Experimental Design: With Application in Management, Engineering, and the Sciences (Instructor's Solution Manual) (Solutions)

159 Pages·2017·2.192 MB·English

by  Paul D. Berger, Robert E. Maurer, Giovana B. Celli

1 SOLUTION MANUAL INTRODUCTION
2
3
4 The end-of-the-chapter exercises have been designed to achieve several ends: (1) to illustrate the
5 use of techniques demonstrated in the text, thereby more effectively giving the students an
6 understanding of what they've read; (2) to extend the application of the techniques beyond what
7 was explicitly presented in the text, and (3) to probe further the theoretical principles upon which
8 the techniques are based. With over 50 years of teaching experience between us, we have come to
9 appreciate more those texts which do more than focus almost exclusively on repetitious drill in
10 their exercises, and we have sought to provide the kind and selection of exercises we most
11 appreciate when we do the teaching.
12 The difficulty of the exercises varies from fairly simple (but not trivial) to fairly
13 challenging. Many exercises require nothing more than a hand calculator, and some, not even that.
14 The more calculation-intensive exercises can be done with Excel, and, for tutorial purposes, we
15 suggest that is what the student does. The quickest way to do many exercises is with a statistical
16 software package, and some of that is encouraged. We remind the reader of the shortcoming of
17 "blindly" plugging into SPSS® or JMP®; the point of doing the exercises is to help master the
18 material, not to get the answers.
19 We have found the writing of the text and the solution manual to be a very demanding and
20 very rewarding undertaking. We hope you find reading and studying our book to be less demanding
21 and even more rewarding. If you care to share your comments, we would be receptive to having
22 them.
23
24 Enjoy!
25
26 PDB
27 REM
28 GBC
29
30
1
1 Table of Contents
2
3 CHAPTER 2 – ONE-FACTOR DESIGNS AND THE ANALYSIS OF VARIANCE ................... 3
4 CHAPTER 3 – SOME FURTHER ISSUES IN ONE-FACTOR DESIGNS AND ANOVA ....... 13
5 CHAPTER 4 – MULTIPLE-COMPARISON TESTING ...................................................... 23
6 CHAPTER 5 – ORTHOGONALITY, ORTHOGONAL DECOMPOSITION, AND THEIR ROLE IN
7 MODERN EXPERIMENTAL DESIGN ............................................................................ 48
8 CHAPTER 6 – TWO-FACTOR CROSS-CLASSIFICATION DESIGNS ................................ 59
9 CHAPTER 7 – NESTED, OR HIERARCHICAL, DESIGNS ................................................ 75
10 CHAPTER 8 –DESIGNS WITH THREE OR MORE FACTORS: LATIN-SQUARE AND
11 RELATED DESIGNS ................................................................................................... 85
12 CHAPTER 9 - TWO-LEVEL FACTORIAL DESIGNS ....................................................... 98
13 CHAPTER 10 – CONFOUNDING/BLOCKING IN 2K DESIGNS ....................................... 106
14 CHAPTER 11 – TWO-LEVEL FRACTIONAL-FACTORIAL DESIGNS ............................ 112
15 CHAPTER 12 – DESIGNS WITH FACTORS AT THREE LEVELS ................................... 127
16 CHAPTER 13 – INTRODUCTION TO TAGUCHI METHODS .......................................... 136
17 CHAPTER 14 – INTRODUCTION TO SIMPLE REGRESSION ......................................... 142
18 CHAPTER 15 – MULTIPLE LINEAR REGRESSION ..................................................... 147
19 CHAPTER 16 – INTRODUCTION TO RESPONSE-SURFACE METHODOLOGY ............... 152
20 CHAPTER 17 – INTRODUCTION TO MIXTURE DESIGNS ............................................ 157
21
22
2
1 CHAPTER 2 – ONE-FACTOR DESIGNS AND THE ANALYSIS OF VARIANCE
2
3
4 2.1
5
Treatment
1 2 3
(C = 3)
6 6 11
Replications 3 5 10
(R = 4) 8 4 8
3 9 11
Column means 5 6 10
Grand Mean 7
6
7 SSB = 4 5 − 7 2 + 6 − 7 2 + 10 − 7 2 = 4 4 + 1 + 9 = 56
c
8 SSW = 6−5 0 + 3−5 0 + 8−5 0 +⋯+ 11−10 0 = 38
9 𝐹 = 56 2 38 9 = 6.632
𝑐𝑎𝑙𝑐
10
11 Alternatively, using Excel, we have
12
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 56 2 28 6.632 0.017 4.257
Within Groups 38 9 4.222

Total 94 11
13
14 Yes, there is sufficient evidence of differences is sales due to the level of the treatment; F =
calc
15 6.632 is well within the rejection region; thus, we reject H .
0
16
17
18
19
3
1 2.2
2
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 112 2 56 15.474 7.411E-05 3.467
Within Groups 76 21 3.619

Total 188 23
3
4 Yes, there is evidence of differences is sales due to the level of the treatment; F = 15.474 is well
calc
5 within the rejection region.
6
7 2.3
8
9 For the "same" data with twice as many replications, MSB is doubled, MSW is reduced by 14%,
c
10 and F is more than doubled. Simultaneously, the change in denominator df reduces the critical
calc
11 value from 4.256 to 3.466. The net result is a change in p-value from .017 to .0000741. In other
12 words, the same difference in means becomes more significant with increased replication because
13 the estimates of the means are better (have narrower confidence intervals).
14
15 2.4
16
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 6.108 4 1.527 6.797 0.003 3.056
Within Groups 3.37 15 0.225

