Solutions Manual for
h h h
Design and Analysis of
h h h h
Experiments, 10e Douh h
glasMontgomery (All
h h h
Chapters)
, SolutionshfromhMontgomery,hD.hC.h(2019)hDesignhandhAnalysishofhExperiments,hWiley,hNY
Chapter 1 I h h
ntroduction h
Solutions
1.1S.h Supposehthathyouhwanthtohdesignhanhexperimenthtohstudyhthehproportionhofhunpoppedhkernelshofhpopco
rn.h Completehstepsh1-
3hofhthehguidelineshforhdesigninghexperimentshinhSectionh1.4.h Arehtherehanyhmajorhsourceshofhvariationhthathw
ouldhbehdifficulthtohcontrol?
Steph1h–hRecognitionhofhandhstatementhofhthehproblem.h Possiblehproblemhstatementhwouldhbeh–
hfindhthehbesthcombinationhofhinputshthathmaximizesh yieldhonhpopcornh–hminimizehunpoppedhkernels.
Steph2h–
hSelectionhofhthehresponsehvariable.h Possiblehresponsesharehnumberhofhunpoppedhkernelshperh100hkernalshinh
experiment,hweighthofhunpoppedhkernelshversushthehtotalhweighthofhkernelshcooked.
Steph3h–
hChoicehofhfactors,hlevelshandhrange.h Possiblehfactorshandhlevelsharehbrandhofhpopcornh(levels:hcheap,hexpensi
ve),hagehofhpopcornh(levels:hfresh,hold),htypehofhcookinghmethodh(levels:hstovetop,hmicrowave),htemperatureh
(levels:h150C,h250C),hcookinghtimeh(levels:h3hminutes,h5hminutes),hamounthofhcookinghoilh(levels,h1hoz,h3hoz),h
etc.
1.2. Supposehthathyouhwanthtohinvestigatehthehfactorshthathpotentiallyhaffecthcookedhrice.
(a) Whathwouldhyouhusehashahresponsehvariablehinhthishexperiment?h Howhwouldhyouhmeasurehtheh
response?
(b) Listhallhofhthehpotentialhsourceshofhvariabilityhthathcouldhimpacththehresponse.
(c) CompletehthehfirsththreehstepshofhthehguidelineshforhdesigninghexperimentshinhSectionh1.4.
Steph1h–
Recognitionhofhandhstatementhofhthehproblem.hSteph2h–
h
h Selectionhofhthehresponsehvariable.
Steph3h–hChoicehofhfactors,hlevelshandhrange.
1.3. Supposehthathyouhwanthtohcomparehthehgrowthhofhgardenhflowershwithhdifferenthconditionshof
hsunlight,h water,hfertilizerhandhsoilhconditions.h Completehstepsh1-
3hofhthehguidelineshforhdesigninghexperimentshinhSectionh1.4.
Steph1h–
Recognitionhofhandhstatementhofhthehproblem.hSteph2h–
h
h Selectionhofhthehresponsehvariable.
Steph3h–hChoicehofhfactors,hlevelshandhrange.
1-1
, SolutionshfromhMontgomery,hD.hC.h(2019)hDesignhandhAnalysishofhExperiments,hWiley,hNY
1.4. Selecthanhexperimenthofhinteresthtohyou.h Completehstepsh1-
3hofhthehguidelineshforhdesigninghexperimentshinhSectionh1.4.
1-2
, SolutionshfromhMontgomery,hD.hC.h(2019)hDesignhandhAnalysishofhExperiments,hWiley,hNY
1.5. SearchhthehWorldhWidehWebhforhinformationhabouthSirhRonaldhA.hFisherhandhhishworkhon
hexperimentalhdesignhinhagriculturalhsciencehaththehRothamstedhExperimentalhStation.
Samplehsearcheshcouldhincludehthehfollowing:
1.6. FindhahWebhSitehforhahbusinesshthathyouharehinterestedhin.h Develophahlisthofhfactorshthathyouhwouldh
usehinhanhexperimentalhdesignhtohimprovehtheheffectivenesshofhthishWebhSite.
