=2.5andσ2=2.8

Samplestatistics:x1=12,n1=40andx2=13,n2=35

A) 0.1052 B) 0.0526 C) 0.4020 D) 0.1138

16) Twosamplesarerandomandindependent.FindtheP–valueusedtotesttheclaimthatμ1>μ2.Useα =0.05.

Populationstatistics:σ1=40andσ2=24

Samplestatistics:x1=615,n1=100andx2=600,n2=125

A) 0.0005 B) 0.0505 C) 0.1015 D) 0.5105

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

17) Testtheclaimthatμ1>μ2.Assumethetwosamplesarerandomandindependent.Useα

=0.01.

Populationstatistics:σ1=45andσ2=25

Samplestatistics:x1=630,n1=100andx2=615,n2=125

18) Testtheclaimthatμ1<μ2.Assumethetwosamplesarerandomandindependent.Useα

=0.05.

Populationstatistics:σ1=2.9andσ2=2.8

Samplestatistics:x1=25.6,n1=35andx2=28.15,n2=42

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19) Testtheclaimthatμ1≠μ2.Assumethetwosamplesarerandomandindependent.Useα

=0.02.

Populationstatistics:σ1=0.76andσ2=0.51

Samplestatistics:x1=5.3,n1=51andx2=5.7,n2=38

20) Astudywasconductedtodetermineifthesalariesofelementaryschoolteachersfromtwoneighboringstates

wereequal.Asampleof100teachersfromeachstatewasrandomlyselected.Themeanfromthefirststatewas

$29,100withapopulationstandarddeviationof$2300.Themeanfromthesecondstatewas$30,500witha

populationstandarddeviationof$2100.Testtheclaimthatthesalariesfrombothstatesareequal.Useα=0.05.

21) Atalocalcollege,65femalestudentswererandomlyselectedanditwasfoundthattheirmeanmonthlyincome

was$616withapopulationstandarddeviationof$121.50.Seventy–fivemalestudentswerealsorandomly

selectedandtheirmeanmonthlyincomewasfoundtobe$658withapopulationstandarddeviationof$168.70.

Testtheclaimthatmalestudentshaveahighermonthlyincomethanfemalestudents.Useα

=0.01.

22) Amedicalresearchersuspectsthatthepulserateofsmokersishigherthanthepulserateofnon–smokers.Test

theresearcherʹssuspicionusingα=0.05.Assumethetwosamplesarerandomandindependent.

SmokersNonsmokers

n1=100n2=100

x1=87x2=84

σ1=4.8σ2=5.3

23) Astatisticsteacherbelievesthatstudentsinaneveningstatisticsclassscorehigherthanthestudentsinaday

class.Theresultsofaspecialexamareshownbelow.Assumethetwosamplesarerandomandindependent.

Cantheteacherconcludethattheeveningstudentshaveahigherscore?Useα=0.01.

DayStudentsEveningStudents

n1=36 n2=41

x1=75 x2=78

s1=5.8 s2=6.3

24) Astatisticsteacherwantedtoseewhethertherewasasignificantdifferenceinagesbetweendaystudentsand

nightstudents.Asampleof35studentsisselectedfromeachgroup.Thedataaregivenbelow.Assumethetwo

samplesarerandomandindependent.Testtheclaimthatthereisnodifferenceinagebetweenthetwogroups.

Useα=0.05.

DayStudents

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Students

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

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

bankchecksthewaitingtimesatbothbanks.Testthelocalbankʹsclaimusingα

=0.05.Assumethetwo

samplesarerandomandindependent.

LocalBankCompetitorBank

n1=45 n2=50

x1=5.6minutes x2=5.9minutes

σ1=1.1minutesσ2=1.0minute

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

bankchecksthewaitingtimesatbothbanks.UseP–valuestotestthelocalbankʹsclaim.Useα=0.05.Assume

thetwosamplesarerandomandindependent.

LocalBankCompetitorBank

n1=45n2=50

x1=5.3minutesx2=5.6minutes

σ1=1.1minutesσ2=1.0minutes

27) AfinancialadvisorwantstoknowwhetherthereisasignificantdifferencebetweentheNYSEandNASDAQ

marketsintheannualdividendratesforpreferredstocks.Asampleof30returnsisselectedfromeachmarket.

Assumethetwosamplesarerandomandindependent.Testtheclaimthatthereisnodifferenceintheannual

dividendratesforthetwomarkets.Useα=0.05.

