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Solutions from Montgomery, D. C. (2012)
Design and Analysis of Experiments
, Wiley, NY
31
Chapter 3
Experiments with a Single Factor:
The Analysis of Variance
Solutions
3.1.
An experimenter has conducted a singlefactor experiment with four levels of the factor, and each
factor level has been replicated six times.
The computed value of the
F
statistic is
F
0
= 3.26.
Find bounds
on the
P
value.
Table
P
value = 0.025, 0.050
Computer
P
value = 0.043
3.2.
An experimenter has conducted a singlefactor experiment with six levels of the factor, and each
factor level has been replicated three times.
The computed value of the
F
statistic is
F
0
= 5.81.
Find
bounds on the
P
value.
Table
P
value < 0.010
Computer
P
value = 0.006
3.3.
A computer ANOVA output is shown below.
Fill in the blanks.
You may give bounds on the
P

value.
Oneway ANOVA
Source
DF
SS
MS
F
P
Factor
3
36.15
?
?
?
Error
?
?
?
Total
19
196.04
Completed table is:
Oneway ANOVA
Source
DF
SS
MS
F
P
Factor
3
36.15
12.05
1.21
0.3395
Error
16
159.89
9.99
Total
19
196.04
3.4.
A computer ANOVA output is shown below.
Fill in the blanks.
You may give bounds on the
P

value.
Oneway ANOVA
Source
DF
SS
MS
F
P
Factor
?
?
246.93
?
?
Error
25
186.53
?
Total
29
1174.24
Solutions from Montgomery, D. C. (2012)
Design and Analysis of Experiments
, Wiley, NY
32
Completed table is:
Oneway ANOVA
Source
DF
SS
MS
F
P
Factor
4
987.71
246.93
33.09
< 0.0001
Error
25
186.53
7.46
Total
29
1174.24
3.5.
An article appeared in
The Wall Street Journal
on Tuesday, April 27, 2010, with the title “Eating
Chocolate Is Linked to Depression.”
The article reported on a study funded by the National Heart, Lung
and Blood Institute (part of the National Institutes of Health) and conducted by the faculty at the University
of California, San Diego, and the University of California, Davis.
The research was also published in the
Archives of Internal Medicine
(2010, pp. 699703).
The study examined 931 adults who were not taking
antidepressants and did not have known cardiovascular disease or diabetes.
The group was about 70% men
and the average age of the group was reported to be about 58.
The participants were asked about chocolate
consumption and then screened for depression using a questionnaire.
People who scored less than 16 on
the questionnaire are not considered depressed, while those with scores above 16 and less than or equal to
22 are considered possibly depressed, while those with scores above 22 are considered likely to be
depressed.
The survey found that people who were not depressed ate an average of 8.4 servings of
chocolate per month, while those individuals who scored above 22 were likely to be depressed ate the most
chocolate, an average of 11.8 servings per month.
No differentiation was made between dark and milk
chocolate.
Other foods were also examined, but no patterned emerged between other foods and depression.
Is this study really a designed experiment?
Does it establish a causeandeffect link between chocolate
consumption and depression?
How would the study have to be conducted to establish such a link?
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