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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...