Total 9.478 19
17
18 Yes, there is sufficient evidence of a difference due to dominant technology; p-value = .0025 <
19 .05.
20
21
4
1 2.5
2
3 n = 100 indicates total df = 99; therefore, error df = 96. F = 15 and MSW = 600 indicates SSB
calc C
4 = 9000. SSQ values follow from these.
5
ANOVA Table
Source of Variability SSQ df MSQ F
calc
Diet 27000 3 9000 15
Error 57600 96 600
Total 84600 99
6
7 2.6
8
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 313.333 3 104.444 4.719 0.012 3.098
Within Groups 442.667 20 22.133

Total 756 23
9
10 Yes, there is sufficient evidence to conclude that the level of the room affects perception of the
11 degree of motion; p-value = .012 < .05.
12
13 2.7
14
15 Sum of Squares for each column = 𝑑𝑓 Standard Deviation 0
16
17 For Column 1:
18 SS = 22 9.18 0 = 1853.993
19
20 SSW = 10056.19
21 df = 100
22 MSW = 100.56
5
1
2 Grand mean = 23 38.12 +35 29.72 +17 33.40 +29 36.15 104 = 33.97
3
4 SSB = 23 38.12−33.97 0 +35 29.72−33.97 0 +17 33.40−33.97 0 +
N
5 29 36.15−33.97 0 = 1171.647
6 df = 3
7 MSB = 390.549
c
8
Species 1 2 3 4 Total
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
Sums of Squares 1853.993 3691.598 2057.53 2453.069 10056.19
9
10 𝐹 = 390.549 100.56 = 3.884; for α = .05 and df = (3, 100), c = 2.68; there is evidence of a
OPQO
11 difference in cost per visit for the four dog species. Since, for α = .01 and df = (3, 100), c = 3.95,
12 .05 > p-value > .01.
13
14 2.8
15
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 35.583 2 17.792 6.188 0.008 3.467
Within Groups 60.375 21 2.875

Total 95.958 23
16
17 The texts are not equally effective; p-value = .008.
18
19
20
21
6
1 2.9
2
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 0.2606 2 0.130 36.024 8.47E-06 3.8853
Within Groups 0.043 12 0.004

Total 0.304 14
3
4 At any traditional value of α, there is substantial evidence of a difference in price among the three
5 cities; p-value = .00000847, essentially zero.
6
7 2.10
8
9 Boynton Beach and Delray Beach
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 0.021 1 0.021 8.186 0.021 5.318
Within Groups 0.021 8 0.003

Total 0.042 9
10
11 Delray Beach and Boca Raton
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 0.123 1 0.123 32.424 0.0005 5.318
Within Groups 0.030 8 0.004

Total 0.154 9
12
13
14
15
7
1 Boynton Beach and Boca Raton
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 0.247 1 0.247 55.205 7.4E-05 5.318
Within Groups 0.036 8 0.005

Total 0.282 9
2
3 There is evidence of significant difference in price for each pair of cities.
4
5 2.11
6
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 20.5 3 6.833 2.523 0.107 3.490
Within Groups 32.5 12 2.708

Total 53 15
7
8 No. There is insufficient evidence at α = .01 that there is a difference in rental duration among the
9 four sizes of cars; p-value = .1071 > .01.
10
11 2.12
12
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 1007.475 3 335.825 106.401 2.494E-39 2.656
Within Groups 555.497 176 3.156

Total 1562.972 179
13
14 Yes, there is a difference in waiting time among the four offices; p-value is essentially zero.
15
16
8
1 2.13
2
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 75257.55 3 25085.850 980.609 7.450E-183 2.627
Within Groups 10130.44 396 25.582

Total 85387.99 399
3
4 Yes, there is a difference in average scores among the four courses; p-value is essentially zero.
5
6 2.14
7
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 2859.524 2 1429.762 0.339 0.717 3.555
Within Groups 75907.143 18 4217.063

Total 78766.667 20
8
9 No, there are not significant differences due to state; p-value = .717 > .05.
10
11 2.15
12
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 4905500 2 2452750 3.651 0.039 3.354
Within Groups 18137500 27 671759.259

Total 23043000 29
13
14 Yes, there are differences in amount of donations due to solicitation approach, though it is a close
15 call; p-value = .039 < .05.
16
9
1 2.16
2
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 2144.724 7 306.389 105.407 9.184E-109 2.021
Within Groups 2302.126 792 2.907

Total 4446.850 799
3
4 Yes, device does affect battery lifetime; p-value is essentially zero.
5
6 2.17
7
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 38.663 1 38.663 0.243 0.624 4.023
Within Groups 8435.248 53 159.156

Total 8473.911 54
8
9 No, mean grade does not differ by evening; p-value = .624 > .05.
10
11 2.18
12
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 727.198 1 727.198 4.975 0.030 4.023
Within Groups 7746.713 53 146.164

Total 8473.911 54
13
14 Yes, mean grade differs by status; p-value = .030 < .05.
15
16
10