NASDAQ

2.00 1.02 2.11 2.56 2.15 0.93 0.91 1.67 1.88 2.13

2.44 1.97 2.00 1.81 2.25 1.72 1.75 1.05 0.90 2.34

0.51 1.00 2.25 0.85 1.50 2.33 1.59 2.25 0.23 1.63

NYSE

1.46 3.00 1.74 5.19 1.69 1.88 2.85 2.00 2.19 2.03

1.81 5.00 1.72 3.38 2.09 4.50 3.07 1.97 1.78 1.50

1.97 4.65 3.12 2.19 2.19 3.50 1.56 4.10 3.00 4.40

28) Arecentstudyof100elementaryschoolteachersinasouthernstatefoundthattheirmeansalarywas$24,700

withapopulationstandarddeviationof$2100.Asimilarstudyof100elementaryschoolteachersinawestern

statefoundthattheirmeansalarywas$35,100withapopulationstandarddeviationof$3200.Testtheclaim

thatthesalariesofelementaryschoolteachersinthewesternstateismorethan$10,000greaterthanthatof

elementaryteachersinthesouthernstate.Useα=0.05.Assumethetwosamplesarerandomandindependent.

29) Atα=0.05,testafinancialadvisorʹsclaimthatthedifferencebetweenthemeandividendrateforlistingsinthe

NYSEmarketandthemeandividendrateforlistingsintheNASDAQmarketismorethan0.75.Assumethe

twosamplesarerandomandindependent.

NYSE NASDAQ

n1=30 n2=50

x1=2.75% x2=1.66%

σ1=1.14% σ2=0.63%

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30) Twogroupsofpatientswithcolorectalcanceraretreatedwithadifferentdrugtoreducepain.Arandom

sampleof140patientsaretreatedusingthedrugIrinoticanandarandomsampleof127patientsaretreated

usingthedrugFluorouracil.Assumethetwosamplesarerandomandindependent.Atα

=0.01,testa

pharmaceuticalrepresentativeʹsclaimthatthedifferencebetweenthemeannumberofpain–freemonthsfor

patientsusingFluorouracilandthemeannumberofpain–freemonthsforpatientsusingIrinoticanislessthan

twomonths.

Fluorouracil Irinotican

n1=127 n2=140

x1=8.5months x2=10.3months

σ1=1.5months σ2=1.2months

3 ConstructaConfidenceIntervalfortheDifferenceBetweenTwoPopulationMeans

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

Provideanappropriateresponse.

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

bankchecksthewaitingtimesatbothbanks.Assumethetwosamplesarerandomandindependent.Use

α=0.05andaconfidenceintervaltotestthelocalbankʹsclaim.

LocalBank CompetitorBank

n1=45 n2=50

x1=5.3minutes x2=5.6minutes

σ1=1.1minutes σ2=1.0minute

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

2) Constructa95%confidenceintervalforμ1–μ2.Assumethetwosamplesarerandomandindependent.The

samplestatisticsaregivenbelow.

Populationstatistics:σ1=1.5andσ2=1.9

Samplestatistics:x1=25,n1=50andx2=23,n2=60

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

3) Constructa95%confidenceintervalforμ1–μ2.Assumethetwosamplesarerandomandindependent.The

samplestatisticsaregivenbelow.

Populationstatistics:σ1=2.5andσ2=2.8

Samplestatistics:x1=12,n1=40andx2=13,n2=35

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

4) Forwhichconfidenceintervalforthedifferenceinthemeansμ1–μ2

wouldyourejectthenullhypothesis?

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

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

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

followingacertaindiet.Atreatmentgroupandacontrolgroupareselected.Assumethetwosamplesare

randomandindependent.Constructa90%confidenceintervalforthedifferencebetweenthetwopopulation

means,μ1–μ2.Wouldyourecommendusingthisdietplan?Explainyourreasoning.

TreatmentGroupControlGroup

n1=100n2=100

x1=178x2=193

σ1=35σ2=37

8.2 TestingtheDifferenceBetweenMeans(IndependentSamples,σ1andσ2Unknown)

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,t0

totesttheclaimthatμ1=μ2.Twosamplesarerandom,independent,andcome

frompopulationsthatarenormal.Thesamplestatisticsaregivenbelow.Assumethatσ2

1≠σ 2

2.Useα=0.05.

n1=25n2=30

x1=17 x2=15

s1=1.5s2=1.9

A) ±2.064 B) ±2.797 C) ±1.711 D) ±2.492

2) Findthecriticalvalues,t0

totesttheclaimthatμ1=μ2.Twosamplesarerandom,independent,andcome

frompopulationsthatarenormal.Thesamplestatisticsaregivenbelow.Assumethatσ2

1=σ 2

2.Useα=0.05.

n1=14n2=12

x1=15 x2=16

s1=2.5s2=2.8

A) ±2.064 B) ±2.492 C) ±1.711 D) ±1.318

3) Findthecriticalvalue,t0

totesttheclaimthatμ1>μ2.Twosamplesarerandom,independent,andcomefrom

populationsthatarenormal.Thesamplestatisticsaregivenbelow.Assumethatσ2

1≠σ 2

2.Useα=0.01.