1.7. Almostheveryonehishconcernedhabouththehrisinghpricehofhgasoline.h Constructhahcausehandheffecthdia
gramhidentifyinghthehfactorshthathpotentiallyhinfluencehthehgasolinehmileagehthathyouhgethinhyourhcar.hHowh
wouldhyouhgohabouthconductinghanhexperimenthtohdeterminehanyhofhthesehfactorshactuallyhaffecthyourhgasol
inehmileage?
1.8. Whathishreplication?h Whyhdohwehneedhreplicationhinhanhexperiment?h Presenthanhexamplehthath
illustrateshthehdifferenceshbetweenhreplicationhandhrepeatedhmeasures.
Repetitionhofhthehexperimentalhruns.h Replicationhenableshthehexperimenterhtohestimatehthehexperimentalherr
or,handhprovideshmorehprecisehestimatehofhthehmeanhforhthehresponsehvariable.
1.9 S.h Whyhishrandomizationhimportanthinhanhexperiment?
Tohassurehthehobservations,horherrors,harehindependentlyhdistributedhrandomehvariableshashrequiredhbyhstatist
icalhmethods.h Also,htoh“averagehout”htheheffectshofhextraneoushfactorshthathmighthoccurhwhilehrunninghthehex
periment.
1.10 S.hWhatharehthehpotentialhriskshofhahsingle,hlarge,hcomprehensivehexperimenthinhcontrasthtohahsequential
h approach?
Thehimportanthfactorshandhlevelsharehnothalwayshknownhaththehbeginninghofhthehexperimentalhprocess.h Evenh
newhresponsehvariableshmighthbehdiscoveredhduringhthehexperimentalhprocess.h Byhrunninghahlargehcompreh
ensivehexperiment,hvaluablehinformationhlearnedhearlyhinhthehexperimentalhprocesshcanhnothlikelyhbehincorp
oratedhinhthehremaininghexperimentalhruns.
1-3
, SolutionshfromhMontgomery,hD.hC.h(2019)hDesignhandhAnalysishofhExperiments,hWiley,hNY
Experimentalhrunshcanhbehexpensivehandhtimehconsuming.h Ifhanherrorhwerehtohoccurhwhilehrunninghthehexpe
riment,hthehcosthofhredoinghthehexperimenthishmuchhmorehmanageablehwithhonehofhthehsmallhsequentialhexper
imentshthanhthehlargehcomprehensivehexperiment.
ReservedhProblems
1.1 R.h Havehyouhreceivedhanhofferhtohobtainhahcredithcardhinhthehmail?h Whath“factors”hwerehassociatedhwithh
thehoffer,hsuchhashintroductoryhinteresthrate?h Dohyouhthinkhthehcredithcardhcompanyhishconductinghexperime
ntshtohinvestigatehwhichhfacorshproducththehhighesth positivehresponsehratehtohtheirhoffer?h Whathpotentialhfa
ctorshinhtheh experimenthcanhyouhidentify?
Interesthrate,hcredithlimit,holdhcredithcardhpay-offhamount,hinteresthfreehperiod,hgifthpoints,hothers.
1.2 R.h Whathfactorshdohyouhthinkhanhe-commercehcompanyhcouldhusehinhanhexperimenthinvolvinghtheirhweb
pagehtohencouragehmorehpeoplehtoh“click-through”hintohtheirhsite?
Fonthsize,hfonthtype,himages/icons,hcolor,hspacing,hanimation,hsound/music,hspeed,hothers.
1.3 R.hTwohofhthehleadinghcontributorshtohdesignhofhexperimentshoverhthehlasth60hyearshwerehGeorgehE.hP.
hBoxhandhJ.hStuarthHunter.h SearchhthehWorldhWidehWebhforhinformationhonhthesehtwohindividualshandhb
rieflyhsummarizehtheirhcontributions.
