An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds.
ID: 3133492 • Letter: A
Question
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants all 3 varieties of the seeds on each of 5 different patches of fields. She then measures the crop yield in bushels per acre. Treating this as a randomized block design, the results are presented in the table that follows.
Fields Smith Walsh Trevor
1 11.1 19.0 14.6
2 13.5 18.0 15.7
3 15.3 19.8 16.8
4 14.6 19.6 16.7
5 9.8 16.6 15.2
Referring to Scenario 11-6, what is the value of the test statistic for the randomized block F test for the difference in the means?
a. 20.56
b. 41.324
c. 6.133
d. 7.975
Explanation / Answer
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants all 3 varieties of the seeds on each of 5 different patches of fields. She then measures the crop yield in bushels per acre. Treating this as a randomized block design, the results are presented in the table that follows.
Fields Smith Walsh Trevor
1 11.1 19.0 14.6
2 13.5 18.0 15.7
3 15.3 19.8 16.8
4 14.6 19.6 16.7
5 9.8 16.6 15.2
Referring to Scenario 11-6, what is the value of the test statistic for the randomized block F test for the difference in the means?
a. 20.56
b. 41.324
c. 6.133
d. 7.975
Answer b. 41.324
Randomized Block Design (ANOVA: Two-Factor Without Replication)
SUMMARY
Count
Sum
Average
Variance
1
4
45.7
11.4250
58.7492
2
4
49.2
12.3000
50.5267
3
4
54.9
13.7250
54.6225
4
4
54.9
13.7250
46.2358
5
4
46.6
11.6500
28.2500
Smith
5
64.3
12.8600
5.4630
Walsh
5
93
18.6000
1.7400
Trevor
5
79
15.8000
0.9050
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Block
24.4573
4
6.1143
6.1338
0.0147
3.8379
Treatment
82.3853
2
41.1927
41.3235
0.0001
4.4590
Error
7.9747
8
0.9968
Total
114.8173
14
Level of significance
0.05
Randomized Block Design (ANOVA: Two-Factor Without Replication)
SUMMARY
Count
Sum
Average
Variance
1
4
45.7
11.4250
58.7492
2
4
49.2
12.3000
50.5267
3
4
54.9
13.7250
54.6225
4
4
54.9
13.7250
46.2358
5
4
46.6
11.6500
28.2500
Smith
5
64.3
12.8600
5.4630
Walsh
5
93
18.6000
1.7400
Trevor
5
79
15.8000
0.9050
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Block
24.4573
4
6.1143
6.1338
0.0147
3.8379
Treatment
82.3853
2
41.1927
41.3235
0.0001
4.4590
Error
7.9747
8
0.9968
Total
114.8173
14
Level of significance
0.05
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