n1=18n2=13

x1=600 x2=585

s1=40s2=25

A) 2.681 B) 1.699 C) 2.179 D) 3.055

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4) Findthecriticalvalue,t0

totesttheclaimthatμ1<μ2.Twosamplesarerandom,independent,andcomefrom

populationsthatarenormal.Thesamplestatisticsaregivenbelow.Assumethatσ2

1=σ 2

2.Useα=0.05.

n1=15n2=15

x1=22.2 x2=24.75

s1=2.9s2=2.8

A) –1.701 B) 2.467 C) –1.313 D) 0.683

5) Findthecriticalvalue,t0

totesttheclaimthatμ1≠μ2.Twosamplesarerandom,independent,andcomefrom

populationsthatarenormal.Thesamplestatisticsaregivenbelow.Assumethatσ2

1≠σ 2

2.Useα=0.02.

n1=11n2=18

x1=3.9 x2=4.3

s1=0.76s2=0.51

A) ±2.764 B) ±0.684 C) ±2.228 D) ±3.169

2 TestaClaimAbouttheDifferenceBetweenTwoPopulation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claimthatμ1=μ2.Twosamplesarerandom,independent,and

comefrompopulationsthatarenormallydistributed.Thesamplestatisticsaregivenbelow.Assumethat

σ2

1≠σ 2

n1=25n2=30

x1=33 x2=31

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claimthatμ1=μ2.Twosamplesarerandom,independent,and

comefrompopulationsthatarenormallydistributed.Thesamplestatisticsaregivenbelow.Assumethat

σ2

1=σ 2

n1=14n2=12

x1=14 x2=15

s1=2.5s2=2.8

A) –0.962 B) –0.813 C) –1.326 D) –1.101

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3) Findthestandardizedteststatistic,t,totesttheclaimthatμ1>μ2.Twosamplesarerandom,independent,and

comefrompopulationsthatarenormallydistributed.Thesamplestatisticsaregivenbelow.Assumethat

σ2

1≠σ 2

n1=18n2=13

x1=515 x2=500

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claimthatμ1<μ2.Twosamplesarerandom,independent,and

comefrompopulationsthatarenormallydistributed.Thesamplestatisticsaregivenbelow.Assumethat

σ2

1=σ 2

n1=15n2=15

x1=21.2 x2=23.75

s1=2.9s2=2.8

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

5) Findthestandardizedteststatistic,t,totesttheclaimthatμ1≠μ2.Twosamplesarerandom,independent,and

comefrompopulationsthatarenormallydistributed.Thesamplestatisticsaregivenbelow.Assumethat

σ2

1≠σ 2

2.

n1=11n2=18

x1=6.9 x2=7.3

s1=0.76s2=0.51

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

6) Supposeyouwanttotesttheclaimthatμ1=μ2.Twosamplesarerandom,independent,andcomefrom

populationsthatarenormallydistributed.Thesamplestatisticsaregivenbelow.Assumethatσ2

1≠σ 2

2.Ata

levelofsignificanceofα=0.01,whenshouldyourejectH0?

n1=25n2=30

x1=23 x2=21

s1=1.5s2=1.9

A) RejectH0ifthestandardizedteststatisticislessthan–2.797orgreaterthan2.797.

B) RejectH0ifthestandardizedteststatisticislessthan–2.789orgreaterthan2.797.

C) RejectH0ifthestandardizedteststatisticislessthan–1.711orgreaterthan1.711.

D) RejectH0ifthestandardizedteststatisticislessthan–2.492orgreaterthan2.492.

Page183

7) Supposeyouwanttotesttheclaimthatμ1=μ2.Twosamplesarerandom,independent,andcomefrom

populationsthatarenormallydistributed.Thesamplestatisticsaregivenbelow.Assumethatσ2

1=σ 2

2.Ata

levelofsignificanceofα=0.05,whenshouldyourejectH0?

n1=14n2=12

x1=21 x2=22

s1=2.5s2=2.8

A) RejectH0ifthestandardizedteststatisticislessthan–2.064orgreaterthan2.064.

B) RejectH0ifthestandardizedteststatisticislessthan–2.492orgreaterthan2.492

C) RejectH0ifthestandardizedteststatisticislessthan–1.711orgreaterthan1.711.

D) RejectH0ifthestandardizedteststatisticislessthan–1.318orgreaterthan1.318.

8) Supposeyouwanttotesttheclaimthatμ1>μ2.Twosamplesarerandom,independent,andcomefrom

populationsthatarenormallydistributed.Thesamplestatisticsaregivenbelow.Assumethatσ2

1≠σ 2

2.Ata

levelofsignificanceofα=0.01,whenshouldyourejectH0?

n1=18n2=13

x1=595 x2=580

s1=40s2=25

A) RejectH0ifthestandardizedteststatisticisgreaterthan2.681.

