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9.40. An experiment is performed to test the effect on corn yield of 4 different fertilizer treatments, A, B, C, D, and of soil variations in two perpendicular directions. The Latin square Table 9-44 is obtained, where the numbers indicate corn yield per unit area. Test at a 0.01 level the hypothesis that there is no difference in (a) fertilizers, (b) soil variations. Table 9-44 C 8 A 10 C 12 B 14 D 16 D 12 B 11 C 16 A 14 B 11 D 15 A 10 C 12
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A 14 D 10 B 7
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9.41. Work Problem 9.40 using a 0.05 level. 9.42. Referring to Problem 9.35 suppose that we introduce an additional factor giving the section E, M, or W of the United States in which a student was born, as shown in Table 9-45. Determine at a 0.05 level whether there is a significant difference in scholastic achievement of female students due to differences in (a) height, (b) hair color, (c) birthplace. Table 9-45 E 75 M 81 W 73 W 78 E 76 M 75 M 80 W 79 E 77
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CHAPTER 9 Analysis of Variance
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9.43. In order to produce a superior type of chicken feed, 4 different quantities of each of two chemicals are added to the basic ingredients. The different quantities of the first chemical are indicated by A, B, C, D while those of the second chemical are indicated by a, b, g, d. The feed is given to baby chicks arranged in groups according to 4 different initial weights, W1, W2, W3, W4, and 4 different species, S1, S2, S3, S4. The increases in weight per unit time are given in the Graeco-Latin square of Table 9-46. Perform an analysis of variance of the experiment at a 0.05 level of significance, stating any conclusions that can be drawn. Table 9-46 W S1 S2 S3 S4 Cg 8 Ad 4 Db 5 Ba 6 W2 Bb Da Ag 6 3 6 W3 Aa 5 Cb 7 Bd 5 W4 Dd 6 Bg 3 Ca 6 Ab 8
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9.44. Four different types of cables, T1, T2, T3, T4, are manufactured by each of 4 companies, C1, C2, C3, C4. Four operators, A, B, C, D, using four different machines, a, b, g, d, measure the cable strengths. The average strengths obtained are given in the Graeco-Latin square of Table 9-47. Perform an analysis of variance at the 0.05 level, stating any conclusions that can be drawn. Table 9-47 C2 Bg 181 Da 162 Cb 221 Ad 172
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C1 T1 T2 T3 T4 Ab 164 Cd 171 Dg 198 Ba 157
C3 Ca 193 Ag 183 Bd 207 Db 166
C4 Dd 160 Bb 145 Aa 188 Cg 136
Miscellaneous problems
9.45. Table 9-48 gives data on the accumulated rust on iron treated with chemical A, B, or C, respectively. Determine at the (a) 0.05, (b) 0.01 level whether there is a significant difference in the treatments.
Table 9-48 A B C 3 4 6 5 2 4 4 3 5 4 3 5 Tall Short Medium 110 95 108
Table 9-49 105 103 112 118 115 93 112 107 104 96 102 90
9.46. An experiment measures the IQs of adult male students of tall, short, and medium stature. The results are indicated in Table 9-49. Determine at the (a) 0.05, (b) 0.01 level whether there is any significant difference in the IQ scores relative to height differences. 9.47. An examination is given to determine whether veterans or nonveterans of different IQs performed better. The scores obtained are shown in Table 9-50. Determine at the 0.05 level whether there is a difference in scores due to differences in (a) veteran status, (b) IQ.
CHAPTER 9 Analysis of Variance
Table 9-50 Medium IQ 81 78
High IQ Veteran Nonveteran 90 85
Low IQ 74 70
9.48. Work Problem 9.47 using a 0.01 level. 9.49. Table 9-51 shows test scores for a sample of college students from different parts of the country having different IQs. Analyze the table at a 0.05 level of significance and state your conclusions. Table 9-51 High Medium East West South North & Central 88 84 86 80 80 78 82 75
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