Solutions Manual for f f
Design and Analysis of
f f f f
Experiments, 10e
f f
Douglas Montgomery
f f
(All Chapters)
f f
, Solutions from Montgomery, D. C. (2019) Design and Analysis of Experiments, Wiley, NY
f f f f f f f f f f f f
Chapter 1 f
f Introduction
f Solutions
1.1S. Suppose that you want to design an experiment to study the proportion of unpopped kernels of
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popcorn. Complete steps 1-3 of the guidelines for designing experiments in Section 1.4. Are there any major
f f f f f f f f f f f f f f f f f
sources of variation that would be difficult to control?
f f f f f f f f f
Step 1 – Recognition of and statement of the problem. Possible problem statement would be – find the best
f f f f f f f f f f f f f f f f f f
combination of inputs that maximizes yield on popcorn – minimize unpopped kernels.
f f f f f f f f f f f f
Step 2 – Selection of the response variable. Possible responses are number of unpopped kernels per 100
f f f f f f f f f f f f f f f f
kernals in experiment, weight of unpopped kernels versus the total weight of kernels cooked.
f f f f f f f f f f f f f f
Step 3 – Choice of factors, levels and range. Possible factors and levels are brand of popcorn (levels: cheap,
f f f f f f f f f f f f f f f f f f
expensive), age of popcorn (levels: fresh, old), type of cooking method (levels: stovetop, microwave),
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temperature (levels: 150C, 250C), cooking time (levels: 3 minutes, 5 minutes), amount of cooking oil (levels,1
f f f f f f f f f f f f f f f f f
oz, 3 oz), etc.
f f f f
1.2. Suppose that you want to investigate the factors that potentially affect cooked rice.
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(a) What would you use as a response variable in this experiment? How would you measure the
f f f f f f f f f f f f f f f
response?
f
(b) List all of the potential sources of variability that could impact the response.
f f f f f f f f f f f f
(c) Complete the first three steps of the guidelines for designing experiments in Section 1.4.
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Step 1 – Recognition of and statement of the problem.
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Step 2 – Selection of the response variable.
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Step 3 – Choice of factors, levels and range.
f f f f f f f f
1.3. Suppose that you want to compare the growth of garden flowers with different conditions of
f f f f f f f f f f f f f f
sunlight, water, fertilizer and soil conditions. Complete steps 1-3 of the guidelines for designing
f f f f f f f f f f f f f f
experiments in Section 1.4.
f f f f
Step 1 – Recognition of and statement of the problem.
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Step 2 – Selection of the response variable.
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Step 3 – Choice of factors, levels and range.
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1.4. Select an experiment of interest to you. Complete steps 1-3 of the guidelines for designing
f f f f f f f f f f f f f f
experiments in Section 1.4.
f f f f
1-1
, Solutions from Montgomery, D. C. (2019) Design and Analysis of Experiments, Wiley, NY
f f f f f f f f f f f f
1.5. Search the World Wide Web for information about Sir Ronald A. Fisher and his work on
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experimental design in agricultural science at the Rothamsted Experimental Station.
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Sample searches could include the following:
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1.6. Find a Web Site for a business that you are interested in. Develop a list of factors that you would
f f f f f f f f f f f f f f f f f f f
use in an experimental design to improve the effectiveness of this Web Site.
f f f f f f f f f f f f f
1.7. Almost everyone is concerned about the rising price of gasoline. Construct a cause and effect
f f f f f f f f f f f f f f
diagram identifying the factors that potentially influence the gasoline mileage that you get in your car.
f f f f f f f f f f f f f f f f
How would you go about conducting an experiment to determine any of these factors actually affect your
f f f f f f f f f f f f f f f f f
gasoline mileage?
f f
1.8. What is replication? Why do we need replication in an experiment? Present an example
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thatillustrates the differences between replication and repeated measures.
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Repetition of the experimental runs. Replication enables the experimenter to estimate the experimental
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error, and provides more precise estimate of the mean for the response variable.
f f f f f f f f f f f f f
1.9 S. f Why fis frandomization fimportant fin fan fexperiment?
To assure the observations, or errors, are independently distributed randome variables as required by
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statistical methods. Also, to “average out” the effects of extraneous factors that might occur while running
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the experiment.
