Question

	Crop
Fertilizer	Corn	Wheat	Rice	Soy
Blend A	128	123	151	166
	150	156	125	178
	174	112	117	187
	116	100	155	153
	109	168	158	195
Blend B	175	135	167	140
	132	130	183	145
	120	176	142	159
	187	120	167	131
	184	155	168	126
Blend C	185	156	175	185
	138	180	173	206
	178	147	154	188
	176	146	191	165
	190	193	169	188

A company has developed a new fertilizer to increase crop production and wants to understand which of the three blends are most effective for four types of crops (corn, wheat, rice, and soy). They randomly test each of the three blends on five samples of each of four types of crops and measure the crop yields.
Use the data listed above.

Complete the ANOVA table (2 decimal places)

a:                                                 d:
b:                                                 e:
c:                                                  f:

g. Conduct the F-test for the interaction (at alpha=0.05). Can you reject the null hypothesis?

              (yes/no):

h. Conduct the F-test for Fertilizer main effect (at alpha=0.05). Can you reject the null hypothesis?

             (yes/no):

i. Conduct the F-test for Crop main effect (at alpha=0.05). Can you reject the null hypothesis?

            (yes/no):

Answer 1

Anova: Two-Factor With Replication
SUMMARY	Corn	Wheat	Rice	Soy	Total
Blend A
Count	5	5	5	5	20
Sum	677	659	706	879	2921
Average	135.4	131.8	141.2	176	146.05
Variance	707.8	844.2	354.2	279	782.37
Blend B
Count	5	5	5	5	20
Sum	798	716	827	701	3042
Average	159.6	143.2	165.4	140	152.1
Variance	978.3	498.7	217.3	166	511.04
Blend C
Count	5	5	5	5	20
Sum	867	822	862	932	3483
Average	173.4	164.4	172.4	186	174.15
Variance	422.8	443.3	175.8	212	329.5
Total
Count	15	15	15	15
Sum	2342	2197	2395	2512
Average	156.1333	146.4667	159.667	167
Variance	866.8381	705.8381	404.952	606
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Fertilizer (Sample)	8749.43	2	4374.72	9.91	0.0003	3.19
Crop (Columns)	3414.20	3	1138.07	2.58	0.0646	2.8
Interaction	6224.70	6	1037.45	2.35	0.0454	2.29
Within	21196.40	48	441.59
Total	39584.73	59

g. Since P-value for interaction=0.0454<0.05 so we reject the null hypothesis. Option yes.

h. Since P-value for Fertilizer=0.0003<0.05 so we reject the null hypothesis. Option yes.

i. Since P-value for Crop=0.0646>0.05 so we fail to reject the null hypothesis. Option No.