1.4 R.hSupposehthathyouhwanthtohmakehbrownies.h Youhplanhtohusehahbrowniehmix,hbuththereharehahnumberhofh
factorshthathcouldhimpacththehresults.
a. Whathwouldhyouhusehashahresponsehvariable?h Couldhtherehbehmorehthanhonehresponse?hTastehwouldh
probablyhbehthehprimaryhfactor.h Otherhfactorshcouldhbehtexturehandharoma.h Possiblyhahcombinationh
ofhallhthree.
b. Identifyhthehfactorshthathmighthimpacththehresults.h Amounthofhoil,hnumberhofheggs,hamounthofhwa
ter,hcosthofhmixh–hexpensivehorhcheap,hbakinghtemperature,hbakinghtime,htypehofhpanh–
hglasshorhmetal.
c. CompletehthehfirsththreehstepshofhthehguidelineshforhdesigninghexperimentshinhSectionh1-4.
1. ProblemhStatementh–
hTohmaximizehbrowniehtastiness.hOrhtohmakehthehbesthbrownie hwhileh minimizinghcosth(Ca
nhahcheaphmixhgivehthehresultshofhanhexpensivehone?)
2. ResponsehVariableh–
hTastinesshishthehprimaryhresponse.h Secondaryhresponseshcouldhalsohbehtexturehandharoma.
3. Choicehofhfactors,hlevelshandhrangeh–
hforhthehmaximizehbrowniehtastiness:h Mixhcosth(cheap,hexpensive),hnumberhofheggsh(2,3),ham
ounthofhoilh(1/2hcup,h¾hcup),hpanhtypeh(glass,hmetal),hovenhtemph(350,h375),hbakehtimeh(35hmi
n,h45hmin).h Onehmighthwanthtohreducehthehnumberhofhfactorshfromh6htoh3-
4htohreducehthehnumberhofhexperimentalhruns.
1-4
, SolutionshfromhMontgomery,hD.hC.h(2019)hDesignhandhAnalysishofhExperiments,hWiley,hNY
Chapter 2 h
Simple Comparative Experiments
h h
Solutions
2.1.
Computerhoutputhforhahrandomhsamplehofhdatahishshownhbelow.h Somehofhthehquantitiesharehmissing.h
Computehthehvalueshofhthehmissinghquantities.
Variable N Mean SEhMean Std.hDev. Variance Minimum Maximum
Y 9 19.96 ? 3.12 ? 15.94 27.16
SEhMeanh=h1.04 Varianceh=h9.73
2.2S.h Computerhoutputhforhahrandomhsamplehofhdatahishshownhbelow.h Somehofhthehquantitiesharehmissing.h
Computehthehvalueshofhthehmissinghquantities.
Variable N Mean SEhMean Std.hDev. Sum
Y 16 ? 0.159 ? 399.851
Meanh=h24.991 Std.hDev.h=h0.636
2.3. Supposeh thath wehareh testinghH0:h µh =h µ0h versush H1:h µh ≠hµ0.h Calculateh theh P-
valuehforhtheh followinghobservedhvalueshofhthehtesthstatistic:
(a) Z0h =h2.25 P-valueh=h0.02445
(b) Z0h =h1.55 P-valueh=h0.12114
(c) Z0h =h2.10 P-valueh=h0.03573
(d) Z0h =h1.95 P-valueh=h0.05118
(e) Z0h =h-0.10 P-valueh=h0.92034
2.4S.h Supposeh thathweh arehtestingh H0:h µh =h µ0h versush H1:h µh >h µ0.h Calculateh theh P-
valuehforh theh followinghobservedhvalueshofhthehtesthstatistic:
(a) Z0h =h2.45 P-valueh=h0.00714
(b) Z0h =h-1.53 P-valueh=h0.93699
2-1
, SolutionshfromhMontgomery,hD.hC.h(2019)hDesignhandhAnalysishofhExperiments,hWiley,hNY
(c) Z0h =h2.15 P-valueh=h0.01578
(d) Z0h =h1.95 P-valueh=h0.02559
(e) Z0h =h-0.25 P-valueh=h0.59871
2.5. SupposehthathweharehtestinghH0:hµ1h=hµ2hversushH1:hµ1h=hµ2hwithhahsamplehsizehofhn1h =hn2h=h12.h Both
