Solutions Manual for
k k k
Design and Analysis of
k k k
Experiments, 10e Dou
k k k
glas Montgomery (All
k k k
Chapters)
, SolutionskfromkMontgomery,kD.kC.k(2019)kDesignkandkAnalysiskofkExperiments,kWiley,kN
Y
Chapter 1 I k k
ntroductionk
Solutions
1.1S.k Supposekthatkyoukwantktokdesignkankexperimentktokstudykthekproportionkofkunpoppedkkernelskofkp
opcorn.k Completekstepsk1-
3kofkthekguidelineskforkdesigningkexperimentskinkSectionk1.4.k Arektherekanykmajorksourceskofkvariationkth
atkwouldkbekdifficultktokcontrol?
Stepk1k–kRecognitionkofkandkstatementkofkthekproblem.k Possiblekproblemkstatementkwouldkbek–
kfindkthekbestkcombinationkofkinputskthatkmaximizeskyieldkonkpopcornk–kminimizekunpoppedkkernels.
Stepk2k–
kSelectionkofkthekresponsekvariable.k Possiblekresponseskareknumberkofkunpoppedkkernelskperk100kkernals
kinkexperiment,kweightkofkunpoppedkkernelskversuskthektotalkweightkofkkernelskcooked.
Stepk3k–
kChoicekofkfactors,klevelskandkrange.k Possiblekfactorskandklevelskarekbrandkofkpopcornk(levels:kcheap,kexp
ensive),kagekofkpopcornk(levels:kfresh,kold),ktypekofkcookingkmethodk(levels:kstovetop,kmicrowave),ktemp
eraturek(levels:k150C,k250C),kcookingktimek(levels:k3kminutes,k5kminutes),kamountkofkcookingkoilk(levels,k
1koz,k3koz),ketc.
1.2. Supposekthatkyoukwantktokinvestigatekthekfactorskthatkpotentiallykaffectkcookedkrice.
(a) Whatkwouldkyoukusekaskakresponsekvariablekinkthiskexperiment?k Howkwouldkyoukmeasurek
thekresponse?
(b) Listkallkofkthekpotentialksourceskofkvariabilitykthatkcouldkimpactkthekresponse.
(c) CompletekthekfirstkthreekstepskofkthekguidelineskforkdesigningkexperimentskinkSectionk1.4.
Stepk1k–
kRecognitionkofkandkstatementkofkthekproblem.kStepk2k
–kSelectionkofkthekresponsekvariable.
Stepk3k–kChoicekofkfactors,klevelskandkrange.
1.3. Supposekthatkyoukwantktokcomparekthekgrowthkofkgardenkflowerskwithkdifferentkcondition
skofksunlight,kwater,kfertilizerkandksoilkconditions.k Completekstepsk1-
3kofkthekguidelineskforkdesigningkexperimentskinkSectionk1.4.
Stepk1k–
kRecognitionkofkandkstatementkofkthekproblem.kStepk2k
–kSelectionkofkthekresponsekvariable.
Stepk3k–kChoicekofkfactors,klevelskandkrange.
1-1
, SolutionskfromkMontgomery,kD.kC.k(2019)kDesignkandkAnalysiskofkExperiments,kWiley,kN
Y
1.4. Selectkankexperimentkofkinterestktokyou.k Completekstepsk1-
3kofkthekguidelineskforkdesigningkexperimentskinkSectionk1.4.
1-2
, SolutionskfromkMontgomery,kD.kC.k(2019)kDesignkandkAnalysiskofkExperiments,kWiley,kN
Y
1.5. SearchkthekWorldkWidekWebkforkinformationkaboutkSirkRonaldkA.kFisherkandkhiskwork
konkexperimentalkdesignkinkagriculturalksciencekatkthekRothamstedkExperimentalkStation.
Sampleksearcheskcouldkincludekthekfollowing:
1.6. FindkakWebkSitekforkakbusinesskthatkyoukarekinterestedkin.k Developkaklistkofkfactorskthatkyoukw
ouldkusekinkankexperimentalkdesignktokimprovekthekeffectivenesskofkthiskWebkSite.
