Chapter 07 Write The Null And Alternative Hypotheses 10

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Ch.7 HypothesisTestingwithOneSample

7.1 IntroductiontoHypothesisTestin

1 IntroductiontoHypothesisTesting

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

Provideanappropriateresponse.

1) Thestatementrepresentsaclaim.WriteitscomplementandstatewhichisH0andwhichisHA.

μ=8.3

A) H0:μ=8.3(claim);Ha:μ≠8.3 B) H0:μ ≠8.3 ;Ha:μ=8.3(claim)

C) H0:μ≥8.3(claim);Ha:μ<8.3 D) H0:μ ≤8.3 ;Ha:μ>8.3(claim)

2) Thestatementrepresentsaclaim.WriteitscomplementandstatewhichisH0andwhichisHA.

p≤0.93

A) H0:p≤0.93(claim);Ha:p>0.93 B) H0:p>0.93;Ha:p≤0.93(claim)

C) H0:p=0.93;Ha:p≠0.93(claim) D) H0:p≥0.93 (claim);Ha:p<0.93

3) Thestatementrepresentsaclaim.WriteitscomplementandstatewhichisH0andwhichisHA.

σ<8.2

A) H0:σ≥8.2;Ha:σ<8.2(claim) B) H0:σ <8.2 (claim);Ha:σ≥8.2

C) H0:σ≤8.2(claim);Ha:σ>8.2 D) H0:σ =8.2;Ha:σ≠8.2(claim)

4) Thealternativehypothesisisgivenwithitsgraph.Statethenullhypothesisandsketchitsgraph.

Ha:μ<9

12345678910111234567891011

A) H0:μ≥9

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B) H0:μ≥9

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C) H0:μ≤9

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D) H0:μ>9

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5) Thealternativehypothesisisgivenwithitsgraph.Statethenullhypothesisandsketchitsgraph.

Ha:μ≠5

12345678910111234567891011

A) H0:μ=5

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B) H0:μ≥5

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C) H0:μ≤5

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D) H0:μ>5

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Page150

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

6) ThemeanageofbusdriversinChicagois48.6 years.Writethenullandalternativehypotheses.

7) ThemeanIQofstatisticsteachersisgreaterthan160.Writethenullandalternativehypotheses.

8) ThemeanscoreforallNBAgamesduringaparticularseasonwaslessthan92 pointspergame.Writethenull

andalternativehypotheses.

9) Acandidateforgovernorofaparticularstateclaimstobefavoredbyatleasthalfofthevoters.Writethenull

andalternativehypotheses.

10) ThedeanofamajoruniversityclaimsthatthemeantimeforstudentstoearnaMasterʹsdegreeisatmost3.3

years.Writethenullandalternativehypotheses.

11) Thebuyerofalocalhikingclubstorerecommendsagainstbuyingthenewdigitalaltimetersbecausetheyvary

morethantheoldaltimeters,whichhadastandarddeviationofoneyard.Writethenullandalternative

hypotheses.

12) ThemeanageofbusdriversinChicagois56.9 years.Statethisclaimmathematically.Writethenulland

alternativehypotheses.Identifywhichhypothesisistheclaim.

13) ThemeanIQofstatisticsteachersisgreaterthan140.Statethisclaimmathematically.Writethenulland

alternativehypotheses.Identifywhichhypothesisistheclaim.

14) ThemeanscoreforallNBAgamesduringaparticularseasonwaslessthan106 pointspergame.Statethis

claimmathematically.Writethenullandalternativehypotheses.Identifywhichhypothesisistheclaim.

15) Acandidateforgovernorofaparticularstateclaimstobefavoredbyatleasthalfofthevoters.Statethisclaim

mathematically.Writethenullandalternativehypotheses.Identifywhichhypothesisistheclaim.

16) ThedeanofamajoruniversityclaimsthatthemeantimeforstudentstoearnaMasterʹsdegreeisatmost4.2

years.Statethisclaimmathematically.Writethenullandalternativehypotheses.Identifywhichhypothesisis

theclaim.

17) Thebuyerofalocalhikingclubstorerecommendsagainstbuyingthenewdigitalaltimetersbecausetheyvary

morethantheoldaltimeters,whichhadastandarddeviationofoneyard.Statethisclaimmathematically.

Writethenullandalternativehypotheses.Identifywhichhypothesisistheclaim.

2 IdentifyWhethertoUseaOne–tailedorTwo–tailedTest

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

Provideanappropriateresponse.

1) GivenH0:p≥80%andHa:p<80%,determinewhetherthehypothesistestisleft–tailed,right–tailed,or

two–tailed.

A) left–tailed B) right–tailed C) two–tailed

2) GivenH0:μ≤25andHa:μ>25,determinewhetherthehypothesistestisleft–tailed,right–tailed,or

two–tailed.

A) right–tailed B) left–tailed C) two–tailed

3) Aresearcherclaimsthat71%ofvotersfavorguncontrol.Determinewhetherthehypothesistestforthisclaim

isleft–tailed,right–tailed,ortwo–tailed.

A) two–tailed B) left–tailed C) right–tailed

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4) Abreweryclaimsthatthemeanamountofbeerintheirbottlesisatleast12ounces.Determinewhetherthe

hypothesistestforthisclaimisleft–tailed,right–tailed,ortwo–tailed.

A) left–tailed B) right–tailed C) two–tailed

5) Acarmakerclaimsthatitsnewsub–compactcargetsbetterthan49 milespergallononthehighway.

Determinewhetherthehypothesistestforthisisleft–tailed,right–tailed,ortwo–tailed.

A) right–tailed B) left–tailed C) two–tailed

6) Theownerofaprofessionalbasketballteamclaimsthatthemeanattendanceatgamesisover22,000 and

thereforetheteamneedsanewarena.Determinewhetherthehypothesistestforthisclaimisleft–tailed,

right–tailed,ortwo–tailed.