hsamplehvariancesharehunknownhbuthassumedhequal.h FindhboundshonhthehP-
valuehforhthehfollowinghobservedhvalueshofhthehtesthstatistic:
(a) t0h =h2.30 TablehP-valueh=h0.02,h0.05 ComputerhP-valueh=h0.0313
(b) t0h =h3.41 TablehP-valueh=h0.002,h0.005 ComputerhP-valueh=h0.0025
(c) t0h =h1.95 TablehP-valueh=h0.1,h0.05 ComputerhP-valueh=h0.0640
(d) t0h =h-2.45 TablehP-valueh=h 0.05,h0.02 ComputerhP-
valueh=h0.0227hNotehthaththehdegreeshofhfreedomhish(12h+12)h–h2h=h22.h Thishishahtwo-
sidedhtest
2.6. SupposehthathweharehtestinghH0:hµ1h=hµ2hversushH1:hµ1h>hµ2hwithhahsamplehsizehofhn1h =hn2h=h10.h Both
hsamplehvariancesharehunknownhbuthassumedhequal.h FindhboundshonhthehP-
valuehforhthehfollowinghobservedhvalueshofhthehtesthstatistic:
(a) t0h =h2.31 TablehP-valueh=h0.01,h0.025 ComputerhP-valueh=h0.01648
(b) t0h =h3.60 TablehP-valueh=h0.001,h0.0005 ComputerhP-valueh=h0.00102
(c) t0h =h1.95 TablehP-valueh=h0.05,h0.025 ComputerhP-valueh=h0.03346
(d) t0h =h2.19 TablehP-valueh=h0.01,h0.025 ComputerhP-
valueh=h0.02097hNotehthaththehdegreeshofhfreedomhish(10h+10)h–h2h=h18.h Thishishahone-
sidedhtest.
2.7. Considerhthehfollowinghsamplehdata:h 9.37,h13.04,h11.69,h8.21,h11.18,h10.41,h13.15,h11.51,h13.21,hand
7.75.h Ishithreasonablehtohassumehthaththishdatahishfromhahnormalhdistribution?h Ishtherehevidencehtohsupporthah
claimhthaththehmeanhofhthehpopulationhish10?
MinitabhOutput
2-2
h h h
Design and Analysis of
h h h h
Experiments, 10e Douh h
glasMontgomery (All
h h h
Chapters)
, SolutionshfromhMontgomery,hD.hC.h(2019)hDesignhandhAnalysishofhExperiments,hWiley,hNY
Chapter 1 I h h
ntroduction h
Solutions
1.1S.h Supposehthathyouhwanthtohdesignhanhexperimenthtohstudyhthehproportionhofhunpoppedhkernelshofhpopco
rn.h Completehstepsh1-
3hofhthehguidelineshforhdesigninghexperimentshinhSectionh1.4.h Arehtherehanyhmajorhsourceshofhvariationhthathw
ouldhbehdifficulthtohcontrol?
Steph1h–hRecognitionhofhandhstatementhofhthehproblem.h Possiblehproblemhstatementhwouldhbeh–
hfindhthehbesthcombinationhofhinputshthathmaximizesh yieldhonhpopcornh–hminimizehunpoppedhkernels.
Steph2h–
hSelectionhofhthehresponsehvariable.h Possiblehresponsesharehnumberhofhunpoppedhkernelshperh100hkernalshinh
experiment,hweighthofhunpoppedhkernelshversushthehtotalhweighthofhkernelshcooked.
Steph3h–
hChoicehofhfactors,hlevelshandhrange.h Possiblehfactorshandhlevelsharehbrandhofhpopcornh(levels:hcheap,hexpensi
ve),hagehofhpopcornh(levels:hfresh,hold),htypehofhcookinghmethodh(levels:hstovetop,hmicrowave),htemperatureh
(levels:h150C,h250C),hcookinghtimeh(levels:h3hminutes,h5hminutes),hamounthofhcookinghoilh(levels,h1hoz,h3hoz),h
etc.
1.2. Supposehthathyouhwanthtohinvestigatehthehfactorshthathpotentiallyhaffecthcookedhrice.
(a) Whathwouldhyouhusehashahresponsehvariablehinhthishexperiment?h Howhwouldhyouhmeasurehtheh
response?
