Solutions Manual for Design and Analysis of
Experiments, 10e by Douglas Montgomery All
Chapters
, Chapter`1`I
ntroduction`
Solutions
1.1S.` Suppose`that`you`want`to`design`an`experiment`to`study`the`proportion`of`unpopped`kernels`of`popc
orn.` Complete`steps`1-
3`of`the`guidelines`for`designing`experiments`in`Section`1.4.` Are`there`any`major`sources`of`variation`that`w
ould`be`difficult`to`control?
Step`1`–`Recognition`of`and`statement`of`the`problem.` Possible`problem`statement`would`be`–
`find`the`best`combination`of`inputs`that`maximizes`yield`on`popcorn`–`minimize`unpopped`kernels.
Step`2`–
`Selection`of`the`response`variable.` Possible`responses`are`number`of`unpopped`kernels`per`100`kernals`in`
experiment,`weight`of`unpopped`kernels`versus`the`total`weight`of`kernels`cooked.
Step`3`–
`Choice`of`factors,`levels`and`range.` Possible`factors`and`levels`are`brand`of`popcorn`(levels:`cheap,`expens
ive),`age`of`popcorn`(levels:`fresh,`old),`type`of`cooking`method`(levels:`stovetop,`microwave),`temperatur
e`(levels:`150C,`250C),`cooking`time`(levels:`3`minutes,`5`minutes),`amount`of`cooking`oil`(levels,`1`oz,`3`oz
),`etc.
1.2. Suppose`that`you`want`to`investigate`the`factors`that`potentially`affect`cooked`rice.
(a) What`would`you`use`as`a`response`variable`in`this`experiment?` How`would`you`measure`the
`response?
(b) List`all`of`the`potential`sources`of`variability`that`could`impact`the`response.
(c) Complete`the`first`three`steps`of`the`guidelines`for`designing`experiments`in`Section`1.4.
Step`1`–
`Recognition`of`and`statement`of`the`problem.`Step`2`–
`Selection`of`the`response`variable.
Step`3`–`Choice`of`factors,`levels`and`range.
1.3. Suppose`that`you`want`to`compare`the`growth`of`garden`flowers`with`different`conditions`o
f`sunlight,`water,`fertilizer`and`soil`conditions.` Complete`steps`1-
3`of`the`guidelines`for`designing`experiments`in`Section`1.4.
Step`1`–
`Recognition`of`and`statement`of`the`problem.`Step`2`–
`Selection`of`the`response`variable.
Step`3`–`Choice`of`factors,`levels`and`range.
1-1
,1.4. Select`an`experiment`of`interest`to`you.` Complete`steps`1-
3`of`the`guidelines`for`designing`experiments`in`Section`1.4.
1-2
, 1.5. Search`the`World`Wide`Web`for`information`about`Sir`Ronald`A.`Fisher`and`his`work`on
`experimental`design`in`agricultural`science`at`the`Rothamsted`Experimental`Station.
Sample`searches`could`include`the`following:
1.6. Find`a`Web`Site`for`a`business`that`you`are`interested`in.` Develop`a`list`of`factors`that`you`woul
d`use`in`an`experimental`design`to`improve`the`effectiveness`of`this`Web`Site.
1.7. Almost`everyone`is`concerned`about`the`rising`price`of`gasoline.` Construct`a`cause`and`effect`dia
gram`identifying`the`factors`that`potentially`influence`the`gasoline`mileage`that`you`get`in`your`car.`How
`would`you`go`about`conducting`an`experiment`to`determine`any`of`these`factors`actually`affect`your`gas
oline`mileage?
1.8. What`is`replication?` Why`do`we`need`replication`in`an`experiment?` Present`an`example`that
`illustrates`the`differences`between`replication`and`repeated`measures.
Repetition`of`the`experimental`runs.` Replication`enables`the`experimenter`to`estimate`the`experimental`err
or,`and`provides`more`precise`estimate`of`the`mean`for`the`response`variable.
1.9 S.` Why`is`randomization`important`in`an`experiment?
To`assure`the`observations,`or`errors,`are`independently`distributed`randome`variables`as`required`by`statis
tical`methods.` Also,`to`“average`out”`the`effects`of`extraneous`factors`that`might`occur`while`running`the`
experiment.
1.10 S.`What`are`the`potential`risks`of`a`single,`large,`comprehensive`experiment`in`contrast`to`a`sequentia
l`approach?
The`important`factors`and`levels`are`not`always`known`at`the`beginning`of`the`experimental`process.` Even
`new`response`variables`might`be`discovered`during`the`experimental`process.` By`running`a`large`compre
hensive`experiment,`valuable`information`learned`early`in`the`experimental`process`can`not`likely`be`incor
porated`in`the`remaining`experimental`runs.
