Solutions Manual for il il
Design and Analysis
il il il
of Experiments, 10e
il il il
il DouglasMontgomery il
(All Chapters)
il il
, Solutions ilfrom ilMontgomery, ilD. ilC. il(2019) ilDesign iland ilAnalysis ilof ilExperiments,
ilWiley, ilNY
Chapter il1
Introductio
il
n ilSolutions
1.1S. i l Suppose ilthat ilyou ilwant ilto ildesign ilan ilexperiment ilto ilstudy ilthe ilproportion ilof ilunpopped
ilkernels ilof ilpopcorn. i l Complete ilsteps il1-3 ilof ilthe ilguidelines ilfor ildesigning ilexperiments ilin ilSection
il1.4. i l Are ilthere ilany ilmajor ilsources ilof ilvariation ilthat ilwould ilbe ildifficult ilto ilcontrol?
Step il1 il– ilRecognition ilof iland ilstatement ilof ilthe ilproblem. i l Possible ilproblem ilstatement ilwould ilbe
il– ilfind ilthe ilbest ilcombination ilof ilinputs ilthat ilmaximizes ilyield ilon ilpopcorn il– ilminimize ilunpopped
ilkernels.
Step il2 il– ilSelection ilof ilthe ilresponse ilvariable. i l Possible ilresponses ilare ilnumber ilof ilunpopped
ilkernels ilper il100 ilkernals ilin ilexperiment, ilweight ilof ilunpopped ilkernels ilversus ilthe iltotal ilweight ilof
ilkernels ilcooked.
Step il3 il– ilChoice ilof ilfactors, illevels iland ilrange. i l Possible ilfactors iland illevels ilare ilbrand ilof ilpopcorn
il(levels: ilcheap, ilexpensive), ilage ilof ilpopcorn il(levels: ilfresh, ilold), iltype ilof ilcooking ilmethod il(levels:
ilstovetop, ilmicrowave), iltemperature il(levels: il150C, il250C), ilcooking iltime il(levels: il3 ilminutes, il5
ilminutes), ilamount ilof ilcooking iloil il(levels, il1 iloz, il3 iloz), iletc.
1.2. Suppose ilthat ilyou ilwant ilto ilinvestigate ilthe ilfactors ilthat ilpotentially ilaffect ilcooked ilrice.
(a) What ilwould ilyou iluse ilas ila ilresponse ilvariable ilin ilthis ilexperiment? i l How ilwould ilyou
ilmeasure ilthe ilresponse?
(b) List ilall ilof ilthe ilpotential ilsources ilof ilvariability ilthat ilcould ilimpact ilthe ilresponse.
(c) Complete ilthe ilfirst ilthree ilsteps ilof ilthe ilguidelines ilfor ildesigning ilexperiments ilin ilSection il1.4.
Step il1 il– ilRecognition ilof iland ilstatement ilof ilthe
ilproblem. ilStep il2 il– ilSelection ilof ilthe ilresponse
ilvariable.
Step il3 il– ilChoice ilof ilfactors, illevels iland ilrange.
1.3. Suppose ilthat ilyou ilwant ilto ilcompare ilthe ilgrowth ilof ilgarden ilflowers ilwith ildifferent
ilconditions ilof ilsunlight, ilwater, ilfertilizer iland ilsoil ilconditions. i l Complete ilsteps il1-3 ilof ilthe
ilguidelines ilfor ildesigning ilexperiments ilin ilSection il1.4.
Step il1 il– ilRecognition ilof iland ilstatement ilof ilthe
ilproblem. ilStep il2 il– ilSelection ilof ilthe ilresponse
ilvariable.
Step il3 il– ilChoice ilof ilfactors, illevels iland ilrange.
1-1
, Solutions ilfrom ilMontgomery, ilD. ilC. il(2019) ilDesign iland ilAnalysis ilof ilExperiments,
1.4. Select ilanilNY
ilWiley, ilexperiment ilof ilinterest ilto ilyou. i l Complete ilsteps il1-3 ilof ilthe ilguidelines
ilfor ildesigning ilexperiments ilin ilSection il1.4.
1-2
, Solutions ilfrom ilMontgomery, ilD. ilC. il(2019) ilDesign iland ilAnalysis ilof ilExperiments,
ilWiley, ilNY
1.5. Search ilthe ilWorld ilWide ilWeb ilfor ilinformation ilabout ilSir ilRonald ilA. ilFisher iland
ilhis ilwork ilon ilexperimental ildesign ilin ilagricultural ilscience ilat ilthe ilRothamsted
ilExperimental ilStation.
Sample ilsearches ilcould ilinclude ilthe ilfollowing:
1.6. Find ila ilWeb ilSite ilfor ila ilbusiness ilthat ilyou ilare ilinterested ilin. i l Develop ila illist ilof ilfactors
ilthat ilyou ilwould iluse ilin ilan ilexperimental ildesign ilto ilimprove ilthe ileffectiveness ilof ilthis ilWeb
ilSite.