(b) Listhallhofhthehpotentialhsourceshofhvariabilityhthathcouldhimpacththehresponse.
(c) CompletehthehfirsththreehstepshofhthehguidelineshforhdesigninghexperimentshinhSectionh1.4.
Steph1h–
Recognitionhofhandhstatementhofhthehproblem.hSteph2h–
h
h Selectionhofhthehresponsehvariable.
Steph3h–hChoicehofhfactors,hlevelshandhrange.
1.3. Supposehthathyouhwanthtohcomparehthehgrowthhofhgardenhflowershwithhdifferenthconditionshof
hsunlight,h water,hfertilizerhandhsoilhconditions.h Completehstepsh1-
3hofhthehguidelineshforhdesigninghexperimentshinhSectionh1.4.
Steph1h–
Recognitionhofhandhstatementhofhthehproblem.hSteph2h–
h
h Selectionhofhthehresponsehvariable.
Steph3h–hChoicehofhfactors,hlevelshandhrange.
1-1
, SolutionshfromhMontgomery,hD.hC.h(2019)hDesignhandhAnalysishofhExperiments,hWiley,hNY
1.4. Selecthanhexperimenthofhinteresthtohyou.h Completehstepsh1-
3hofhthehguidelineshforhdesigninghexperimentshinhSectionh1.4.
1-2
, SolutionshfromhMontgomery,hD.hC.h(2019)hDesignhandhAnalysishofhExperiments,hWiley,hNY
1.5. SearchhthehWorldhWidehWebhforhinformationhabouthSirhRonaldhA.hFisherhandhhishworkhon
hexperimentalhdesignhinhagriculturalhsciencehaththehRothamstedhExperimentalhStation.
Samplehsearcheshcouldhincludehthehfollowing:
1.6. FindhahWebhSitehforhahbusinesshthathyouharehinterestedhin.h Develophahlisthofhfactorshthathyouhwouldh
usehinhanhexperimentalhdesignhtohimprovehtheheffectivenesshofhthishWebhSite.
1.7. Almostheveryonehishconcernedhabouththehrisinghpricehofhgasoline.h Constructhahcausehandheffecthdia
gramhidentifyinghthehfactorshthathpotentiallyhinfluencehthehgasolinehmileagehthathyouhgethinhyourhcar.hHowh
wouldhyouhgohabouthconductinghanhexperimenthtohdeterminehanyhofhthesehfactorshactuallyhaffecthyourhgasol
inehmileage?
1.8. Whathishreplication?h Whyhdohwehneedhreplicationhinhanhexperiment?h Presenthanhexamplehthath
illustrateshthehdifferenceshbetweenhreplicationhandhrepeatedhmeasures.
Repetitionhofhthehexperimentalhruns.h Replicationhenableshthehexperimenterhtohestimatehthehexperimentalherr
or,handhprovideshmorehprecisehestimatehofhthehmeanhforhthehresponsehvariable.
1.9 S.h Whyhishrandomizationhimportanthinhanhexperiment?
Tohassurehthehobservations,horherrors,harehindependentlyhdistributedhrandomehvariableshashrequiredhbyhstatist
icalhmethods.h Also,htoh“averagehout”htheheffectshofhextraneoushfactorshthathmighthoccurhwhilehrunninghthehex
periment.
1.10 S.hWhatharehthehpotentialhriskshofhahsingle,hlarge,hcomprehensivehexperimenthinhcontrasthtohahsequential
h approach?
Thehimportanthfactorshandhlevelsharehnothalwayshknownhaththehbeginninghofhthehexperimentalhprocess.h Evenh
newhresponsehvariableshmighthbehdiscoveredhduringhthehexperimentalhprocess.h Byhrunninghahlargehcompreh
ensivehexperiment,hvaluablehinformationhlearnedhearlyhinhthehexperimentalhprocesshcanhnothlikelyhbehincorp
oratedhinhthehremaininghexperimentalhruns.
