A farmer was planting corn and was interested in the effects of three different
ID: 3128283 • Letter: A
Question
A farmer was planting corn and was interested in the effects of three different seed types and five different fertilizers on the height of the corn after three months. The data is summarized below. (Note: there are two observations for each different seed/fertilizer combination)
Fert I
Fert II
Fert III
Fert IV
Fert V
Seed A
106 110
95 100
94 107
103 104
100 102
Seed B
110 112
98 99
100 101
108 112
105 107
Seed C
94 97
86 87
98 99
99 101
94 98
A. Either use Minitab or find the ANOVA table by hand. If using Minitab, attach output. (Note: include interaction!!)
B. Perform a hypothesis test for the global model using the ANOVA table in part A.
C. Perform a hypothesis for the interaction using the ANOVA table in part A.
D. Based on the results for part C should you perform a hypothesis test for each main effect? If yes, then perform a hypothesis test for each main effect using the ANOVA table in part A.
Fert I
Fert II
Fert III
Fert IV
Fert V
Seed A
106 110
95 100
94 107
103 104
100 102
Seed B
110 112
98 99
100 101
108 112
105 107
Seed C
94 97
86 87
98 99
99 101
94 98
Explanation / Answer
The ANOVA Table is given by
B) Since the p-value 0.000008 < 0.05, conclude that there is a significant difference between the seeds
C) Since the p-value for intercation is 0.12209 > 0.05, conclude that there is no interaction effect on the output
ANOVA Source of Variation SS df MS F P-value F crit Sample 512.8667 2 256.4333 28.28309 8.14E-06 3.68232 Columns 449.4667 4 112.3667 12.39338 0.000119 3.055568 Interaction 143.1333 8 17.89167 1.973346 0.12209 2.640797 Within 136 15 9.066667 Total 1241.467 29
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