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
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