1.7. Almostkeveryonekiskconcernedkaboutkthekrisingkpricekofkgasoline.k Constructkakcausekandkeffectk
diagramkidentifyingkthekfactorskthatkpotentiallykinfluencekthekgasolinekmileagekthatkyoukgetkinkyourkcar
.kHowkwouldkyoukgokaboutkconductingkankexperimentktokdeterminekanykofkthesekfactorskactuallykaffect
kyourkgasolinekmileage?
1.8. Whatkiskreplication?k Whykdokwekneedkreplicationkinkankexperiment?k Presentkankexamplekt
hatkillustrateskthekdifferenceskbetweenkreplicationkandkrepeatedkmeasures.
Repetitionkofkthekexperimentalkruns.k Replicationkenableskthekexperimenterktokestimatekthekexperimentalk
error,kandkprovideskmorekprecisekestimatekofkthekmeankforkthekresponsekvariable.
1.9 S.k Whykiskrandomizationkimportantkinkankexperiment?
Tokassurekthekobservations,korkerrors,karekindependentlykdistributedkrandomekvariableskaskrequiredkbykst
atisticalkmethods.k Also,ktok“averagekout”kthekeffectskofkextraneouskfactorskthatkmightkoccurkwhilekrunnin
gkthekexperiment.
1.10 S.kWhatkarekthekpotentialkriskskofkaksingle,klarge,kcomprehensivekexperimentkinkcontrastktokakseque
ntialkapproach?
Thekimportantkfactorskandklevelskareknotkalwayskknownkatkthekbeginningkofkthekexperimentalkprocess.k E
venknewkresponsekvariableskmightkbekdiscoveredkduringkthekexperimentalkprocess.k Bykrunningkaklargekc
omprehensivekexperiment,kvaluablekinformationklearnedkearlykinkthekexperimentalkprocesskcanknotklikely
kbekincorporatedkinkthekremainingkexperimentalkruns.
1-3
k k k
Design and Analysis of
k k k
Experiments, 10e Dou
k k k
glas Montgomery (All
k k k
Chapters)
, SolutionskfromkMontgomery,kD.kC.k(2019)kDesignkandkAnalysiskofkExperiments,kWiley,kN
Y
Chapter 1 I k k
ntroductionk
Solutions
1.1S.k Supposekthatkyoukwantktokdesignkankexperimentktokstudykthekproportionkofkunpoppedkkernelskofkp
opcorn.k Completekstepsk1-
3kofkthekguidelineskforkdesigningkexperimentskinkSectionk1.4.k Arektherekanykmajorksourceskofkvariationkth
atkwouldkbekdifficultktokcontrol?
Stepk1k–kRecognitionkofkandkstatementkofkthekproblem.k Possiblekproblemkstatementkwouldkbek–
kfindkthekbestkcombinationkofkinputskthatkmaximizeskyieldkonkpopcornk–kminimizekunpoppedkkernels.
Stepk2k–
kSelectionkofkthekresponsekvariable.k Possiblekresponseskareknumberkofkunpoppedkkernelskperk100kkernals
kinkexperiment,kweightkofkunpoppedkkernelskversuskthektotalkweightkofkkernelskcooked.
Stepk3k–
kChoicekofkfactors,klevelskandkrange.k Possiblekfactorskandklevelskarekbrandkofkpopcornk(levels:kcheap,kexp
ensive),kagekofkpopcornk(levels:kfresh,kold),ktypekofkcookingkmethodk(levels:kstovetop,kmicrowave),ktemp
eraturek(levels:k150C,k250C),kcookingktimek(levels:k3kminutes,k5kminutes),kamountkofkcookingkoilk(levels,k
1koz,k3koz),ketc.
1.2. Supposekthatkyoukwantktokinvestigatekthekfactorskthatkpotentiallykaffectkcookedkrice.
(a) Whatkwouldkyoukusekaskakresponsekvariablekinkthiskexperiment?k Howkwouldkyoukmeasurek
thekresponse?