A) right–tailed B) left–tailed C) two–tailed

7) Anelementaryschoolclaimsthatthestandarddeviationinreadingscoresofitsfourthgradestudentsisless

than3.75.Determinewhetherthehypothesistestforthisclaimisleft–tailed,right–tailed,ortwo–tailed.

A) left–tailed B) right–tailed C) two–tailed

3 IdentifyTypeIandTypeIIErrors

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

Provideanappropriateresponse.

1) ThemeanageofbusdriversinChicagois51.3 years.IdentifythetypeIandtypeIIerrorsforthehypothesis

testofthisclaim.

2) ThemeanIQofstatisticsteachersisgreaterthan130.IdentifythetypeIandtypeIIerrorsforthehypothesis

testofthisclaim.

3) ThemeanscoreforallNBAgamesduringaparticularseasonwaslessthan90 pointspergame.Identifythe

typeIandtypeIIerrorsforthehypothesistestofthisclaim.

4) Acandidateforgovernorofacertainstateclaimstobefavoredbyatleasthalfofthevoters.IdentifythetypeI

andtypeIIerrorsforthehypothesistestofthisclaim.

4 InterpretaDecisionBasedontheResultsofaStatisticalTest

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

Provideanappropriateresponse.

1) ThemeanageofbusdriversinChicagois51.5 years.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μ =51.5.

B) Thereisnotsufficientevidencetorejecttheclaimμ =51.5.

C) Thereissufficientevidencetosupporttheclaimμ=51.5.

D) Thereisnotsufficientevidencetosupporttheclaimμ =51.5.

2) ThemeanageofbusdriversinChicagois50.3 years.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rejecttheclaimμ =50.3.

B) Thereissufficientevidencetorejecttheclaimμ =50.3.

C) Thereissufficientevidencetosupporttheclaimμ=50.3.

D) Thereisnotsufficientevidencetosupporttheclaimμ =50.3.

Page152

3) ThemeanageofbusdriversinChicagoisgreaterthan54.1 years.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μ>54.1.

B) Thereissufficientevidencetorejecttheclaimμ >54.1.

C) Thereisnotsufficientevidencetorejecttheclaimμ >54.1.

D) Thereisnotsufficientevidencetosupporttheclaimμ >54.1.

4) ThemeanageofbusdriversinChicagoisgreaterthan54.4 years.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μ >54.4.

B) Thereissufficientevidencetorejecttheclaimμ >54.4.

C) Thereisnotsufficientevidencetorejecttheclaimμ >54.4.

D) Thereissufficientevidencetosupporttheclaimμ>54.4.

5) ThemeanIQofstatisticsteachersisgreaterthan130.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μ>130.

B) Thereissufficientevidencetorejecttheclaimμ >130.

C) Thereisnotsufficientevidencetorejecttheclaimμ >130.

D) Thereisnotsufficientevidencetosupporttheclaimμ >130.

6) ThemeanIQofstatisticsteachersisgreaterthan110.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μ >110.

B) Thereissufficientevidencetorejecttheclaimμ >110.

C) Thereisnotsufficientevidencetorejecttheclaimμ >110.

D) Thereissufficientevidencetosupporttheclaimμ>110.

7) ThemeanscoreforallNBAgamesduringaparticularseasonwaslessthan104 pointspergame.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μ<104.

B) Thereissufficientevidencetorejecttheclaimμ <104.

C) Thereisnotsufficientevidencetorejecttheclaimμ <104.

D) Thereisnotsufficientevidencetosupporttheclaimμ <104.

8) ThemeanscoreforallNBAgamesduringaparticularseasonwaslessthan104 pointspergame.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μ <104.

B) Thereissufficientevidencetorejecttheclaimμ <104.

C) Thereisnotsufficientevidencetorejecttheclaimμ <104.

D) Thereissufficientevidencetosupporttheclaimμ<104.

9) Acandidateforgovernorofacertainstateclaimstobefavoredbyatleasthalfofthevoters.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ρ ≥0.5.

B) Thereisnotsufficientevidencetorejecttheclaimρ ≥0.5.

C) Thereissufficientevidencetosupporttheclaimρ ≥0.5.

D) Thereisnotsufficientevidencetosupporttheclaimρ ≥0.5.

Page153

10) Acandidateforgovernorofacertainstateclaimstobefavoredbyatleasthalfofthevoters.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rejecttheclaimρ ≥0.5.

B) Thereissufficientevidencetorejecttheclaimρ ≥0.5.

C) Thereissufficientevidencetosupporttheclaimρ ≥0.5.

D) Thereisnotsufficientevidencetosupporttheclaimρ ≥0.5.

11) ThedeanofamajoruniversityclaimsthatthemeantimeforstudentstoearnaMasterʹsdegreeisatmost3.5

years.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μ ≤3.5.

B) Thereisnotsufficientevidencetorejecttheclaimμ ≤3.5.

C) Thereissufficientevidencetosupporttheclaimμ≤3.5.

D) Thereisnotsufficientevidencetosupporttheclaimμ ≤3.5.

12) ThedeanofamajoruniversityclaimsthatthemeantimeforstudentstoearnaMasterʹsdegreeisatmost4.1

years.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rejecttheclaimμ ≤4.1.

B) Thereissufficientevidencetorejecttheclaimμ ≤4.1.

C) Thereissufficientevidencetosupporttheclaimμ≤4.1.

D) Thereisnotsufficientevidencetosupporttheclaimμ ≤4.1.

5 UseConfidenceIntervalstoMakeDecisions

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

Provideanappropriateresponse.

1) GivenH0:μ≤12,forwhichconfidenceintervalshouldyourejectH0?

A) (13,16) B) (11.5,12.5) C) (10,13)

2) GivenH0:p≥0.45,forwhichconfidenceintervalshouldyourejectH0?

A) (0.32,0.40) B) (0.40,0.50) C) (0.42,0.47)

6 Concepts

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

Provideanappropriateresponse.

1) GivenH0:p=0.85andα=0.10,whichlevelofconfidenceshouldyouusetotesttheclaim?

