Question

A new fertilizer has been developed to increase the yield on crops, and the makers of the fertilizer want to better understand which of the two blends of this fertilizer are most effective for wheat, corn, and soy beans crops. They test each of the two blends on one sample of each of the three types of crops.

Inner Totals in ()

Figure 1 – Data for Example 1

	Type of Crop
Blend	Wheat	Corn	Soy	Total
Blend X	23 (79) 56	28   (78) 50	66   (144) 78	301
Blend Y	35 (65) 30	75   (107) 32	40   (88) 48	260
Total	144	185	232	561

	a.	At the 5% significance level, can you conclude there is a difference in the crop yields?
	b.	At the 5% significance level, can you conclude there is a difference in the blend yields?
	c.	At the 5% significance level, is there interaction between the blend and the type of crop?

Answer 1

Anova: Two-Factor With Replication
SUMMARY	wheat	corn	soy	Total
blend x
Count	2	2	2	6
Sum	79	78	144	301
Average	39.5	39	72	50.16667
Variance	544.5	242	72	457.7667
blend y
Count	2	2	2	6
Sum	65	107	88	260
Average	32.5	53.5	44	43.33333
Variance	12.5	924.5	32	282.2667
Total
Count	4	4	4
Sum	144	185	232
Average	36	46.25	58
Variance	202	458.9167	296
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	140.08	1	140.08	0.46	0.5229	5.99
Columns	969.50	2	484.75	1.59	0.2789	5.14
Interaction	903.17	2	451.58	1.48	0.2998	5.14
Within	1827.50	6	304.58
Total	3840.25	11

a)

p value for crop yields = 0.2789

p value > 0.05, not significant

there is not a difference in the crop yields

.................

b)

p value for blend yields = 0.5229

p value > 0.05 , not significant

here is not any difference in the blend yields

........................................

c)

p value for interaction = 0.2998

p value > 0.05 , not significant

there is not any interaction between the blend and the type of crop