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1.10 S. fWhat fare fthe fpotential frisks fof fa fsingle, flarge, fcomprehensive fexperiment fin fcontrast fto fa fsequential
approach?
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The important factors and levels are not always known at the beginning of the experimental process. Even
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new response variables might be discovered during the experimental process. By running a large
f f f f f f f f f f f f f f
comprehensive experiment, valuable information learned early in the experimental process can not likely
f f f f f f f f f f f f f
be incorporated in the remaining experimental runs.
f f f f f f f
1-2
, Solutions from Montgomery, D. C. (2019) Design and Analysis of Experiments, Wiley, NY
f f f f f f f f f f f f
Experimental runs can be expensive and time consuming. If an error were to occur while running the
f f f f f f f f f f f f f f f f
experiment, the cost of redoing the experiment is much more manageable with one of the small sequential
f f f f f f f f f f f f f f f f f
experiments than the large comprehensive experiment.
f f f f f f
Reserved Problems f
1.1 R. fHave fyou freceived fan foffer fto fobtain fa fcredit fcard fin fthe fmail? fWhat f“factors” fwere fassociated fwith
the offer, such as introductory interest rate? Do you think the credit card company is conducting
f f f f f f f f f f f f f f f f
experiments to investigate which facors product the highest positive response rate to their offer? What
f f f f f f f f f f f f f f f
potential factors in the experiment can you identify?
f f f f ff f f f
Interest rate, credit limit, old credit card pay-off amount, interest free period, gift points, others.
f f f f f f f f f f f f f f
1.2 R. f What ffactors fdo fyou fthink fan fe-commerce fcompany fcould fuse fin fan fexperiment finvolving ftheir fweb
page to encourage more people to “click-through” into their site?
f f f f f f f f f
Font size, font type, images/icons, color, spacing, animation, sound/music, speed, others.
f f f f f f f f f f
1.3 R. fTwo fof fthe fleading fcontributors fto fdesign fof fexperiments fover fthe flast f60 fyears fwere fGeorge fE. fP.
Box and J. Stuart Hunter. Search the World Wide Web for information on these two individuals and
f f f f f f f f f f f f f f f f f
briefly summarize their contributions.
f f f f
1.4 R. fSuppose fthat fyou fwant fto fmake fbrownies. f You fplan fto fuse fa fbrownie fmix, fbut fthere fare fa fnumber fof
factors that could impact the results.
f f f f f f
a. What would you use as a response variable? Could there be more than one response? Taste would
f f f f f f f f f f f f f f f f
probably be the primary factor. Other factors could be texture and aroma. Possibly a combination
f f f f f f f f f f f f f f f
of all three. f f f
b. Identify the factors that might impact the results. Amount of oil, number of eggs, amount of
f f f f f f f f f f f f f f f
water, cost of mix – expensive or cheap, baking temperature, baking time, type of pan – glass or
f f f f f f f f f f f f f f f f f f
metal. f
c. Complete the first three steps of the guidelines for designing experiments in Section 1-4. f f f f f f f f f f f f f
1. Problem Statement – To maximize brownie tastiness. Or to make the best brownie while f f f f f f f f f f f f f
minimizing cost (Can a cheap mix give the results of an expensive one?)
f f f f f f f f f f f f f
2. Response Variable – Tastiness is the primary response. Secondary responses could also be f f f f f f f f f f f f
texture and aroma. f f f
3. Choice of factors, levels and range – for the maximize brownie tastiness: Mix cost (cheap, f f f f f f f f f f f f f f
expensive), number of eggs (2,3), amount of oil (1/2 cup, ¾ cup), pan type (glass, metal),
f f f f f f f f f f f f f f f f
oven temp (350, 375), bake time (35 min, 45 min). One might want to reduce the number of
f f f f f f f f f f f f f f f f f f
factors from 6 to 3-4 to reduce the number of experimental runs.