A) 90% B) 95% C) 99% D) 80%

2) GivenH0:μ≥23.5andα=0.05,whichlevelofconfidenceshouldyouusetotesttheclaim?

A) 90% B) 99% C) 80% D) 95%

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7.2 HypothesisTestingfortheMean(σKnown)

1 UseP–valuestoDetermineWhethertoRejecttheNullHypothesis

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

Provideanappropriateresponse.

1) TheP–valueforahypothesistestisP=0.034.DoyourejectorfailtorejectH0whenthelevelofsignificanceis

α=0.01?

A) failtorejectH0

B) rejectH0

C) notsufficientinformationtodecide

2) TheP–valueforahypothesistestisP=0.066.DoyourejectorfailtorejectH0whenthelevelofsignificanceis

α=0.05?

A) failtorejectH0

B) rejectH0

C) notsufficientinformationtodecide

3) TheP–valueforahypothesistestisP=0.006.DoyourejectorfailtorejectH0whenthelevelofsignificanceis

α=0.01?

A) rejectH0

B) failtorejectH0

C) notsufficientinformationtodecide

4) FindtheP–valueforthehypothesistestwiththestandardizedteststatisticz.DecidewhethertorejectH0for

thelevelofsignificanceα.

Right–tailedtest

z=0.52

α=0.05

A) 0.3015;FailtorejectH0B) 0.0195;RejectH0

C) 0.3015;RejectH0D) 0.6030;FailtorejectH0

5) FindtheP–valueforthehypothesistestwiththestandardizedteststatisticz.DecidewhethertorejectH0for

thelevelofsignificanceα.

Right–tailedtest

z=1.43

α=0.05

A) 0.0764;FailtorejectH0B) 0.0764;rejectH0

C) 0.1528;failtorejectH0D) 0.1528;rejectH0

6) FindtheP–valueforthehypothesistestwiththestandardizedteststatisticz.DecidewhethertorejectH0for

thelevelofsignificanceα.

Left–tailedtest

z=–1.83

α=0.05

A) 0.0336;rejectH0B) 0.0672;rejectH0

C) 0.9664;failtorejectH0D) 0.0672;failtorejectH0

Page155

7) FindtheP–valueforthehypothesistestwiththestandardizedteststatisticz.DecidewhethertorejectH0for

thelevelofsignificanceα.

Left–tailedtest

z=–2.05

α=0.05

Theteststatisticinaleft–tailedtestisz=–2.05.

A) 0.0202;rejectH0B) 0.4798;failtorejectH0

C) 0.0404;rejectH0D) 0.0453failtorejectH0

8) FindtheP–valueforthehypothesistestwiththestandardizedteststatisticz.DecidewhethertorejectH0for

thelevelofsignificanceα.

Two–tailedtest

z=1.95

α=0.05

A) 0.0512;failtorejectH0B) 0.0256;rejectH0

C) 0.0512;rejectH0D) 0.9744;failtorejectH0

9) FindtheP–valueforthehypothesistestwiththestandardizedteststatisticz.DecidewhethertorejectH0for

thelevelofsignificanceα.

Two–tailedtest

z=–1.63

α=0.05

A) 0.1032;failtorejectH0B) 0.9484;failtorejectH0

C) 0.0516;rejectH0D) 0.0516;failtorejectH0

2FindCriticalValuesandRejectionRegions

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

Provideanappropriateresponse.

1) Findthecriticalvalueandrejectionregionforthetypeofz–testwithlevelofsignificanceα.

Right–tailedtest,α=0.01

A) z0=2.33;z>2.33 B) z0=2.575;z>2.575

C) z0=1.645;z>1.645 D) z0=1.96;;z>1.96

2) Findthecriticalvalueandrejectionregionforthetypeofz–testwithlevelofsignificanceα.

Two–tailedtest,α=0.01

A) –z0=–2.575,z0=2.575;z<–2.575,z>2.575 B) –z0= –2.33,z0=2.33;z<–2.33,z>2.33

C) –z0=–1.645,z0=1.645;z<–1.645,z>1.645 D) –z0= –1.96,z0=1.96;z<–1.96,z>1.96

3) Findthecriticalvalueandrejectionregionforthetypeofz–testwithlevelofsignificanceα.

Left–tailedtest,α=0.05

A) z0=–1.645;z<–1.645 B) z0= –2.33;z< –2.33

C) z0=–2.575;z<–2.575 D) z0= –1.96;z< –1.96

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4) Findthecriticalvalueandrejectionregionforthetypeofz–testwithlevelofsignificanceα.

Two–tailedtest,α=0.10

A) –z0=–1.645,z0=1.645;z<–1.645,z>1.645 B) –z0= –2.33,z0=2.33;z<–2.33,z>2.33

C) –z0=–2.575,z0=2.575;z<–2.575,z>2.575 D) –z0=–1.96,z0=1.96;z<–1.96,z>1.96

5) Findthecriticalvalueandrejectionregionforthetypeofz–testwithlevelofsignificanceα.

Left–tailedtest,α=0.025

A) z0=–1.96;z<–1.96 B) z0= –2.33;z< –2.33

C) z0=–2.575;z<–2.575 D) z0= –1.645;z< –1.645

6) Findthecriticalvalueandrejectionregionforthetypeofz–testwithlevelofsignificanceα.

Two–tailedtest,α=0.06

A) –z0=–1.88

z0=1.88;z<1.88

z>1.88 B) –z0= –2.33,z0=2.33;z<–2.33,z>2.33

C) –z0=–2.575,z0=2.575;z<–2.575,z>2.575 D) –z0= –1.96,z0=1.96;z<–1.96,z>1.96

3 TestaClaimAboutaMeanUsingP–values

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

Provideanappropriateresponse.

1) Testtheclaimaboutthepopulationmeanμatthelevelofsignificanceα.Assumethepopulationisnormally

distributed.

