Instructors Solutions Manual Experimental Design With Application in Management, Engineering, and th

INSTRUCTORS SOLUTION MANUAL

SOLUTION MANUAL INTRODUCTION

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The end-of-the-chapter exercises have been designed to achieve several ends: (1) to illustrate the

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use of techniques demonstrated in the text, thereby more effectively giving the students an

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understanding of what they've read; (2) to extend the application of the techniques beyond what

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was explicitly presented in the text, and (3) to probe further the theoretical principles upon which

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the techniques are based. With over 50 years of teaching experience between us, we have come to

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appreciate more those texts which do more than focus almost exclusively on repetitious drill in

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their exercises, and we have sought to provide the kind and selection of exercises we most

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appreciate when we do the teaching.

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The difficulty of the exercises varies from fairly simple (but not trivial) to fairly

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challenging. Many exercises require nothing more than a hand calculator, and some, not even that.

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The more calculation-intensive exercises can be done with Excel, and, for tutorial purposes, we

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suggest that is what the student does. The quickest way to do many exercises is with a statistical

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software package, and some of that is encouraged. We remind the reader of the shortcoming of

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"blindly" plugging into SPSS® or JMP®; the point of doing the exercises is to help master the

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material, not to get the answers.

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We have found the writing of the text and the solution manual to be a very demanding and

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very rewarding undertaking. We hope you find reading and studying our book to be less demanding

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and even more rewarding. If you care to share your comments, we would be receptive to having

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them.

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Enjoy!

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PDB

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REM

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GBC

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Table of Contents

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CHAPTER 2 – ONE-FACTOR DESIGNS AND THE ANALYSIS OF VARIANCE ................... 3

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CHAPTER 3 – SOME FURTHER ISSUES IN ONE-FACTOR DESIGNS AND ANOVA ....... 13

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CHAPTER 4 – MULTIPLE-COMPARISON TESTING ...................................................... 23

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CHAPTER 5 – ORTHOGONALITY, ORTHOGONAL DECOMPOSITION, AND THEIR ROLE IN

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MODERN EXPERIMENTAL DESIGN ............................................................................ 48

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CHAPTER 6 – TWO-FACTOR CROSS-CLASSIFICATION DESIGNS ................................ 59

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CHAPTER 7 – NESTED, OR HIERARCHICAL, DESIGNS ................................................ 75

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CHAPTER 8 –DESIGNS WITH THREE OR MORE FACTORS: LATIN-SQUARE AND

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RELATED DESIGNS ................................................................................................... 85

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CHAPTER 9 - TWO-LEVEL FACTORIAL DESIGNS ....................................................... 98

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CHAPTER 10 – CONFOUNDING/BLOCKING IN 2K DESIGNS ....................................... 106

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CHAPTER 11 – TWO-LEVEL FRACTIONAL-FACTORIAL DESIGNS ............................ 112

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CHAPTER 12 – DESIGNS WITH FACTORS AT THREE LEVELS ................................... 127

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CHAPTER 13 – INTRODUCTION TO TAGUCHI METHODS .......................................... 136

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CHAPTER 14 – INTRODUCTION TO SIMPLE REGRESSION ......................................... 142

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CHAPTER 15 – MULTIPLE LINEAR REGRESSION ..................................................... 147

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CHAPTER 16 – INTRODUCTION TO RESPONSE-SURFACE METHODOLOGY ............... 152

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CHAPTER 17 – INTRODUCTION TO MIXTURE DESIGNS ............................................ 157

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CHAPTER 2 – ONE-FACTOR DESIGNS AND THE ANALYSIS OF VARIANCE

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2.1

5 Treatment

1

2

3

6

6

11

Replications

3

5

10

(R = 4)

8

4

8

3

9

11

5

6

10

(C = 3)

