Solutions Manual for Design and Analysis of Experiments, 10th Edition by Douglas C. Montgomery

Solutions Manual for
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Design and Analysis of
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Experiments, 10e Douh h




glasMontgomery (All
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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.




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