1-3
, SolutionshfromhMontgomery,hD.hC.h(2019)hDesignhandhAnalysishofhExperiments,hWiley,hNY
Experimentalhrunshcanhbehexpensivehandhtimehconsuming.h Ifhanherrorhwerehtohoccurhwhilehrunninghthehexpe
riment,hthehcosthofhredoinghthehexperimenthishmuchhmorehmanageablehwithhonehofhthehsmallhsequentialhexper
imentshthanhthehlargehcomprehensivehexperiment.
ReservedhProblems
1.1 R.h Havehyouhreceivedhanhofferhtohobtainhahcredithcardhinhthehmail?h Whath“factors”hwerehassociatedhwithh
thehoffer,hsuchhashintroductoryhinteresthrate?h Dohyouhthinkhthehcredithcardhcompanyhishconductinghexperime
ntshtohinvestigatehwhichhfacorshproducththehhighesth positivehresponsehratehtohtheirhoffer?h Whathpotentialhfa
ctorshinhtheh experimenthcanhyouhidentify?
Interesthrate,hcredithlimit,holdhcredithcardhpay-offhamount,hinteresthfreehperiod,hgifthpoints,hothers.
1.2 R.h Whathfactorshdohyouhthinkhanhe-commercehcompanyhcouldhusehinhanhexperimenthinvolvinghtheirhweb
pagehtohencouragehmorehpeoplehtoh“click-through”hintohtheirhsite?
Fonthsize,hfonthtype,himages/icons,hcolor,hspacing,hanimation,hsound/music,hspeed,hothers.
1.3 R.hTwohofhthehleadinghcontributorshtohdesignhofhexperimentshoverhthehlasth60hyearshwerehGeorgehE.hP.
hBoxhandhJ.hStuarthHunter.h SearchhthehWorldhWidehWebhforhinformationhonhthesehtwohindividualshandhb
rieflyhsummarizehtheirhcontributions.
1.4 R.hSupposehthathyouhwanthtohmakehbrownies.h Youhplanhtohusehahbrowniehmix,hbuththereharehahnumberhofh
factorshthathcouldhimpacththehresults.
a. Whathwouldhyouhusehashahresponsehvariable?h Couldhtherehbehmorehthanhonehresponse?hTastehwouldh
probablyhbehthehprimaryhfactor.h Otherhfactorshcouldhbehtexturehandharoma.h Possiblyhahcombinationh
ofhallhthree.
b. Identifyhthehfactorshthathmighthimpacththehresults.h Amounthofhoil,hnumberhofheggs,hamounthofhwa
ter,hcosthofhmixh–hexpensivehorhcheap,hbakinghtemperature,hbakinghtime,htypehofhpanh–
hglasshorhmetal.
c. CompletehthehfirsththreehstepshofhthehguidelineshforhdesigninghexperimentshinhSectionh1-4.
1. ProblemhStatementh–
hTohmaximizehbrowniehtastiness.hOrhtohmakehthehbesthbrownie hwhileh minimizinghcosth(Ca
nhahcheaphmixhgivehthehresultshofhanhexpensivehone?)
2. ResponsehVariableh–
hTastinesshishthehprimaryhresponse.h Secondaryhresponseshcouldhalsohbehtexturehandharoma.
3. Choicehofhfactors,hlevelshandhrangeh–
hforhthehmaximizehbrowniehtastiness:h Mixhcosth(cheap,hexpensive),hnumberhofheggsh(2,3),ham
ounthofhoilh(1/2hcup,h¾hcup),hpanhtypeh(glass,hmetal),hovenhtemph(350,h375),hbakehtimeh(35hmi
n,h45hmin).h Onehmighthwanthtohreducehthehnumberhofhfactorshfromh6htoh3-
4htohreducehthehnumberhofhexperimentalhruns.
1-4
, SolutionshfromhMontgomery,hD.hC.h(2019)hDesignhandhAnalysishofhExperiments,hWiley,hNY
Chapter 2 h
Simple Comparative Experiments
h h
Solutions
2.1.
Computerhoutputhforhahrandomhsamplehofhdatahishshownhbelow.h Somehofhthehquantitiesharehmissing.h
Computehthehvalueshofhthehmissinghquantities.