B) RejectH0ifthestandardizedteststatisticisgreaterthan1.699.

C) RejectH0ifthestandardizedteststatisticisgreaterthan2.179.

D) RejectH0ifthestandardizedteststatisticisgreaterthan3.055.

9) Supposeyouwanttotesttheclaimthatμ1<μ2.Twosamplesarerandom,independent,andcomefrom

populationsthatarenormallydistributed.Thesamplestatisticsaregivenbelow.Assumethatσ2

1=σ 2

2.Ata

levelofsignificanceofα=0.10, whenshouldyourejectH0?

n1=15n2=15

x1=27.37 x2=29.92

s1=2.9s2=2.8

A) RejectH0ifthestandardizedteststatisticislessthan–1.313.

B) RejectH0ifthestandardizedteststatisticislessthan–2.467.

C) RejectH0ifthestandardizedteststatisticislessthan–1.701.

D) RejectH0ifthestandardizedteststatisticislessthan–0.683.

Page184

10) Supposeyouwanttotesttheclaimthatμ1≠μ2.TTwosamplesarerandom,independent,andcomefrom

populationsthatarenormallydistributed.Thesamplestatisticsaregivenbelow.Assumethatσ2

1≠σ 2

2.Ata

levelofsignificanceofα=0.20,whenshouldyourejectH0?

n1=11n2=18

x1=2.9 x2=3.3

s1=0.76s2=0.51

A) RejectH0ifthestandardizedteststatisticislessthan–1.372orgreaterthan1.372.

B) RejectH0ifthestandardizedteststatisticislessthan–0.684orgreaterthan0.684.

C) RejectH0ifthestandardizedteststatisticislessthan–2.228orgreaterthan2.228.

D) RejectH0ifthestandardizedteststatisticislessthan–3.169orgreaterthan3.169.

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

11) Testtheclaimthatμ1=μ2.Twosamplesarerandom,independent,andcomefrompopulationsthatare

normallydistributed.Thesamplestatisticsaregivenbelow.Assumethatσ2

1≠σ 2

2.Useα=0.05.

n1=25n2=30

x1=18 x2=16

s1=1.5s2=1.9

12) Testtheclaimthatμ1=μ2.Twosamplesarerandom,independent,andcomefrompopulationsthatare

normallydistributed.Thesamplestatisticsaregivenbelow.Assumethatσ2

1=σ 2

2.Useα=0.05.

n1=14n2=12

x1=12 x2=13

s1=2.5s2=2.8

13) Testtheclaimthatμ1>μ2.Twosamplesarerandom,independent,andcomefrompopulationsthatare

normallydistributed.Thesamplestatisticsaregivenbelow.Assumethatσ2

1≠σ 2

2.Useα=0.01.

n1=18n2=13

x1=520 x2=505

s1=40s2=25

14) Testtheclaimthatμ1<μ2.Twosamplesarerandom,independent,andcomefrompopulationsthatare

normallydistributed.Thesamplestatisticsaregivenbelow.Assumethatσ2

1=σ 2

2.Useα=0.025.

n1=15n2=15

x1=24.63 x2=27.18

s1=2.9s2=2.8

Page185

15) Testtheclaimthatμ1≠μ2.Twosamplesarerandom,independent,andcomefrompopulationsthatare

normallydistributed.Thesamplestatisticsaregivenbelow.Assumethatσ2

1≠σ 2

2.Useα=0.02.

n1=11n2=18

x1=4x2=4.4

s1=0.76s2=0.51

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

bankchecksthewaitingtimesatbothbanks.Assumethesamplesarerandomandindependent,andthe

populationsarenormallydistributed.Testthelocalbankʹsclaim:(a)assumingthatσ2

1=σ 2

2,and(b)

assumingthatσ 2

1≠σ 2

2.Useα=0.05.

LocalBankCompetitorBank

n1=15 n2=16

x1=5.3minutes x2=5.6minutes

s1=1.1minutes s2=1.0minutes

17) Astudywasconductedtodetermineifthesalariesofelementaryschoolteachersfromtwoneighboring

districtswereequal.Asampleof15teachersfromeachdistrictwasrandomlyselected.Themeanfromthefirst

districtwas$28,900withastandarddeviationof$2300.Themeanfromtheseconddistrictwas$30,300witha

standarddeviationof$2100.Testtheclaimthatthesalariesfrombothdistrictsareequal.Assumethesamples

arerandomandindependent,andthepopulationsarenormallydistributed.Also,assumethatσ2

1=σ 2

2.Use

α=0.05.