Claim:μ>28;α=0.05;σ=1.2

Samplestatistics:x=28.3,n=50

A) RejectH0.Thereisenoughevidenceatthe5%levelofsignificancetosupporttheclaim.

B) FailtorejectH0.Thereisnotenoughevidenceatthe5%levelofsignificancetosupporttheclaim.

C) Notenoughinformationtodecide.

2) Testtheclaimaboutthepopulationmeanμatthelevelofsignificanceα.Assumethepopulationisnormally

distributed.

Claim:μ≠35;α=0.05;σ=2.7

Samplestatistics:x=34.1,n=35

A) RejectH0.Thereisenoughevidenceatthe5%levelofsignificancetosupporttheclaim.

B) FailtorejectH0.Thereisnotenoughevidenceatthe5%levelofsignificancetosupporttheclaim.

C) Notenoughinformationtodecide.

3) Testtheclaimaboutthepopulationmeanμatthelevelofsignificanceα.Assumethepopulationisnormally

distributed.

Claim:μ≤47;α=0.01;σ=4.3

Samplestatistics:x=48.8,n=40

A) RejectH0.Thereisenoughevidenceatthe1%levelofsignificancetorejecttheclaim.

B) FailtorejectH0.Thereisenoughevidenceatthe1%levelofsignificancetosupporttheclaim.

C) Notenoughinformationtodecide.

Page157

4) Testtheclaimaboutthepopulationmeanμatthelevelofsignificanceα.Assumethepopulationisnormally

distributed.

Claim:μ=1400;α=0.01;σ=82

Samplestatistics:x=1370,n=35

A) FailtorejectH0.Thereisenoughevidenceatthe1%levelofsignificancetosupporttheclaim.

B) RejectH0.Thereisenoughevidenceatthe1%levelofsignificancetorejecttheclaim.

C) Notenoughinformationtodecide.

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

5) Afastfoodoutletclaimsthatthemeanwaitingtimeinlineislessthan3.8 minutes.Arandomsampleof60

customershasameanof3.7minuteswithapopulationstandarddeviationof0.6minute.Ifα

=0.05,testthe

fastfoodoutletʹsclaim.

4 TestaClaimAboutaMeanUsingRejectionRegions

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

Provideanappropriateresponse.

1) Youwishtotesttheclaimthatμ>33atalevelofsignificanceofα =0.05andaregivensamplestatisticsn=50,

x=33.3.Assumethepopulationstandarddeviationis1.2.Computethevalueofthestandardizedteststatistic.

Roundyouranswertotwodecimalplaces.

A) 1.77 B) 2.31 C) 0.98 D) 3.11

2) Youwishtotesttheclaimthatμ≠14atalevelofsignificanceofα =0.05andaregivensamplestatisticsn=35,

x=13.1.Assumethepopulationstandarddeviationis2.7.Computethevalueofthestandardizedteststatistic.

Roundyouranswertotwodecimalplaces.

A) –1.97 B) –3.12 C) –2.86 D) –1.83

3) Youwishtotesttheclaimthatμ≤24atalevelofsignificanceofα =0.01andaregivensamplestatisticsn=40

x=25.8.Assumethepopulationstandarddeviationis4.3.Computethevalueofthestandardizedteststatistic.

Roundyouranswertotwodecimalplaces.

A) 2.65 B) 3.51 C) 2.12 D) 1.96

4) Youwishtotesttheclaimthatμ=1430 atalevelofsignificanceofα =0.01andaregivensamplestatistics

n=35,x=1400.Assumethepopulationstandarddeviationis82.Computethevalueofthestandardizedtest

statistic.Roundyouranswertotwodecimalplaces.

A) –2.16 B) –3.82 C) –4.67 D) –5.18

5) Supposeyouwanttotesttheclaimthatμ=3.5.Givenasamplesizeofn=40 andalevelofsignificanceof

α=0.05,whenshouldyourejectH0?

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

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

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

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

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6) Supposeyouwanttotesttheclaimthatμ>25.6.Givenasamplesizeofn=55 andalevelofsignificanceof

α=0.01,whenshouldyourejectH0?

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

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

C) RejectH0ifthestandardizedteststatisticisgreaterthan1.28.

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

7) Supposeyouwanttotesttheclaimthatμ<65.4.Givenasamplesizeofn=35andalevelofsignificanceof

α=0.05,whenshouldyourejectH0?

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

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

C) RejectH0ifthestandardizedteststatisticislessthan–1.28.

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

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

8) Testtheclaimthatμ>18,giventhat,σ=1.2,α=0.05andthesamplestatisticsaren=50andx=18.3.

9) Testtheclaimthatμ≠13,giventhatσ=2.7,α=0.05andthesamplestatisticsaren=35andx=12.1.

10) Testtheclaimthatμ≤40,giventhatσ=4.3,α=0.01andthesamplestatisticsaren=40andx=41.8.

11) Testtheclaimthatμ=740,giventhatσ=82,α=0.01andthesamplestatisticsaren=35andx=710

12) Alocalbrewerydistributesbeerinbottleslabeled32 ounces.Agovernmentagencythinksthatthebreweryis

cheatingitscustomers.Theagencyselects50ofthesebottles,measurestheircontents,andobtainsasample

meanof31.7ounceswithapopulationstandarddeviationof0.70ounce.Usea0.01significanceleveltotestthe

agencyʹsclaimthatthebreweryischeatingitscustomers.

13) Amanufacturerclaimsthatthemeanlifetimeofitsfluorescentbulbsis1500 hours.Ahomeownerselects40

bulbsandfindsthemeanlifetimetobe1480hourswithapopulationstandarddeviationof80hours.Testthe

manufacturerʹsclaim.Useα=0.05.

14) Atruckingfirmsuspectsthatthemeanlifetimeofacertaintireitusesislessthan36,000miles.Tocheckthe

claim,thefirmrandomlyselectsandtests54ofthesetiresandgetsameanlifetimeof35,630mileswitha

populationstandarddeviationof1200miles.Atα=0.05,testthetruckingfirmʹsclaim.