f f f f f f f f f f f f
1-3
Design and Analysis of
f f f f
Experiments, 10e
f f
Douglas Montgomery
f f
(All Chapters)
f f
, Solutions from Montgomery, D. C. (2019) Design and Analysis of Experiments, Wiley, NY
f f f f f f f f f f f f
Chapter 1 f
f Introduction
f Solutions
1.1S. Suppose that you want to design an experiment to study the proportion of unpopped kernels of
f f f f f f f f f f f f f f f f
popcorn. Complete steps 1-3 of the guidelines for designing experiments in Section 1.4. Are there any major
f f f f f f f f f f f f f f f f f
sources of variation that would be difficult to control?
f f f f f f f f f
Step 1 – Recognition of and statement of the problem. Possible problem statement would be – find the best
f f f f f f f f f f f f f f f f f f
combination of inputs that maximizes yield on popcorn – minimize unpopped kernels.
f f f f f f f f f f f f
Step 2 – Selection of the response variable. Possible responses are number of unpopped kernels per 100
f f f f f f f f f f f f f f f f
kernals in experiment, weight of unpopped kernels versus the total weight of kernels cooked.
f f f f f f f f f f f f f f
Step 3 – Choice of factors, levels and range. Possible factors and levels are brand of popcorn (levels: cheap,
f f f f f f f f f f f f f f f f f f
expensive), age of popcorn (levels: fresh, old), type of cooking method (levels: stovetop, microwave),
f f f f f f f f f f f f f f
temperature (levels: 150C, 250C), cooking time (levels: 3 minutes, 5 minutes), amount of cooking oil (levels,1
f f f f f f f f f f f f f f f f f
oz, 3 oz), etc.
f f f f
1.2. Suppose that you want to investigate the factors that potentially affect cooked rice.
f f f f f f f f f f f f
(a) What would you use as a response variable in this experiment? How would you measure the
f f f f f f f f f f f f f f f
response?
f
(b) List all of the potential sources of variability that could impact the response.
f f f f f f f f f f f f
(c) Complete the first three steps of the guidelines for designing experiments in Section 1.4.
f f f f f f f f f f f f f
Step 1 – Recognition of and statement of the problem.
f f f f f f f f f
Step 2 – Selection of the response variable.
f f f f f f f f
Step 3 – Choice of factors, levels and range.
f f f f f f f f
1.3. Suppose that you want to compare the growth of garden flowers with different conditions of
f f f f f f f f f f f f f f
sunlight, water, fertilizer and soil conditions. Complete steps 1-3 of the guidelines for designing
f f f f f f f f f f f f f f
experiments in Section 1.4.
f f f f
Step 1 – Recognition of and statement of the problem.
f f f f f f f f f
Step 2 – Selection of the response variable.
f f f f f f f f
Step 3 – Choice of factors, levels and range.
f f f f f f f f
1.4. Select an experiment of interest to you. Complete steps 1-3 of the guidelines for designing
f f f f f f f f f f f f f f
experiments in Section 1.4.
f f f f
1-1
, Solutions from Montgomery, D. C. (2019) Design and Analysis of Experiments, Wiley, NY
f f f f f f f f f f f f
1.5. Search the World Wide Web for information about Sir Ronald A. Fisher and his work on
f f f f f f f f f f f f f f f
experimental design in agricultural science at the Rothamsted Experimental Station.
f f f f f f f f f f
Sample searches could include the following:
f f f f f
1.6. Find a Web Site for a business that you are interested in. Develop a list of factors that you would
f f f f f f f f f f f f f f f f f f f
use in an experimental design to improve the effectiveness of this Web Site.
f f f f f f f f f f f f f
1.7. Almost everyone is concerned about the rising price of gasoline. Construct a cause and effect
f f f f f f f f f f f f f f
diagram identifying the factors that potentially influence the gasoline mileage that you get in your car.
f f f f f f f f f f f f f f f f
How would you go about conducting an experiment to determine any of these factors actually affect your
f f f f f f f f f f f f f f f f f
gasoline mileage?
f f
1.8. What is replication? Why do we need replication in an experiment? Present an example
f f f f f f f f f f f f f
thatillustrates the differences between replication and repeated measures.
f f f f f f f f f
Repetition of the experimental runs. Replication enables the experimenter to estimate the experimental
f f f f f f f f f f f f
error, and provides more precise estimate of the mean for the response variable.