18) AsportsanalystclaimsthatthemeanbattingaverageforteamsintheAmericanLeagueisnotequaltothe

meanbattingaverageforteamsintheNationalLeaguebecauseapitcherdoesnotbatintheAmericanLeague.

Thedatalistedbelowarerandom,independent,andcomefrompopulationsthatarenormallydistributed.At

α=0.05,testthesportsanalystʹsclaim.Assumethepopulationvariancesareequal.

AmericanLeague NationalLeague

0.279 0.274 0.271 0.268 0.284 0.267 0.266 0.263

0.265 0.254 0.240 0.261 0.259 0.256

Page186

19) Awomenʹsadvocacygroupclaimsthatwomengolfersreceivesignificantlylessprizemoneythantheirmale

counterpartswhentheywinfirstplaceinaprofessionaltournament.Thedatalistedbelowarethefirstplace

prizemoniesfrommaleandfemaletournamentwinners.Assumethesamplesarerandom,independent,and

comefrompopulationsthatarenormallydistributed.Atα=0.01,testthegroupʹsclaim.Assumethe

populationvariancesarenotequal.

FemaleGolfers

180,000 150,000 240,000 195,000 202,500

120,000 165,000 225,000 150,000 315,000

MaleGolfers

864,000 810,000 1,170,000 810,000 630,000

1,050,000 945,000 1,008,000 900,000 756,000

630,000 900,000

3 ConstructaConfidenceIntervalfortheDifferenceBetweenTwoPopulationMeans

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

Provideanappropriateresponse.

1) Constructa90%confidenceintervalforμ1–μ2.Twosamplesarerandom,independent,andcomefrom

populationsthatarenormallydistributed.Thesamplestatisticsaregivenbelow.Assumethatσ2

1=σ 2

n1=10n2=12

x1=25x2=23

s1=1.5s2=1.9

A) (0.721,3.279) 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random,independent,andcomefrom

populationsthatarenormallydistributedThesamplestatisticsaregivenbelow.Assumethatσ2

1=σ 2

n1=11n2=18

x1=4.8x2=5.2

s1=0.76s2=0.51

A) (–0.883,0.083) 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random,independent,andcomefrom

populationsthatarenormallydistributed.Thesamplestatisticsaregivenbelow.Assumethatσ2

1=σ 2

n1=8n2=7

x1=4.1x2=5.5

s1=0.76s2=2.51

A) (–3.406,0.606) B) (–1.132,1.543) C) (–1.679,1.987) D) (2.112,2.113)

Page187

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

4) AsportsanalystclaimsthatthemeanbattingaverageforteamsintheAmericanLeagueisnotequaltothe

meanbattingaverageforteamsintheNationalLeaguebecauseapitcherdoesnotbatintheAmericanLeague.

Thedatalistedbelowarerandom,independent,andcomefrompopulationsthatarenormallydistributed.

Constructa95%confidenceintervalforthedifferenceinthemeansμ

1–μ2.Assumethepopulationvariances

areequal.

AmericanLeague NationalLeague

0.279 0.274 0.271 0.268 0.284 0.267 0.266 0.263

0.265 0.254 0.240 0.261 0.259 0.256

5) Awomenʹsadvocacygroupclaimsthatwomengolfersreceivesignificantlylessprizemoneythantheirmale

counterpartswhentheywinfirstplaceinaprofessionaltournament.Thedatalistedbelowarethefirstplace

prizemoniesfrommaleandfemaletournamentwinners.Assumethesamplesarerandom,independent,and

comefrompopulationsthatarenormallydistributed.Constructa99%confidenceintervalforthedifferencein

themeansμ1–μ2.Assumethepopulationvariancesarenotequal.

FemaleGolfers

180,000 150,000 240,000 195,000 202,500

120,000 165,000 225,000 150,000 315,000

MaleGolfers

864,000 810,000 1,170,000 810,000 630,000

1,050,000 945,000 1,008,000 900,000 756,000

630,000 900,000

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

6) Astudywasconductedtodetermineifthesalariesofelementaryschoolteachersfromtwoneighboring

districtswereequal.Asampleof15teachersfromeachdistrictwasrandomlyselected.Themeanfromthefirst

districtwas$28,900withastandarddeviationof$2300.Themeanfromtheseconddistrictwas$30,300witha

standarddeviationof$2100.Assumethesamplesarerandom,independent,andcomefrompopulationsthat

arenormallydistributed.Constructa95%confidenceintervalforμ1–μ2.Assumethatσ2

1=σ 2

A) (–3047,247) B) (–2054,238) C) (–2871,567) D) (–4081,597)

8.3 TestingtheDifferenceBetweenMeans(DependentSamples)

1 TestaClaimAbouttheDifferenceBetweenTwoPopulationMeans

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

Provideanappropriateresponse.