15) Alocalpolitician,runningforreelection,claimsthatthemeanprisontimeforcarthievesislessthanthe

required4years.Asampleof80convictedcarthieveswasrandomlyselected,andthemeanlengthofprison

timewasfoundtobe3yearsand6months,withapopulationstandarddeviationof1yearand3months.At

α=0.05,testthepoliticianʹsclaim.

16) Alocalgroupclaimsthatthepoliceissueatleast60speedingticketsadayintheirarea.Toprovetheirpoint,

theyrandomlyselectonemonth.Theirresearchyieldsthenumberofticketsissuedforeachday.Thedataare

listedbelow.Assumethepopulationstandarddeviationis12.2tickets.Atα

=0.01,testthegroupʹsclaim.

70484168695570576083

32607258884859605665

66606842575949707563

Page159

17) Afastfoodoutletclaimsthatthemeanwaitingtimeinlineislessthan3.5minutes.Arandomsampleof60

customershasameanof3.6minuteswithapopulationstandarddeviationof0.6minute.Ifα

=0.05,testthe

fastfoodoutletʹsclaimusingcriticalvaluesandrejectionregions.

18) Afastfoodoutletclaimsthatthemeanwaitingtimeinlineislessthan3.5minutes.Arandomsampleof60

customershasameanof3.6minuteswithapopulationstandarddeviationof0.6minute.Ifα

=0.05,testthe

fastfoodoutletʹsclaimusingconfidenceintervals.

7.3 HypothesisTestingfortheMean(σUnknown)

1 FindCriticalValuesinat–distribution

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

Provideanappropriateresponse.

1) Findthecriticalvalueandrejectionregionforthetypeoft–testwithlevelofsignificanceαandsamplesizen.

Left–tailedtest,α=0.1,n=22

A) t0=–1.323;t<–1.323 B) t0= –1.321;t< –1.321

C) t0=1.323;t>1.323 D) t0= –2.518;t< –2.518

2) Findthecriticalvalueandrejectionregionforthetypeoft–testwithlevelofsignificanceαandsamplesizen.

Right–tailedtest,α=0.1,n=35

A) t0=1.307;t>1.307 B) t0=1.306;t>1.306 C) t0=1.307;t<1.307 D) t0=2.441;t>2.441

3) Findthecriticalvalueandrejectionregionforthetypeoft–testwithlevelofsignificanceαandsamplesizen.

Two–tailedtest,α=0.05,n=38

A) t0=–2.026

t0=2.026;t<–2.026

t>2.026 B) t0= –2.024

t0=2.024;t<–2.024

t>2.024

C) t0=2.026;t>2.026 D) t0= –1.687

t0=1.687;t<–1.687

t>1.687

4) Findthecriticalvaluesforasamplewithn=12 andα =0.01 ifH0:μ =20.

A) ±3.106 B) ±2.201 C) ±1.796 D) ±2.718

2 TestaClaimAboutaMean

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forasamplewithn=12,x=31.2,s=2.2,andα=0.01ifH0:μ=30.Round

youranswertothreedecimalplaces.

A) 1.890 B) 1.991 C) 2.132 D) 2.001

2) Findthestandardizedteststatistictforasamplewithn=10,x=16.5,s=1.3,andα=0.05ifH0:μ≥17.4.

Roundyouranswertothreedecimalplaces.

A) –2.189 B) –3.186 C) –3.010 D) –2.617

3) Findthestandardizedteststatistictforasamplewithn=15,x=7.2,s=0.8,andα=0.05ifH0:μ≤6.9.Round

youranswertothreedecimalplaces.

A) 1.452 B) 1.728 C) 1.631 D) 1.312

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4) Findthestandardizedteststatistictforasamplewithn=20,x=6.9,s=2.0,andα=0.05ifHa:μ<7.3.Round

youranswertothreedecimalplaces.

A) –0.894 B) –0.872 C) –1.265 D) –1.233

5) Findthestandardizedteststatistictforasamplewithn=25,x=28,s=3,andα=0.005ifHa:μ>27.Round

youranswertothreedecimalplaces.

A) 1.667 B) 1.997 C) 1.452 D) 1.239

6) Findthestandardizedteststatistictforasamplewithn=12,x=21.7,s=2.1,andα=0.01ifHa:μ≠22.2.

Roundyouranswertothreedecimalplaces.

A) –0.825 B) –0.008 C) –0.037 D) –0.381

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

7) Testtheclaimaboutthepopulationmeanμatthelevelofsignificanceα.Assumethepopulationisnormally

distributed.

Claimμ=24;α=0.01.Samplestatistics:x=25.2,s=2.2,n=12

8) Testtheclaimaboutthepopulationmeanμatthelevelofsignificanceα.Assumethepopulationisnormally

distributed.

Claimμ≥13.9;α=0.05.Samplestatistics:x=13,s=1.3,n=10

9) Testtheclaimaboutthepopulationmeanμatthelevelofsignificanceα.Assumethepopulationisnormally

distributed.

Claimμ≤6.4;α=0.05.Samplestatistics:x=6.7,s=0.8,n=15

10) Testtheclaimaboutthepopulationmeanμatthelevelofsignificanceα.Assumethepopulationisnormally

distributed.

Claimμ<7.4;α=0.10.Samplestatistics:x=7,s=2.0,n=20

11) Testtheclaimaboutthepopulationmeanμatthelevelofsignificanceα.Assumethepopulationisnormally

distributed.

Claimμ>33;α=0.005.Samplestatistics:x=34,s=3,n=25

12) Testtheclaimaboutthepopulationmeanμatthelevelofsignificanceα.Assumethepopulationisnormally

distributed.

Claimμ=19.3;α=0.01.Samplestatistics:x=18.8,s=2.1,n=12

13) TheMetropolitanBusCompanyclaimsthatthemeanwaitingtimeforabusduringrushhourislessthan5

minutes.Arandomsampleof20waitingtimeshasameanof3.7minuteswithastandarddeviationof2.1

minutes.Atα=0.01,testthebuscompanyʹsclaim.Assumethedistributionisnormallydistributed.