Variable N Mean SEhMean Std.hDev. Variance Minimum Maximum
Y 9 19.96 ? 3.12 ? 15.94 27.16
SEhMeanh=h1.04 Varianceh=h9.73
2.2S.h Computerhoutputhforhahrandomhsamplehofhdatahishshownhbelow.h Somehofhthehquantitiesharehmissing.h
Computehthehvalueshofhthehmissinghquantities.
Variable N Mean SEhMean Std.hDev. Sum
Y 16 ? 0.159 ? 399.851
Meanh=h24.991 Std.hDev.h=h0.636
2.3. Supposeh thath wehareh testinghH0:h µh =h µ0h versush H1:h µh ≠hµ0.h Calculateh theh P-
valuehforhtheh followinghobservedhvalueshofhthehtesthstatistic:
(a) Z0h =h2.25 P-valueh=h0.02445
(b) Z0h =h1.55 P-valueh=h0.12114
(c) Z0h =h2.10 P-valueh=h0.03573
(d) Z0h =h1.95 P-valueh=h0.05118
(e) Z0h =h-0.10 P-valueh=h0.92034
2.4S.h Supposeh thathweh arehtestingh H0:h µh =h µ0h versush H1:h µh >h µ0.h Calculateh theh P-
valuehforh theh followinghobservedhvalueshofhthehtesthstatistic:
(a) Z0h =h2.45 P-valueh=h0.00714
(b) Z0h =h-1.53 P-valueh=h0.93699
2-1
, SolutionshfromhMontgomery,hD.hC.h(2019)hDesignhandhAnalysishofhExperiments,hWiley,hNY
(c) Z0h =h2.15 P-valueh=h0.01578
(d) Z0h =h1.95 P-valueh=h0.02559
(e) Z0h =h-0.25 P-valueh=h0.59871
2.5. SupposehthathweharehtestinghH0:hµ1h=hµ2hversushH1:hµ1h=hµ2hwithhahsamplehsizehofhn1h =hn2h=h12.h Both
hsamplehvariancesharehunknownhbuthassumedhequal.h FindhboundshonhthehP-
valuehforhthehfollowinghobservedhvalueshofhthehtesthstatistic:
(a) t0h =h2.30 TablehP-valueh=h0.02,h0.05 ComputerhP-valueh=h0.0313
(b) t0h =h3.41 TablehP-valueh=h0.002,h0.005 ComputerhP-valueh=h0.0025
(c) t0h =h1.95 TablehP-valueh=h0.1,h0.05 ComputerhP-valueh=h0.0640
(d) t0h =h-2.45 TablehP-valueh=h 0.05,h0.02 ComputerhP-
valueh=h0.0227hNotehthaththehdegreeshofhfreedomhish(12h+12)h–h2h=h22.h Thishishahtwo-
sidedhtest
2.6. SupposehthathweharehtestinghH0:hµ1h=hµ2hversushH1:hµ1h>hµ2hwithhahsamplehsizehofhn1h =hn2h=h10.h Both
hsamplehvariancesharehunknownhbuthassumedhequal.h FindhboundshonhthehP-
valuehforhthehfollowinghobservedhvalueshofhthehtesthstatistic:
(a) t0h =h2.31 TablehP-valueh=h0.01,h0.025 ComputerhP-valueh=h0.01648
(b) t0h =h3.60 TablehP-valueh=h0.001,h0.0005 ComputerhP-valueh=h0.00102
(c) t0h =h1.95 TablehP-valueh=h0.05,h0.025 ComputerhP-valueh=h0.03346
(d) t0h =h2.19 TablehP-valueh=h0.01,h0.025 ComputerhP-
valueh=h0.02097hNotehthaththehdegreeshofhfreedomhish(10h+10)h–h2h=h18.h Thishishahone-
sidedhtest.
2.7. Considerhthehfollowinghsamplehdata:h 9.37,h13.04,h11.69,h8.21,h11.18,h10.41,h13.15,h11.51,h13.21,hand
7.75.h Ishithreasonablehtohassumehthaththishdatahishfromhahnormalhdistribution?h Ishtherehevidencehtohsupporthah
claimhthaththehmeanhofhthehpopulationhish10?
MinitabhOutput
2-2