1-3
Experiments, 10e by Douglas Montgomery All
Chapters
, Chapter`1`I
ntroduction`
Solutions
1.1S.` Suppose`that`you`want`to`design`an`experiment`to`study`the`proportion`of`unpopped`kernels`of`popc
orn.` Complete`steps`1-
3`of`the`guidelines`for`designing`experiments`in`Section`1.4.` Are`there`any`major`sources`of`variation`that`w
ould`be`difficult`to`control?
Step`1`–`Recognition`of`and`statement`of`the`problem.` Possible`problem`statement`would`be`–
`find`the`best`combination`of`inputs`that`maximizes`yield`on`popcorn`–`minimize`unpopped`kernels.
Step`2`–
`Selection`of`the`response`variable.` Possible`responses`are`number`of`unpopped`kernels`per`100`kernals`in`
experiment,`weight`of`unpopped`kernels`versus`the`total`weight`of`kernels`cooked.
Step`3`–
`Choice`of`factors,`levels`and`range.` Possible`factors`and`levels`are`brand`of`popcorn`(levels:`cheap,`expens
ive),`age`of`popcorn`(levels:`fresh,`old),`type`of`cooking`method`(levels:`stovetop,`microwave),`temperatur
e`(levels:`150C,`250C),`cooking`time`(levels:`3`minutes,`5`minutes),`amount`of`cooking`oil`(levels,`1`oz,`3`oz
),`etc.
1.2. Suppose`that`you`want`to`investigate`the`factors`that`potentially`affect`cooked`rice.
(a) What`would`you`use`as`a`response`variable`in`this`experiment?` How`would`you`measure`the
`response?
(b) List`all`of`the`potential`sources`of`variability`that`could`impact`the`response.
(c) Complete`the`first`three`steps`of`the`guidelines`for`designing`experiments`in`Section`1.4.
Step`1`–
`Recognition`of`and`statement`of`the`problem.`Step`2`–
`Selection`of`the`response`variable.
Step`3`–`Choice`of`factors,`levels`and`range.
1.3. Suppose`that`you`want`to`compare`the`growth`of`garden`flowers`with`different`conditions`o
f`sunlight,`water,`fertilizer`and`soil`conditions.` Complete`steps`1-
3`of`the`guidelines`for`designing`experiments`in`Section`1.4.
Step`1`–
`Recognition`of`and`statement`of`the`problem.`Step`2`–
`Selection`of`the`response`variable.
Step`3`–`Choice`of`factors,`levels`and`range.
1-1
,1.4. Select`an`experiment`of`interest`to`you.` Complete`steps`1-
3`of`the`guidelines`for`designing`experiments`in`Section`1.4.
1-2
, 1.5. Search`the`World`Wide`Web`for`information`about`Sir`Ronald`A.`Fisher`and`his`work`on
`experimental`design`in`agricultural`science`at`the`Rothamsted`Experimental`Station.
Sample`searches`could`include`the`following:
1.6. Find`a`Web`Site`for`a`business`that`you`are`interested`in.` Develop`a`list`of`factors`that`you`woul
d`use`in`an`experimental`design`to`improve`the`effectiveness`of`this`Web`Site.
1.7. Almost`everyone`is`concerned`about`the`rising`price`of`gasoline.` Construct`a`cause`and`effect`dia
gram`identifying`the`factors`that`potentially`influence`the`gasoline`mileage`that`you`get`in`your`car.`How
`would`you`go`about`conducting`an`experiment`to`determine`any`of`these`factors`actually`affect`your`gas
oline`mileage?
1.8. What`is`replication?` Why`do`we`need`replication`in`an`experiment?` Present`an`example`that
`illustrates`the`differences`between`replication`and`repeated`measures.
Repetition`of`the`experimental`runs.` Replication`enables`the`experimenter`to`estimate`the`experimental`err
or,`and`provides`more`precise`estimate`of`the`mean`for`the`response`variable.
1.9 S.` Why`is`randomization`important`in`an`experiment?
To`assure`the`observations,`or`errors,`are`independently`distributed`randome`variables`as`required`by`statis
tical`methods.` Also,`to`“average`out”`the`effects`of`extraneous`factors`that`might`occur`while`running`the`
experiment.
1.10 S.`What`are`the`potential`risks`of`a`single,`large,`comprehensive`experiment`in`contrast`to`a`sequentia
l`approach?
The`important`factors`and`levels`are`not`always`known`at`the`beginning`of`the`experimental`process.` Even
`new`response`variables`might`be`discovered`during`the`experimental`process.` By`running`a`large`compre
hensive`experiment,`valuable`information`learned`early`in`the`experimental`process`can`not`likely`be`incor
porated`in`the`remaining`experimental`runs.
1-3