Column means Grand Mean

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6 7

SSBc = 4 5 − 7 2 + 6 − 7 2 + 10 − 7 2 = 4 4 + 1 + 9 = 56

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SSW =

6 − 5 0 + 3 − 5 0 + 8 − 5 0 + ⋯ + 11 − 10 0 = 38

𝐹𝑐𝑎𝑙𝑐 = 56 2

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38 9 = 6.632

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Alternatively, using Excel, we have

12 ANOVA Source of Variation

SS

df

MS

F

Between Groups

56

2

28

Within Groups

38

9

4.222

Total

94

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P-value 6.632

0.017

F crit 4.257

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Yes, there is sufficient evidence of differences is sales due to the level of the treatment; Fcalc =

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6.632 is well within the rejection region; thus, we reject H0.

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3

1

2.2

2 ANOVA Source of Variation

3

SS

df

MS

Between Groups

112

2

56

Within Groups

76

21

3.619

Total

188

23

F

P-value

15.474

7.411E-05

F crit 3.467

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Yes, there is evidence of differences is sales due to the level of the treatment; Fcalc = 15.474 is well

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within the rejection region.

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2.3

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For the "same" data with twice as many replications, MSBc is doubled, MSW is reduced by 14%,

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and Fcalc is more than doubled. Simultaneously, the change in denominator df reduces the critical

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value from 4.256 to 3.466. The net result is a change in p-value from .017 to .0000741. In other

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words, the same difference in means becomes more significant with increased replication because

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the estimates of the means are better (have narrower confidence intervals).

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2.4

16 ANOVA Source of Variation

SS

df

MS

Between Groups

6.108

4

1.527

Within Groups

3.37

15

0.225

Total

9.478

19

F

P-value 6.797

0.003

F crit 3.056

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Yes, there is sufficient evidence of a difference due to dominant technology; p-value = .0025 <

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.05.

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4

1

2.5

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n = 100 indicates total df = 99; therefore, error df = 96. Fcalc = 15 and MSW = 600 indicates SSBC

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= 9000. SSQ values follow from these.

5 ANOVA Table Source of Variability

SSQ

df

MSQ

Fcalc

Diet

27000

3

9000

15

Error

57600

96

600

Total

84600

99

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2.6

8 ANOVA Source of Variation

SS

Between Groups

313.333

3

104.444

Within Groups

442.667

20

22.133

756

23

Total

df

MS

F

P-value 4.719

0.012

F crit 3.098

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Yes, there is sufficient evidence to conclude that the level of the room affects perception of the

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degree of motion; p-value = .012 < .05.

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2.7

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Sum of Squares for each column = 𝑑𝑓 Standard Deviation 0

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For Column 1: SS = 22 9.18 0 = 1853.993

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SSW = 10056.19

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df = 100

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MSW = 100.56

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1 Grand mean = 23 38.12 + 35 29.72 + 17 33.40 + 29 36.15

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104 = 33.97

3 SSBN = 23 38.12 − 33.97 0 + 35 29.72 − 33.97 0 + 17 33.40 − 33.97 0 +

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29 36.15 − 33.97 0 = 1171.647

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df = 3

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MSBc = 390.549

8 Species

1

2

3

4

Column Mean

38.12

29.72

33.40

36.15

Standard Deviation

9.18

10.42

11.34

9.36

Sample Size

23

35

17

29

104

df

22

34

16

28

100

1853.993

3691.598

2057.53

2453.069

10056.19

Sums of Squares

Total

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𝐹OPQO = 390.549 100.56 = 3.884; for α = .05 and df = (3, 100), c = 2.68; there is evidence of a

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difference in cost per visit for the four dog species. Since, for α = .01 and df = (3, 100), c = 3.95,

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.05 > p-value > .01.

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2.8

15 ANOVA Source of Variation

SS

Between Groups

35.583

Within Groups Total

df

MS

F

2

17.792

6.188

60.375

21

2.875

95.958

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P-value 0.008

F crit 3.467

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The texts are not equally effective; p-value = .008.

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