1.7. Almost ileveryone ilis ilconcerned ilabout ilthe ilrising ilprice ilof ilgasoline. i l Construct ila ilcause
iland ileffect ildiagram ilidentifying ilthe ilfactors ilthat ilpotentially ilinfluence ilthe ilgasoline ilmileage
ilthat ilyou ilget ilin ilyour ilcar. ilHow ilwould ilyou ilgo ilabout ilconducting ilan ilexperiment ilto ildetermine
ilany ilof ilthese ilfactors ilactually ilaffect ilyour ilgasoline ilmileage?
1.8. What ilis ilreplication? i l Why ildo ilwe ilneed ilreplication ilin ilan ilexperiment? i l Present ilan
ilexample ilthat ilillustrates ilthe ildifferences ilbetween ilreplication iland ilrepeated ilmeasures.
Repetition ilof ilthe ilexperimental ilruns. i l Replication ilenables ilthe ilexperimenter ilto ilestimate ilthe
ilexperimental ilerror, iland ilprovides ilmore ilprecise ilestimate ilof ilthe ilmean ilfor ilthe ilresponse
ilvariable.
1.9 S. i l Why ilis ilrandomization ilimportant ilin ilan ilexperiment?
To ilassure ilthe ilobservations, ilor ilerrors, ilare ilindependently ildistributed ilrandome ilvariables ilas
ilrequired ilby ilstatistical ilmethods. i l Also, ilto il“average ilout” ilthe ileffects ilof ilextraneous ilfactors ilthat
ilmight iloccur ilwhile ilrunning ilthe ilexperiment.
1.10 S. ilWhat ilare ilthe ilpotential ilrisks ilof ila ilsingle, illarge, ilcomprehensive ilexperiment ilin ilcontrast ilto
ila ilsequential ilapproach?
The ilimportant ilfactors iland illevels ilare ilnot ilalways ilknown ilat ilthe ilbeginning ilof ilthe ilexperimental
ilprocess. i l Even ilnew ilresponse ilvariables ilmight ilbe ildiscovered ilduring ilthe ilexperimental ilprocess.
i l By ilrunning ila illarge ilcomprehensive ilexperiment, ilvaluable ilinformation illearned ilearly ilin ilthe
ilexperimental ilprocess ilcan ilnot illikely ilbe ilincorporated ilin ilthe ilremaining ilexperimental ilruns.
1-3
Design and Analysis
il il il
of Experiments, 10e
il il il
il DouglasMontgomery il
(All Chapters)
il il
, Solutions ilfrom ilMontgomery, ilD. ilC. il(2019) ilDesign iland ilAnalysis ilof ilExperiments,
ilWiley, ilNY
Chapter il1
Introductio
il
n ilSolutions
1.1S. i l Suppose ilthat ilyou ilwant ilto ildesign ilan ilexperiment ilto ilstudy ilthe ilproportion ilof ilunpopped
ilkernels ilof ilpopcorn. i l Complete ilsteps il1-3 ilof ilthe ilguidelines ilfor ildesigning ilexperiments ilin ilSection
il1.4. i l Are ilthere ilany ilmajor ilsources ilof ilvariation ilthat ilwould ilbe ildifficult ilto ilcontrol?
Step il1 il– ilRecognition ilof iland ilstatement ilof ilthe ilproblem. i l Possible ilproblem ilstatement ilwould ilbe
il– ilfind ilthe ilbest ilcombination ilof ilinputs ilthat ilmaximizes ilyield ilon ilpopcorn il– ilminimize ilunpopped
ilkernels.
Step il2 il– ilSelection ilof ilthe ilresponse ilvariable. i l Possible ilresponses ilare ilnumber ilof ilunpopped
ilkernels ilper il100 ilkernals ilin ilexperiment, ilweight ilof ilunpopped ilkernels ilversus ilthe iltotal ilweight ilof
ilkernels ilcooked.
Step il3 il– ilChoice ilof ilfactors, illevels iland ilrange. i l Possible ilfactors iland illevels ilare ilbrand ilof ilpopcorn
il(levels: ilcheap, ilexpensive), ilage ilof ilpopcorn il(levels: ilfresh, ilold), iltype ilof ilcooking ilmethod il(levels:
ilstovetop, ilmicrowave), iltemperature il(levels: il150C, il250C), ilcooking iltime il(levels: il3 ilminutes, il5
ilminutes), ilamount ilof ilcooking iloil il(levels, il1 iloz, il3 iloz), iletc.
1.2. Suppose ilthat ilyou ilwant ilto ilinvestigate ilthe ilfactors ilthat ilpotentially ilaffect ilcooked ilrice.
(a) What ilwould ilyou iluse ilas ila ilresponse ilvariable ilin ilthis ilexperiment? i l How ilwould ilyou
ilmeasure ilthe ilresponse?