1) Findd.Assumethesamplesarerandomanddependent,andthepopulationsarenormallydistributed.

A13 11 30 26 14

B11 7 8 18 5

A) 9.0 B) –5.1 C) 33.1 D) 25.2

Page188

2) Findd.Assumethesamplesarerandomanddependent,andthepopulationsarenormallydistributed.

A2.5 3.5 5.4 2.4 2.5

B 4.9 3.8 3.7 3.6 5.0

A) –0.94 B) –0.76 C) 0.58 D) 0.89

3) Findsd.Assumethesamplesarerandomanddependent,andthepopulationsarenormallydistributed.

A27 25 44 40 28

B25 21 2232 19

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

4) Findsd.Assumethesamplesarerandomanddependent,andthepopulationsarenormallydistributed.

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

B 7.7 6.6 6.5 6.4 7.8

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

5) Findthecriticalvalue,t0

totesttheclaimthatμd=0.Assumethesamplesarerandomanddependent,andthe

populationsarenormallydistributed.Useα=0.05.

A19 17 36 32 20

B17 13 1424 11

A) ±2.776 B) 2.132 C) ±4.604 D) 3.747

6) Findthecriticalvalue,t0

totesttheclaimthatμd=0.Assumethesamplesarerandomanddependent,andthe

populationsarenormallydistributed.Useα=0.01.

A8.2 9.2 11.1 8.1 8.2

B 10.6 9.5 9.4 9.3 10.7

A) ±4.604 B) ±3.747 C) 2.132 D) 0.741

7) Findthecriticalvalue,t0

totesttheclaimthatμd=0.Assumethesamplesarerandomanddependent,andthe

populationsarenormallydistributed.Useα=0.02.

A89.2 11.1 8.1 8.2

B 5.4 4.3 5.2 4.1 5.5

A) ±3.747 B) ±4.604 C) 2.132 D) 0.741

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

8) Testtheclaimthatthepairedsampledataisfromapopulationwithameandifferenceof0.Assumethe

samplesarerandomanddependent,andthepopulationsarenormallydistributed.Useα

=0.05.

A30 28 47 43 31

B28 24 2535 22

9) Testtheclaimthatthepairedsampledataisfromapopulationwithameandifferenceof0.Assumethe

samplesarerandomanddependent,andthepopulationsarenormallydistributed.Useα

=0.01.

A5.6 6.6 8.5 5.5 5.6

B 8.0 6.9 6.8 6.7 8.1

Page189

10) Testtheclaimthatμd=0usingthesamplestatisticsbelow.Assumethesamplesarerandomanddependent,

andthepopulationsarenormallydistributed.Useα=0.05.

Samplestatistics:n=12,d=6.0,sd=1.3

11) Testtheclaimthatμd>0usingthesamplestatisticsbelow.Assumethesamplesarerandomanddependent,

andthepopulationsarenormallydistributed.Useα=0.01.

Samplestatistics:n=15,d=4.0,sd=0.2

12) Testtheclaimthatμd<0usingthesamplestatisticsbelow.Assumethesamplesarerandomanddependent,

andthepopulationsarenormallydistributed.Useα=0.10.

Samplestatistics:n=18,d=-1.5,sd=0.2

13) Testtheclaimthatμd≠0usingthesamplestatisticsbelow.Assumethesamplesarerandomanddependent,

andthepopulationsarenormallydistributed.Useα=0.02.

Samplestatistics:n=13,d=1.1,sd=5.3

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

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

scores.Assumethesamplesarerandomanddependent,andthepopulationsarenormallydistributed.Useα

0.05.

Student 1234567 8 9

Scoresbeforecourse 720 860 850 880 860 710 850 1200 950

Scoresaftercourse 740 860 840 920 890 720 840 1240 970

15) Aweight–liftingcoachclaimsthatweight–lifters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.Assumethesamplesarerandomanddependent,andthepopulationsarenormallydistributed.Useα

=0.05.

Athlete 123456789

Before 215 240 188 212 275 260 225 200 185

After 225 245 188 210 282 275 230 195 190

16) 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.

Assumethesamplesarerandomanddependent,andthepopulationsarenormallydistributed.Useα=0.01.

Subject

Before

After

195

180

225

220

202

210

195

175

170

250

235

205

268

250

190

240

225

Page190

17) Inastudyofeffectivenessofphysicalexerciseonweightloss,20peoplewererandomlyselectedtoparticipate

inaprogramfor30days.Testtheclaimthatexercisehadnobearingonweightloss.Assumethesamplesare

randomanddependent,andthepopulationsarenormallydistributed.Use

α=0.02.