14) Alocalbrewerydistributesbeerinbottleslabeled12ounces.Agovernmentagencythinksthatthebreweryis

cheatingitscustomers.Theagencyselects20ofthesebottles,measurestheircontents,andobtainsasample

meanof11.7ounceswithastandarddeviationof0.7ounce.Usea0.01significanceleveltotesttheagencyʹs

claimthatthebreweryischeatingitscustomers.

Page161

15) Alocalgroupclaimsthatthepoliceissuemorethan60speedingticketsadayintheirarea.Toprovetheir

point,theyrandomlyselecttwoweeks.Theirresearchyieldsthenumberofticketsissuedforeachday.The

dataarelistedbelow.Atα=0.01,testthegroupʹsclaim.

70 48 41 68 69 55 70

57 60 83 32 60 72 58

16) Alocalgroupclaimsthatthepoliceissuemorethan60speedingticketsadayintheirarea.Toprovetheir

point,theyrandomlyselecttwoweeks.Theirresearchyieldsthenumberofticketsissuedforeachday.The

dataarelistedbelow.Atα=0.02,testthegroupʹsclaimusingconfidenceintervals.

70 48 41 68 69 55 70

57 60 83 32 60 72 58

17) Amanufacturerclaimsthatthemeanlifetimeofitsfluorescentbulbsis1400 hours.Ahomeownerselects25

bulbsandfindsthemeanlifetimetobe1390hourswithastandarddeviationof80hours.Testthe

manufacturerʹsclaim.Useα=0.05.

18) Amanufacturerclaimsthatthemeanlifetimeofitsfluorescentbulbsis1000hours.Ahomeownerselects25

bulbsandfindsthemeanlifetimetobe980hourswithastandarddeviationof80hours.Ifα

=0.05,testthe

manufacturerʹsclaimusingconfidenceintervals.

19) Atruckingfirmsuspectsthatthemeanlifeofacertaintireitusesislessthan35,000miles.Tochecktheclaim,

thefirmrandomlyselectsandtests18ofthesetiresandgetsameanlifetimeof34,350mileswithastandard

deviationof1200miles.Atα=0.05,testthetruckingfirmʹsclaim.

3 TestaClaimAboutaMeanUsingaP–value

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

Provideanappropriateresponse.

1) Alocalgroupclaimsthatthepoliceissuemorethan60speedingticketsadayintheirarea.Toprovetheir

point,theyrandomlyselecttwoweeks.Theirresearchyieldsthenumberofticketsissuedforeachday.The

dataarelistedbelow.Atα=0.01,testthegroupʹsclaimusingP–values.

70 48 41 68 69 55 70

57 60 83 32 60 72 58

2) Amanufacturerclaimsthatthemeanlifetimeofitsfluorescentbulbsis1000hours.Ahomeownerselects25

bulbsandfindsthemeanlifetimetobe980hourswithastandarddeviationof80hours.Ifα

=0.05,testthe

manufacturerʹsclaimusingP–values.

3) Afastfoodoutletclaimsthatthemeanwaitingtimeinlineislessthan4.9 minutes.Arandomsampleof20

customershasameanof4.7minuteswithastandarddeviationof0.8minute.Ifα

=0.05,testthefastfood

outletʹsclaimusingP–values.

Page162

4) Alocalschooldistrictclaimsthatthenumberofschooldaysmissedbyitsteachersduetoillnessisbelowthe

nationalaverageofμ=5.Arandomsampleof28teachersprovidedthedatabelow.Atα

=0.05,testthe

districtʹsclaimusingP–values.

0363354135

7312332416

25283125

7.4 HypothesisTestingforProportions

1 TestaClaimAboutaProportion

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

Provideanappropriateresponse.

1) Determinewhetherthenormalsamplingdistributioncanbeused.Theclaimisp>0.015andthesamplesizeis

n=150.

A) Donotusethenormaldistribution. B) Usethenormaldistribution.

2) Determinewhetherthenormalsamplingdistributioncanbeused.Theclaimisp≥0.675andthesamplesizeis

n=42.

A) Usethenormaldistribution. B) Donotusethenormaldistribution.

3) Determinethecriticalvalue,z0

totesttheclaimaboutthepopulationproportionp≠0.325givenn=42

andp

^=0.247.Useα=0.05.

A) ±1.96 B) ±2.575 C) ±1.645 D) ±2.33

4) Determinethestandardizedteststatistic,z,totesttheclaimaboutthepopulationproportionp≥0.132 given

n=48andp

^=0.11.Useα=0.05.

A) -0.45 B) -1.645 C) -0.568 D) -0.124

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

5) Testtheclaimaboutthepopulationproportionp=0.250givenn=48andp

=0.231.Useα=0.01.

6) Fifty–fivepercentofregisteredvotersinacongressionaldistrictareregisteredDemocrats.TheRepublican

candidatetakesapolltoassesshischancesinatwo–candidaterace.Hepolls1200potentialvotersandfinds

that621plantovotefortheRepublicancandidate.DoestheRepublicancandidatehaveachancetowin?Use

α=0.05.

7) Anairlineclaimsthattheno–showrateforpassengersislessthan5%.Inasampleof420randomlyselected

reservations,19wereno–shows.Atα=0.01,testtheairlineʹsclaim.

8) Arecentstudyclaimedthatatleast15%ofjuniorhighstudentsareoverweight.Inasampleof160students,18

werefoundtobeoverweight.Atα=0.05,testtheclaim.

9) Arecentstudyclaimedthatatleast15%ofjuniorhighstudentsareoverweight.Inasampleof160students,18

werefoundtobeoverweight.Ifα=0.05,testtheclaimusingP–values.

10) Arecentstudyclaimedthatatleast15%ofjuniorhighstudentsareoverweight.Inasampleof160students,18

werefoundtobeoverweight.Ifα=0.05,testtheclaimusingconfidenceintervals.

