# Homework

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• Published : March 11, 2013

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(a) Does cotton percentage affect breaking strength? Draw
t is shown below. Fill in the
comparative box plots and perform an analysis of
he P-value.
variance. Use a P-value approach.
(b) Plot average tensile strength against cotton percentage
IE5002 results.
and interpret theSpring 2012: Homework 3
5-8 (c) Which speciﬁc means are different? SAMPLES?
WHAT IF WE HAVE MORE THAN TWO
289
5-77 We study an experiment of the tensile strength of a synthetic ﬁber. It is suspected that (d) Perform residual analysis and model checking.
MS
F strength is related to the percentage of cotton in the ﬁber. Five levels of cotton percentage P
are ?
used, and 5-78. An experiment in random order, resulting in the data that follow. ﬁve replicates are run was run to determine whether four
5-8
246.93
?
speciﬁc ﬁring temperatures affect the density of a certain type ?
of brick. The experiment led to the following data.
t is shown below. Fill in the
Observations
he P-value.
(a) Does the ﬁring temperature affect the density of the
Cotton
bricks?
Percentage
1
2
3
4
5
(b) Find the P-value for the F-statistic computed in part (a). r Process Optimization and
15
7
7
15
11
9
g” (Solid State Technology,
Temperature ( F12
)
20
12
17
18
18
MS
F
P
lie describe an experiment to
?
?
?
14
18
18
19
19
10025
125
150
175
rate on the uniformity of the
?
30
19
25
19
23
Density 22
tegrated circuit manufactur35
7
10
11
15
11
e experiment, and the result21.8
21.7
21.9
21.9
replicates is shown here.
21.9
21.4
21.8
21.7
(a) Does cotton percentage affect breaking strength? Draw
21.7
21.5
21.8
21.8
t is shown below. Fill in the
comparative box plots and perform an analysis of
(a) Does cotton percentage aﬀect breaking strength? Draw comparative box plots and per21.6 21.6
21.7
servations
he P-value.
variance. Use a21.5
P-value approach.
form an analysis of variance. Use a P -value approach.
(b) Plot average tensile strength against cotton percentage
21.7

21.5
21.6
(b) 6
Plot average and interpret the results. cotton percentage and interpret the results. tensile strength against
4
5
21.5

21.8
Which speciﬁc means are diﬀerent? different?
(c) Which speciﬁc means are
.6
3.0
3.2 (c) 3.8
21.8

(d) Perform residual model and model
Perform residual analysis andanalysischecking. checking.
.0
4.2
3.6 (d)4.2
MS
F
P
5-78. An experiment was run to determine whether four
was carried
.9 246.93 5-79 A study was 5-79. A studydetermine ifout to determine if curing temper- aﬀects the tensile 3.5
4.1
5.1
?
?
carried out to
curing density
signiﬁcantly
speciﬁc ﬁring temperatures affect thetemperature certain type ature signiﬁcantly affects the tensile strength ofof a
silicone rubber.
?
strength of silicone rubber. An axially controlled automated hydraulic force applicator was of axially controlled automated hydraulic force applicator was Anbrick. The experiment led to the following data.

used boxmeasure the tensile strength (in megapascals, MPa) of each of the specimens. The to
h uniformity? Construct
(a) Does the ﬁring temperature affect the density of the
results are used to measure the tensile strength (in megapascals, MPa) of els and perform the analysis given below. specimens. The results are given below. eachbricks?
of the
oximate P-value? What are
(b) Find the P-value for the F-statistic computed in part (a). r Process Optimization and
Temperature, Celsius
g” (Solid mean etch unifordifferent State Technology,
Temperature ( F)
25
40
55
lie describe an experiment to
100
125
150
175
rate on the uniformity of the
2.09
2.22
2.03
of Experiments, 7th edition
Density
tegrated circuit describes an
2.14
2.09
2.22
. Montgomery manufacture experiment, and theﬁber is
result21.8
21.7
21.9
21.9
2.18
2.10
2.10
rength of a synthetic
replicates is...