(b) List ilall ilof ilthe ilpotential ilsources ilof ilvariability ilthat ilcould ilimpact ilthe ilresponse.
(c) Complete ilthe ilfirst ilthree ilsteps ilof ilthe ilguidelines ilfor ildesigning ilexperiments ilin ilSection il1.4.
Step il1 il– ilRecognition ilof iland ilstatement ilof ilthe
ilproblem. ilStep il2 il– ilSelection ilof ilthe ilresponse
ilvariable.
Step il3 il– ilChoice ilof ilfactors, illevels iland ilrange.
1.3. Suppose ilthat ilyou ilwant ilto ilcompare ilthe ilgrowth ilof ilgarden ilflowers ilwith ildifferent
ilconditions ilof ilsunlight, ilwater, ilfertilizer iland ilsoil ilconditions. i l Complete ilsteps il1-3 ilof ilthe
ilguidelines ilfor ildesigning ilexperiments ilin ilSection il1.4.
Step il1 il– ilRecognition ilof iland ilstatement ilof ilthe
ilproblem. ilStep il2 il– ilSelection ilof ilthe ilresponse
ilvariable.
Step il3 il– ilChoice ilof ilfactors, illevels iland ilrange.
1-1
, Solutions ilfrom ilMontgomery, ilD. ilC. il(2019) ilDesign iland ilAnalysis ilof ilExperiments,
1.4. Select ilanilNY
ilWiley, ilexperiment ilof ilinterest ilto ilyou. i l Complete ilsteps il1-3 ilof ilthe ilguidelines
ilfor ildesigning ilexperiments ilin ilSection il1.4.
1-2
, Solutions ilfrom ilMontgomery, ilD. ilC. il(2019) ilDesign iland ilAnalysis ilof ilExperiments,
ilWiley, ilNY
1.5. Search ilthe ilWorld ilWide ilWeb ilfor ilinformation ilabout ilSir ilRonald ilA. ilFisher iland
ilhis ilwork ilon ilexperimental ildesign ilin ilagricultural ilscience ilat ilthe ilRothamsted
ilExperimental ilStation.
Sample ilsearches ilcould ilinclude ilthe ilfollowing:
1.6. Find ila ilWeb ilSite ilfor ila ilbusiness ilthat ilyou ilare ilinterested ilin. i l Develop ila illist ilof ilfactors
ilthat ilyou ilwould iluse ilin ilan ilexperimental ildesign ilto ilimprove ilthe ileffectiveness ilof ilthis ilWeb
ilSite.
1.7. Almost ileveryone ilis ilconcerned ilabout ilthe ilrising ilprice ilof ilgasoline. i l Construct ila ilcause
iland ileffect ildiagram ilidentifying ilthe ilfactors ilthat ilpotentially ilinfluence ilthe ilgasoline ilmileage
ilthat ilyou ilget ilin ilyour ilcar. ilHow ilwould ilyou ilgo ilabout ilconducting ilan ilexperiment ilto ildetermine
ilany ilof ilthese ilfactors ilactually ilaffect ilyour ilgasoline ilmileage?
1.8. What ilis ilreplication? i l Why ildo ilwe ilneed ilreplication ilin ilan ilexperiment? i l Present ilan
ilexample ilthat ilillustrates ilthe ildifferences ilbetween ilreplication iland ilrepeated ilmeasures.
Repetition ilof ilthe ilexperimental ilruns. i l Replication ilenables ilthe ilexperimenter ilto ilestimate ilthe
ilexperimental ilerror, iland ilprovides ilmore ilprecise ilestimate ilof ilthe ilmean ilfor ilthe ilresponse
ilvariable.
1.9 S. i l Why ilis ilrandomization ilimportant ilin ilan ilexperiment?
To ilassure ilthe ilobservations, ilor ilerrors, ilare ilindependently ildistributed ilrandome ilvariables ilas
ilrequired ilby ilstatistical ilmethods. i l Also, ilto il“average ilout” ilthe ileffects ilof ilextraneous ilfactors ilthat
ilmight iloccur ilwhile ilrunning ilthe ilexperiment.
1.10 S. ilWhat ilare ilthe ilpotential ilrisks ilof ila ilsingle, illarge, ilcomprehensive ilexperiment ilin ilcontrast ilto
ila ilsequential ilapproach?
The ilimportant ilfactors iland illevels ilare ilnot ilalways ilknown ilat ilthe ilbeginning ilof ilthe ilexperimental
ilprocess. i l Even ilnew ilresponse ilvariables ilmight ilbe ildiscovered ilduring ilthe ilexperimental ilprocess.
i l By ilrunning ila illarge ilcomprehensive ilexperiment, ilvaluable ilinformation illearned ilearly ilin ilthe
ilexperimental ilprocess ilcan ilnot illikely ilbe ilincorporated ilin ilthe ilremaining ilexperimental ilruns.
1-3
