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SUPPLEMENTARY EXERCISES FOR CHAPTER 9 461
(c) Variable Effect Variable Effect
A7.50 AE 7.00
B19.75 BC 3.00
AD −4.00
0.75
0.9
0.95
0.99
0.999
E
B
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2. Source DF SS MS F P
Gypsum 2 0.096717 0.048358 0.94836 0.439
3. Source DF SS MS F P
4. (a) 23 −3−2−6 = 12
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SUPPLEMENTARY EXERCISES FOR CHAPTER 9 463
(h) MSB/MSE = 7.521/2.68775 = 2.798
5. (a) No. The variances are not constant across groups. In particular, there is an outlier in group 1.
6. (a) Main Effects Main Effects
Interactions
(b) Source DF SS MS F P
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464 CHAPTER 9
7. The recommendation is not a good one. The engineer is trying to interpret the main effects without
8. (a) The main effects are:
A: (1/4)(−79.8 + 69.0−72.3 + 71.2−91.3 + 95.4−92.7 + 91.5) = −2.25.
(c) Sum of Mean
Variable Effect DF Squares Square F P
A−2.25 1 10.125 10.125 0.98684 0.394
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9. (a) Source DF SS MS F P
10. (a) Main Effects Main Effects
of Fertilizer of Zone
Low −5.2630 Southern −2.3852
(b) Source DF SS MS F P
Fertilizer 2 565.36 282.68 33.896 0.000
11. (a) Source DF SS MS F P
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466 CHAPTER 9
12. (a) The estimates are: A: 1.6875, B: 0.8125, C: 1.1875, AB: 0.6875, AC: 1.8125, BC: −0.3125,
(b) Sum of Mean
Variable Effect DF Squares Square F P
A1.6875 1 22.781 22.781 9.3863 0.005
(c) The sum of squares for interactions is 3.7812 + 26.281 + 0.78125 + 0.28125 = 31.1247. There are
13. Source DF SS MS F P
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14. (a) Source DF SS MS F P
Concentration 3 8.5768 2.8589 345.58 0.000
(b) q4,12,.05 = 4.20, MSE = 0.0082729, so the 5% critical point is 4.20p0.0082729/4 = 0.191. The sample
15. (a) From Exercise 11, MSE = 29.026, so s=√29.026 = 5.388.
(b) The MINITAB output for the power calculation is
The sample size is for each level.
(c) The MINITAB output for the power calculation is
Power and Sample Size
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16. (a) From Exercise 14, MSE = 0.0082729, so s=√0.0082729 = 0.0910.
(b) The MINITAB output for the power calculation is
Power and Sample Size
(c) The MINITAB output for the power calculation is
Power and Sample Size
17. (a) Variable Effect Variable Effect Variable Effect Variable Effect
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SUPPLEMENTARY EXERCISES FOR CHAPTER 9 469
(c) Sum of Mean
Variable Effect DF Squares Square F P
A3.9875 1 63.601 63.601 68.415 0.000
B2.0375 1 16.606 16.606 17.863 0.008
(d) The Fstatistics are computed by dividing the mean square for each effect (equal to its sum of squares)
by the error mean square 1.04. The degrees of freedom for each Fstatistic are 1 and 4. The results
are summarized in the following table.
Sum of Mean
Variable Effect DF Squares Square F P
A3.9875 1 63.601 63.601 61.154 0.001
B2.0375 1 16.606 16.606 15.967 0.016
(e) Yes. None of the P-values for the third- or higher-order interactions are small.
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18. (a) Source DF SS MS F P
(b) No. F21,96 = 0.93397, P > 0.10 (P= 0.550).
19. Source DF SS MS F P
20. The sample standard deviations vary by a factor of about 9. Since the sample sizes are reasonably
21. (a) Source DF SS MS F P
H2SO42 457.65 228.83 8.8447 0.008
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SUPPLEMENTARY EXERCISES FOR CHAPTER 9 471
22. Source DF SS MS F P
23. Source DF SS MS F P
24. (a) Source DF SS MS F P
Distance 5 3.2226 0.64452 3.4668 0.012
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