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)Conʹt

Weightafterprogram

(inpounds)Conʹt

186

180

172

173

166

165

184

186

225

240

145

138

208

203

214

203

148

142

174

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

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

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

d.Assumethe

samplesarerandomanddependent,andthepopulationsarenormallydistributed.

Student 1234567 89

Scoresbeforecourse 720 860 850 880 860 710 850 1200 950

Scoresaftercourse 740 860 840 920 890 720 840 1240 970

A) (–30.50,–0.62) B) (–20.34,4.85) C) (–10.32,15.44) D) (1.65,30.59)

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

19) Alocalschooldistrictisconcernedaboutthenumberofschooldaysmissedbyitsteachersduetoillness.A

randomsampleof10teachers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teachers.Assumethesamplesarerandomanddependent,andthepopulationsarenormally

distributed.Useα=0.05.

Teacher

Daysabsentbefore

incentive

Daysabsentafter

incentive

A

B

C

D

E

F

G

H

I

J

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

personlistenstoarelaxationtapeeachevening.Tensubjectsarerandomlyselectedandpretested.Theirblood

pressures,measuredinmillimetersofmercury,arelistedbelow.The10patientsaregiventhetapesandtoldto

listentothem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.Assumethesamplesarerandomanddependent,andthe

populationsarenormallydistributed.Useα=0.01.

Patient

Before

After

1

2

3

4

5

6

7

8

9

10

Page191

2 ConstructaConfidenceIntervalfortheDifferenceBetweenTwoPopulation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datasetsAandB.DatasetsAandBarerandomanddependent,and

thepopulationsarenormallydistributed.Roundtothenearesttenth.

A30 28 47 43 31

824253522

A) (–0.7,18.7) B) (–1.3,9.0) C) (–0.1,12.8) D) (–15.3,15.4)

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

thepopulationsarenormallydistributed.Roundtothenearesttenth.

A5.8 6.8 8.7 5.7 5.8

B 8.2 7.1 7.0 6.9 8.3

A) (–4.5,2.6) B) (–25.1,5.8) C) (–21.3,19.0) D) (–15.1,15.1)

8.4 TestingtheDifferenceBetweenProportions

1 TestaClaimAbout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) Findtheweightedestimate,ptotesttheclaimthatp1=p2.Useα=0.05.Assumethesamplesarerandomand

independent.

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

A) 0.682 B) 0.328 C) 0.238 D) 1.367

2) Findtheweightedestimate,ptotesttheclaimthatp1>p2.Useα=0.01.Assumethesamplesarerandomand

independent.

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

A) 0.367 B) 0.523 C) 0.179 D) 0.633

3) Findtheweightedestimate,p,totesttheclaimthatp1<p2.Useα=0.10.Assumethesamplesarerandomand

independent.

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

A) 0.255 B) 0.730 C) 0.338 D) 1.116

4) Findtheweightedestimate,ptotesttheclaimthatp1≠p2.Useα=0.02.Assumethesamplesarerandomand

independent.

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

A) 0.202 B) 0.789 C) 0.110 D) 0.138

Page192

5) Findthestandardizedteststatistic,ztotesttheclaimthatp1=p2.Assumethesamplesarerandomand

independent.

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

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

6) Findthestandardizedteststatisticestimate,z,totesttheclaimthatp1>p2.Assumethesamplesarerandom

andindependent.

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

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

7) Findthestandardizedteststatistic,z,totesttheclaimthatp1<p2.Assumethesamplesarerandomand

independent.

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

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

8) Findthestandardizedteststatistic,z,totesttheclaimthatp1≠p2.Assumethesamplesarerandomand

independent.

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

A) 5.09 B) 2.80 C) 4.76 D) 3.21

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

9) Testtheclaimthatp1=p2.Useα=0.05.Assumethesamplesarerandomandindependent.

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

10) Testtheclaimthatp1>p2.Useα=0.01.Assumethesamplesarerandomandindependent.

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

11) Testtheclaimthatp1<p2.Useα=0.10.Assumethesamplesarerandomandindependent.

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

12) Testtheclaimthatp1≠p2.Useα=0.02.Assumethesamplesarerandomandindependent.

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

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

stricterguncontrollaws.Inarandomsampleof1000men,60%favoredstricterguncontrollaws.Testtheclaim

thatthepercentageofmenandwomenfavoringstricterguncontrollawsisthesame.Use α=0.05.

14) Arecentsurveyshowedthatinarandomsampleof100elementaryschoolteachers,15smoked.Inarandom

sampleof180highschoolteachers,36smoked.Istheproportionofhighschoolteacherswhosmokegreater

thantheproportionofelementaryteacherswhosmoke?Useα=0.01.