11) Theengineeringschoolatamajoruniversityclaimsthat20%ofitsgraduatesarewomen.Inagraduatingclass

of210students,58werewomen.Doesthissuggestthattheschoolisbelievable?Useα



=0.05.

Page163

12) Acoinistossed1000timesand570headsappear.Atα=0.05,testtheclaimthatthisisnotabiasedcoin.Does

thissuggestthecoinisfair?

13) Atelephonecompanyclaimsthat20%ofitscustomershaveatleasttwotelephonelines.Thecompanyselectsa

randomsampleof500customersandfindsthat88havetwoormoretelephonelines.Atα



=0.05,doesthedata

supporttheclaim?UseaP–value.

14) Atelephonecompanyclaimsthat20%ofitscustomershaveatleasttwotelephonelines.Thecompanyselects

arandomsampleof500customersandfindsthat88havetwoormoretelephonelines.Ifα

=0.05,testthe

companyʹsclaimusingcriticalvaluesandrejectionregions.

15) Atelephonecompanyclaimsthat20%ofitscustomershaveatleasttwotelephonelines.Thecompanyselects

arandomsampleof500customersandfindsthat88havetwoormoretelephonelines.Ifα



=0.05,testthe

companyʹsclaimusingconfidenceintervals.

16) Acoinistossed1000timesand530headsappear.Atα=0.05,testtheclaimthatthisisnotabiasedcoin.Usea

P–value.Doesthissuggestthecoinisfair?

7.5 HypothesisTestingforVarianceandStandardDeviatio

1 FindCriticalValues

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

Provideanappropriateresponse.

1) Findthecriticalvalueandrejectionregionforthetypeofchi–squaretestwithsamplesizenandlevelof

significanceα.

Two–tailedtest,

n=12,α=0.05

A) χ2L=3.816,χ2R=21.920;χ2<3.816,χ2>21.920

B) χ2L=2.603,χ2R=26.757;χ2<2.603,χ2>26.757

C) χ2L=3.053,χ2R=24.725;χ2<3.053,χ2>24.725

D) χ2L=4.575,χ2R=19.675;χ2<4.575,χ2>19.675

2) Findthecriticalvalueandrejectionregionforthetypeofchi–squaretestwithsamplesizenandlevelof

significanceα.

Left–tailedtest,

n=15,α=0.05

A) χ20=6.571;χ2<6.571 B) χ20=4.075;χ2<4.075

C) χ20=4.660;χ2<4.660 D) χ20=5.629;χ2<5.629

3) Findthecriticalvalueandrejectionregionforthetypeofchi–squaretestwithsamplesizenandlevelof

significanceα.

Right–tailedtest,

n=20,α=0.01

A) χ20=36.191;χ2>36.191 B) χ20=27.204;χ2>27.204

C) χ20=30.144;χ2>30.144 D) χ20=32.852;χ2>32.852

Page164

4) Findthecriticalvalueandrejectionregionforthetypeofchi–squaretestwithsamplesizenandlevelof

significanceα.

Right–tailedtest,

n=18,α=0.01

A) χ20=33.409;χ2>33.409 B) χ20=27.587;χ2>27.587

C) χ20=30.181;χ2>30.181 D) χ20=35.718;χ2>35.718

5) Findthecriticalvalueandrejectionregionforthetypeofchi–squaretestwithsamplesizenandlevelof

significanceα.

Left–tailedtest,

n=28,α=0.10

A) χ20=18.114;χ2<18.114 B) χ20=14.573;χ2<14.573

C) χ20=16.151;χ2<16.151 D) χ20=36.741;χ2<36.741

6) Findthecriticalvalueandrejectionregionforthetypeofchi–squaretestwithsamplesizenandlevelof

significanceα.

Two–tailedtest,

n=10,α=0.01

FindthecriticalX2–valuestotesttheclaimσ2≠6.8ifn=10andα=0.01.

A) χ2L=1.735,χ2R=23.589;χ2<1.735,χ2>23.589

B) χ2L=2.088,χ2R=21.666;χ2<2.088,χ2>21.666

C) χ2L=2.700,χ2R=19.023;χ2<2.700,χ2>19.023

D) χ2L=3.325,χ2R=16.919;χ2<3.325,χ2>16.919

2TestClaimsAboutVariancesandStandardDeviations

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

Provideanappropriateresponse.

1) Computethestandardizedteststatistic,X2,totesttheclaimσ2=25.8ifn=12,s2=21.6,andα=0.05.

A) 9.209 B) 12.961 C) 18.490 D) 0.492

2) Computethestandardizedteststatistic,X2,totesttheclaimσ2≥12.6ifn=15,s2=10.5,andα=0.05.

A) 11.667 B) 8.713 C) 12.823 D) 23.891

3) Computethestandardizedteststatistic,X2,totesttheclaimσ2≤16ifn=20,s2=31,andα=0.01.

A) 36.813 B) 9.322 C) 12.82 D) 33.41

4) Computethestandardizedteststatistic,X2,totesttheclaimσ2>15.2ifn=18,s2=21.6,andα=0.01.

A) 24.158 B) 28.175 C) 33.233 D) 43.156

5) Computethestandardizedteststatistic,X2,totesttheclaimσ2<11.2ifn=28,s2=7,andα=0.10.

A) 16.875 B) 14.324 C) 18.132 D) 21.478

6) Computethestandardizedteststatistic,X2totesttheclaimσ2≠40.8ifn=10,s2=45,andα=0.01.

A) 9.926 B) 3.276 C) 4.919 D) 12.008

Page165

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

7) Testtheclaimthatσ2=34.4ifn=12,s2=28.8andα=0.05.Assumethatthepopulationisnormally

distributed.

8) Testtheclaimthatσ2≥16.2ifn=15,s2=13.5,andα=0.05.Assumethatthepopulationisnormally

distributed.

9) Testtheclaimthatσ2≤6.4ifn=20,s2=12.4,andα=0.01.Assumethatthepopulationisnormallydistributed.