(b) Listkallkofkthekpotentialksourceskofkvariabilitykthatkcouldkimpactkthekresponse.
(c) CompletekthekfirstkthreekstepskofkthekguidelineskforkdesigningkexperimentskinkSectionk1.4.
Stepk1k–
kRecognitionkofkandkstatementkofkthekproblem.kStepk2k
–kSelectionkofkthekresponsekvariable.
Stepk3k–kChoicekofkfactors,klevelskandkrange.
1.3. Supposekthatkyoukwantktokcomparekthekgrowthkofkgardenkflowerskwithkdifferentkcondition
skofksunlight,kwater,kfertilizerkandksoilkconditions.k Completekstepsk1-
3kofkthekguidelineskforkdesigningkexperimentskinkSectionk1.4.
Stepk1k–
kRecognitionkofkandkstatementkofkthekproblem.kStepk2k
–kSelectionkofkthekresponsekvariable.
Stepk3k–kChoicekofkfactors,klevelskandkrange.
1-1
, SolutionskfromkMontgomery,kD.kC.k(2019)kDesignkandkAnalysiskofkExperiments,kWiley,kN
Y
1.4. Selectkankexperimentkofkinterestktokyou.k Completekstepsk1-
3kofkthekguidelineskforkdesigningkexperimentskinkSectionk1.4.
1-2
, SolutionskfromkMontgomery,kD.kC.k(2019)kDesignkandkAnalysiskofkExperiments,kWiley,kN
Y
1.5. SearchkthekWorldkWidekWebkforkinformationkaboutkSirkRonaldkA.kFisherkandkhiskwork
konkexperimentalkdesignkinkagriculturalksciencekatkthekRothamstedkExperimentalkStation.
Sampleksearcheskcouldkincludekthekfollowing:
1.6. FindkakWebkSitekforkakbusinesskthatkyoukarekinterestedkin.k Developkaklistkofkfactorskthatkyoukw
ouldkusekinkankexperimentalkdesignktokimprovekthekeffectivenesskofkthiskWebkSite.
1.7. Almostkeveryonekiskconcernedkaboutkthekrisingkpricekofkgasoline.k Constructkakcausekandkeffectk
diagramkidentifyingkthekfactorskthatkpotentiallykinfluencekthekgasolinekmileagekthatkyoukgetkinkyourkcar
.kHowkwouldkyoukgokaboutkconductingkankexperimentktokdeterminekanykofkthesekfactorskactuallykaffect
kyourkgasolinekmileage?
1.8. Whatkiskreplication?k Whykdokwekneedkreplicationkinkankexperiment?k Presentkankexamplekt
hatkillustrateskthekdifferenceskbetweenkreplicationkandkrepeatedkmeasures.
Repetitionkofkthekexperimentalkruns.k Replicationkenableskthekexperimenterktokestimatekthekexperimentalk
error,kandkprovideskmorekprecisekestimatekofkthekmeankforkthekresponsekvariable.
1.9 S.k Whykiskrandomizationkimportantkinkankexperiment?
Tokassurekthekobservations,korkerrors,karekindependentlykdistributedkrandomekvariableskaskrequiredkbykst
atisticalkmethods.k Also,ktok“averagekout”kthekeffectskofkextraneouskfactorskthatkmightkoccurkwhilekrunnin
gkthekexperiment.
1.10 S.kWhatkarekthekpotentialkriskskofkaksingle,klarge,kcomprehensivekexperimentkinkcontrastktokakseque
ntialkapproach?
Thekimportantkfactorskandklevelskareknotkalwayskknownkatkthekbeginningkofkthekexperimentalkprocess.k E
venknewkresponsekvariableskmightkbekdiscoveredkduringkthekexperimentalkprocess.k Bykrunningkaklargekc
omprehensivekexperiment,kvaluablekinformationklearnedkearlykinkthekexperimentalkprocesskcanknotklikely
kbekincorporatedkinkthekremainingkexperimentalkruns.
1-3
