Question

Part B (Two Factor ANOVA) Farmers are interested in whether four different types of seeds grow at the same pace. They are also interested in finding out whether the three fertilizers they own are equally effective. They plant three different types of seeds with each of the fertilizers. Two weeks later they measure and record the growth of the crop in millimetres as illustrated below: Fertilizer 1 Seed 1 Seed 2 Seed 3 Seed 4 135 128 115 131 129 137 147 132 139 129 125 120 Fertilizer 2 100 105 154 100 108 97 113 98 101 100 129 115 Fertilizer 3 138 123 141 137 102 147 134 139 145 124 156 113

Answer 1

Using Excel, go to Data, select Data Analysis, choose Anova: Two-Factor With Replication. No. of rows = 3

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Fertilizer	3885.389	2	1942.694	10.928	0.000	3.403
Seed	763.222	3	254.407	1.431	0.258	3.009
Interaction	1377.278	6	229.546	1.291	0.299	2.508
Within	4266.667	24	177.778
Total	10292.556	35

H₀: There is no difference in the effectiveness of the 3 fertilizers

H₁: There is a difference in the effectiveness of at least two of the fertilizers

p-value = 0.000

Since p-value is less than 0.05, we reject the null hypothesis.

There is a difference in the effectiveness of at least two of the fertilizers. (B)

H₀: There is no difference in the growth of the four types of seeds

H₁: There is a difference in the growth of at least two of the seeds

p-value = 0.258

Since p-value is more than 0.05, we do not reject the null hypothesis.

There is no difference in the growth of the four types of seeds. (C)

Answer: Both B and C (Option D)