10) Testtheclaimthatσ2>9.5ifn=18,s2=13.5,andα=0.01.Assumethatthepopulationisnormally

distributed.

11) Testtheclaimthatσ2<22.4ifn=28,s2=14,andα=0.10.Assumethatthepopulationisnormallydistributed.

12) Testtheclaimthatσ2≠47.6ifn=10,s2=52.5,andα=0.01.Assumethatthepopulationisnormally

distributed.

13) Testtheclaimthatσ=6.21ifn=12,s=5.7

andα =0.05.Assumethatthepopulationisnormallydistributed.

14) Testtheclaimthatσ≥6.7ifn=15,s=6.1

andα =0.05.Assumethatthepopulationisnormallydistributed.

15) Testtheclaimthatσ≤10.74ifn=20,s=14.94

andα =0.01.Assumethatthepopulationisnormally

distributed.

16) Testtheclaimthatσ>2.76ifn=18,s=3.28

andα =0.01.Assumethatthepopulationisnormallydistributed.

17) Testtheclaimthatσ<16.59ifn=28,s=13.09 andα =0.10.Assumethatthepopulationisnormally

distributed.

18) Testtheclaimthatσ≠23.49ifn=10,s=24.66

andα =0.01.Assumethatthepopulationisnormally

distributed.

19) Listedbelowisthenumberofticketsissuedbyalocalpolicedepartment.Assumingthatthedataisnormally

distributed,testtheclaimthatthestandarddeviationforthedatais15tickets.Useα

=0.01.

70 48 41 68 69 55 70

57 60 83 32 60 72 58

20) Theheights(ininches)of20randomlyselectedadultmalesarelistedbelow.Testtheclaimthatthevarianceis

lessthan6.25.Useα=0.05.Assumethepopulationisnormallydistributed.

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

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

21) Theheights(ininches)of20randomlyselectedadultmalesarelistedbelow.Testtheclaimthatthevarianceis

lessthan6.25.Assumethepopulationisnormallydistributed.Useα=0.05andconfidenceintervals.

70 72 71 70 69 73 69 68 70 71

67 71 70 74 69 68 71 71 71 72

Page166

22) Atruckingfirmsuspectsthatthevarianceforacertaintireisgreaterthan1,000,000.Tochecktheclaim,the

firmputs101ofthesetiresonitstrucksandgetsastandarddeviationof1200miles.Atα

=0.05,testthe

truckingfirmʹsclaim.

23) Atruckingfirmsuspectsthatthevarianceforacertaintireisgreaterthan1,000,000.Tochecktheclaim,the

firmputs101ofthesetiresonitstrucksandgetsastandarddeviationof1200miles.Ifα

=0.05,testthe

truckingfirmʹsclaimusingconfidenceintervals.

24) Alocalbankneedsinformationconcerningthestandarddeviationofthecheckingaccountbalancesofits

customers.Frompreviousinformationitwasassumedtobe$250.Arandomsampleof61accountswas

checked.Thestandarddeviationwas$286.20.Atα=0.01,testthebankʹsassumption.Assumethattheaccount

balancesarenormallydistributed.

25) Inonearea,monthlyincomesofcollegegraduateshaveastandarddeviationof$650.Itisbelievedthatthe

standarddeviationofmonthlyincomesofnon–collegegraduatesishigher.Asampleof71non–college

graduatesarerandomlyselectedandfoundtohaveastandarddeviationof$950.Testtheclaimthat

non–collegegraduateshaveahigherstandarddeviation.Useα=0.05.

26) Astatisticsprofessoratanall–womenʹscollegedeterminedthatthestandarddeviationofwomenʹsheightsis

2.5inches.Theprofessorthenrandomlyselected41malestudentsfromanearbyall–malecollegeandfound

thestandarddeviationtobe2.9inches.Testtheprofessorʹsclaimthatthestandarddeviationofmaleheightsis

greaterthan2.5inches.Useα=0.01.

3 TestClaimsAboutVariancesandStandardDeviationsUsingaP–value

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

Provideanappropriateresponse.

1) Theheights(ininches)of20randomlyselectedadultmalesarelistedbelow.Testtheclaimthatthevarianceis

lessthan6.25.Assumethepopulationisnormallydistributed.Useα=0.05andP–values.

70 72 71 70 69 73 69 68 70 71

67 71 70 74 69 68 71 71 71 72

2) Atruckingfirmsuspectsthatthevarianceforacertaintireisgreaterthan1,000,000.Tochecktheclaim,the

firmputs101ofthesetiresonitstrucksandgetsastandarddeviationof1200miles.Ifα

=0.05,testthe

truckingfirmʹsclaimusingP–values.

Page167

Ch.7 HypothesisTestingwithOneSample

AnswerKey

7.1 IntroductiontoHypothesisTestin

1 IntroductiontoHypothesisTesting

2 IdentifyWhethertoUseaOne–tailedorTwo–tailedTest

3 IdentifyTypeIandTypeIIErrors

4 InterpretaDecisionBasedontheResultsofaStatisticalTest

Page168

6 Concepts

7.2 HypothesisTestingfortheMean(σKnown)

1 UseP–valuestoDetermineWhethertoRejecttheNullHypothesis

2 FindCriticalValuesandRejectionRegions

3 TestaClaimAboutaMeanUsingP–values

4TestaClaimAboutaMeanUsingRejectionRegions

Page169

7.3 HypothesisTestingfortheMean(σUnknown)

1 FindCriticalValuesinat–distribution

2 TestaClaimAboutaMean

3 TestaClaimAboutaMeanUsingaP–value

7.4 HypothesisTestingforProportions

1 TestaClaimAboutaProportion

Page170

7.5 HypothesisTestingforVarianceandStandardDeviatio

1 FindCriticalValues

2 TestClaimsAboutVariancesandStandardDeviations

Page171

Page172

3 TestClaimsAboutVariancesandStandardDeviationsUsingaP–value

Page173