Page193

15) Inarandomsurveyof500doctorsthatpracticespecializedmedicine,20%feltthatthegovernmentshould

controlhealthcare.Inarandomsampleof800doctorsthatweregeneralpractitioners,30%feltthatthe

governmentshouldcontrolhealthcare.Testtheclaimthatthereisadifferenceintheproportions.Useα

=0.10.

16) AnutritionistbelievesthatobesityismoreprevalentamongAmericanadultsthanitwasinthepast.He

discoversthatinastudyconductedintheyear1994,380ofthe1630randomlychosenadultswereclassifiedas

obese.However,inamorerecentstudy,hefinds726outof2350randomlychosenadultswereclassifiedas

obese.Atα=0.05,dothesestudiesprovideevidencetosupportthenutritionistʹsclaimthattheproportionof

obeseadultshassignificantlyincreasedsince1994?

17) Totesttheeffectivenessofanewdrugdesignedtorelievepain,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.

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

helpwithahomeworkassignmentinscience.Asecondsampleof100differentstudentswasaskedthesame

questionforanassignmentinhistory.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claimwhetherthedifference

betweentheproportionsisduetochance.Useα=0.02.

19) IntheinitialtestoftheSalkvaccineforpolio,400,000childrenwererandomly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claimthattheSalkvaccineiseffectiveinloweringthepoliorate.

Useα=0.01.

20) Awell–knownstudyof22,000randomlyselected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.

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21) Ayouthpreventionorganizationisexaminingtheeffectofparentalsmokingonthedecisionoftheirteenagers

tosmoke.Asurveyof1150teenagers,ages11to17yearswhosmokedinthelast30days,wasconducted.The

randomsampleconsistedof500teenagerswhohadatleastoneparentthatsmokedand650whohadparents

thatdidnotsmoke.Theresultsareshowninthefigure.Atα=0.01,canyousupporttheorganizationʹsclaim

thattheproportionofteenswhodecidetosmokeisgreaterwhenoneorbothoftheirparentssmoke?

22) Ayouthpreventionorganizationisexaminingtheeffectofpeerpressureonthedecisionofteenagerstosmoke.

Asurveyof97teenagers,ages11to17yearswhosmokedinthelast30days,wasconducted.Therandom

sampleconsistedof25teenagerswhosaidall/mostoftheirfriendssmoke,40whosaidsomeoftheirfriends

smoke,and32whosaidnoneoftheirfriendssmoke.Theresultsareshowninthefigure.Atα



=0.01,canyou

supporttheorganizationʹsclaimthattheproportionofteenswhodecidetosmokeislowerwhennoneoftheir

friendssmoke?

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2 ConstructaConfidenceInterval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.Assumethesamplesarerandomandindependent.

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.Assumethesamplesarerandomandindependent.

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guncontrollaws,arandomsampleof1000womenshowedthat65%wereinfavorof

stricterguncontrollaws.Inarandomsampleof1000men,60%favoredstricterguncontrollaws.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randomlyselectedmalesand

41%of200randomlyselected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)

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

5) AnutritionistbelievesthatobesityismoreprevalentamongAmericanadultsthanitwasinthepast.He

discoversthatinastudyconductedintheyear1994,380ofthe1630randomlychosenadultswereclassifiedas

obese.However,inamorerecentstudy,hefinds726outof2350randomlychosenadultswereclassifiedas

obese.Constructa95%confidenceintervalforthedifferenceinproportionsp1–p2.

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

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

helpwithahomeworkassignmentinscience.Asecondrandomsampleof100differentstudentswasaskedthe

samequestionforanassignmentinhistory.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)

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Ch.8 HypothesisTestingwithTwoSamples

AnswerKey

8.1 TestingtheDifferenceBetweenMeans(IndependentSamples,σ1andσ2Known)

1 DeterminetheDifferenceBetweenDependentandIndependentSamples

2 TestaClaimAbouttheDifferenceBetweenTwoPopulationMeans

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3 ConstructaConfidenceIntervalfortheDifferenceBetweenTwoPopulationMeans

8.2 TestingtheDifferenceBetweenMeans(IndependentSamples,σ1andσ2Unknown)

1 FindCriticalValues

2 TestaClaimAbouttheDifferenceBetweenTwoPopulationMeans

3 ConstructaConfidenceIntervalfortheDifferenceBetweenTwoPopulationMeans

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8.3 TestingtheDifferenceBetweenMeans(DependentSamples)

1 TestaClaimAbouttheDifferenceBetweenTwoPopulationMeans

2 ConstructaConfidenceIntervalfortheDifferenceBetweenTwoPopulationMeans

8.4 TestingtheDifferenceBetweenProportions

1 TestaClaimAbouttheDifferenceBetweenTwoPopulationProportions

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2 ConstructaConfidenceIntervalfortheDifferenceBetweenTwoPopulationProportions

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