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450 CHAPTER 9
18. (a) Source DF SS MS F P
Wafer 2 262627.1 131313.6 24118.8 0.000
(b) With the balance powered up continuously, there are no apparent differences in measurements obtained
19. (a) Source DF SS MS F P
(b) Since the interaction terms are not equal to 0, (F4,18 = 5.2567, P= 0.006), we cannot interpret the
main effects. Therefore we compute the cell means. These are
DCM (ml)
PVAL 50 40 30
Section 9.4
1. (a) NaOH concentration is the blocking factor, age is the treatment factor.
Page 450
SECTION 9.4 451
(b) Source DF SS MS F P
(c) Yes, F3,12 = 211.14, P≈0 (P= 1.202 ×10−10)
2. (a) Source DF SS MS F P
3. (a) Let Ibe the number of levels for lighting method, let Jbe the number of levels for blocks, and let K
be the number of replications. Then I= 4, J= 3, and K= 3.
Page 451
452 CHAPTER 9
(b) Yes. The P-value for interactions is large (0.431).
4. (a) Let Ibe the number of levels for coating, let Jbe the number of levels for blocks, and let Kbe the
number of replications. Then I= 3, J= 10, and K= 2.
(b) No. The P-value for interactions is 0.004, so we cannot conclude that there is no interaction between
treatment and block.
Page 452
SECTION 9.4 453
5. (a) Source DF SS MS F P
Variety 9 339032 37670 2.5677 0.018
6. (a) Day is the blocking factor, Sprinkler is the treatment factor.
(b) Source DF SS MS F P
Sprinkler 3 328.69 109.56 55.308 0.000
7. (a) Source DF SS MS F P
Page 453
454 CHAPTER 9
(c) To determine which effects differ at the 5% level, we should use q4,42,.05. This value is not found in
8. (a) Blocking factor is job, treatment factor is machine.
(b) Source DF SS MS F P
9. (a) One motor of each type should be tested on each day. The order in which the motors are tested on
any given day should be chosen at random. This is a randomized block design, in which the days are
10. (a) Use of the randomized block design assumes that there are no interactions between treatments and
SECTION 9.5 455
Section 9.5
1. A B C D
1− − − −
The alias pairs are {A, BCD},{B, ACD},{C, ABD},
{D, ABC},{AB, CD},{AC, BD}, and {AD, BC}
2. An experiment in which the effect of the presence or absence of several catalysts on yield is being
3. (a) Sum of Mean
Variable Effect DF Squares Square F P
A6.75 1 182.25 182.25 11.9508 0.009
Page 455
456 CHAPTER 9
(b) Factors A and B (temperature and concentration) seem to have an effect on yield. There is no evidence
4. (a) Sum of Mean
Variable Effect DF Squares Square F P
A−0.04625 1 0.0085562 0.0085562 1.5718 0.245
5. (a) Variable Effect
A3.3750
(b) No, since the design is unreplicated, there is no error sum of squares.
SECTION 9.5 457
(d) If the additive model is known to hold, then the ANOVA table below shows that the main effect of B
Sum of Mean
Variable Effect DF Squares Square F P
A3.3750 1 22.781 22.781 2.7931 0.170
(b) No, since the design is unreplicated, there is no error sum of squares.
(c)
−0.06 −0.04 −0.02 0 0.02 0.04
0.001
0.01
0.05
0.1
0.25
0.5
0.75
0.9
0.95
0.99
0.999
Effect
The estimates lie nearly on a straight line, so none of the
factors can clearly be said to influence the thickness.
Page 457
7. (a) Term Effect
A−119.25
B 259.25
8. (a) Let xbe the required value.
(b) Variable Effect
Page 458
9. (a) Variable Effect
A1.2
B3.25
(b) Factor Cis the only one that really stands out.
10. (a) Term Effect Term Effect
A−2251.3ABC −16.1
B72.6ABD −1.3
ABCDE −1.9
Page 459
11. (a) Sum of Mean
Variable Effect DF Squares Square F P
A14.245 1 811.68 811.68 691.2 0.000
(b) All main effects are significant, as is the AB interaction. Only the BC interaction has a Pvalue that
12. (a) Variable Effect Variable Effect
A49.337 AE 16.112