f f f f f f f f f f f f f
1.9 S. f Why fis frandomization fimportant fin fan fexperiment?
To assure the observations, or errors, are independently distributed randome variables as required by
f f f f f f f f f f f f f
statistical methods. Also, to “average out” the effects of extraneous factors that might occur while running
f f f f f f f f f f f f f f f f
the experiment.
f f
1.10 S. fWhat fare fthe fpotential frisks fof fa fsingle, flarge, fcomprehensive fexperiment fin fcontrast fto fa fsequential
approach?
f
The important factors and levels are not always known at the beginning of the experimental process. Even
f f f f f f f f f f f f f f f f
new response variables might be discovered during the experimental process. By running a large
f f f f f f f f f f f f f f
comprehensive experiment, valuable information learned early in the experimental process can not likely
f f f f f f f f f f f f f
be incorporated in the remaining experimental runs.
f f f f f f f
1-2
, Solutions from Montgomery, D. C. (2019) Design and Analysis of Experiments, Wiley, NY
f f f f f f f f f f f f
Experimental runs can be expensive and time consuming. If an error were to occur while running the
f f f f f f f f f f f f f f f f
experiment, the cost of redoing the experiment is much more manageable with one of the small sequential
f f f f f f f f f f f f f f f f f
experiments than the large comprehensive experiment.
f f f f f f
Reserved Problems f
1.1 R. fHave fyou freceived fan foffer fto fobtain fa fcredit fcard fin fthe fmail? fWhat f“factors” fwere fassociated fwith
the offer, such as introductory interest rate? Do you think the credit card company is conducting
f f f f f f f f f f f f f f f f
experiments to investigate which facors product the highest positive response rate to their offer? What
f f f f f f f f f f f f f f f
potential factors in the experiment can you identify?
f f f f ff f f f
Interest rate, credit limit, old credit card pay-off amount, interest free period, gift points, others.
f f f f f f f f f f f f f f
1.2 R. f What ffactors fdo fyou fthink fan fe-commerce fcompany fcould fuse fin fan fexperiment finvolving ftheir fweb
page to encourage more people to “click-through” into their site?
f f f f f f f f f
Font size, font type, images/icons, color, spacing, animation, sound/music, speed, others.
f f f f f f f f f f
1.3 R. fTwo fof fthe fleading fcontributors fto fdesign fof fexperiments fover fthe flast f60 fyears fwere fGeorge fE. fP.
Box and J. Stuart Hunter. Search the World Wide Web for information on these two individuals and
f f f f f f f f f f f f f f f f f
briefly summarize their contributions.
f f f f
1.4 R. fSuppose fthat fyou fwant fto fmake fbrownies. f You fplan fto fuse fa fbrownie fmix, fbut fthere fare fa fnumber fof
factors that could impact the results.
f f f f f f
a. What would you use as a response variable? Could there be more than one response? Taste would
f f f f f f f f f f f f f f f f
probably be the primary factor. Other factors could be texture and aroma. Possibly a combination
f f f f f f f f f f f f f f f
of all three. f f f
b. Identify the factors that might impact the results. Amount of oil, number of eggs, amount of
f f f f f f f f f f f f f f f
water, cost of mix – expensive or cheap, baking temperature, baking time, type of pan – glass or
f f f f f f f f f f f f f f f f f f
metal. f
c. Complete the first three steps of the guidelines for designing experiments in Section 1-4. f f f f f f f f f f f f f
1. Problem Statement – To maximize brownie tastiness. Or to make the best brownie while f f f f f f f f f f f f f
minimizing cost (Can a cheap mix give the results of an expensive one?)
f f f f f f f f f f f f f
2. Response Variable – Tastiness is the primary response. Secondary responses could also be f f f f f f f f f f f f
texture and aroma. f f f
3. Choice of factors, levels and range – for the maximize brownie tastiness: Mix cost (cheap, f f f f f f f f f f f f f f
expensive), number of eggs (2,3), amount of oil (1/2 cup, ¾ cup), pan type (glass, metal),
f f f f f f f f f f f f f f f f
oven temp (350, 375), bake time (35 min, 45 min). One might want to reduce the number of
f f f f f f f f f f f f f f f f f f
factors from 6 to 3-4 to reduce the number of experimental runs.
f f f f f f f f f f f f
1-3
