Corn Yields and Fertilizers:
Three types of fertilizers are to be tested to see which to see which one yields more corn crop. Forty similar plots of land were available for testing purposes. The 40 plots were divided at random into 4 groups, ten for each groups. Fertilizer 1 was applied to the plots in group 1, and Fertilizers 2 and 3 were applied to groups 2 and 3. The corn plants in groups 4 were not given any fertilizer and will serve as the control group. The table below gives the corn yields for each of the forty plots:
|
Fertilizer 1
|
Fertilizer 2
|
Fertilizer 3
|
Control Group
|
|
31
|
27
|
36
|
33
|
|
34
|
27
|
37
|
27
|
|
34
|
25
|
37
|
35
|
|
34
|
34
|
34
|
25
|
|
43
|
21
|
37
|
29
|
|
35
|
36
|
28
|
20
|
|
38
|
34
|
33
|
25
|
|
36
|
30
|
29
|
40
|
|
36
|
32
|
36
|
35
|
|
45
|
33
|
42
|
29
|
a. Create 3 dummy variables X1, X2, and X3 one for each fertilizer groups.
b. Test the hypothesis that none of the three fertilizers has an effect on corn crops. Define the model; specify the hypothesis to be tested, the test used and your conclusion at the 5% significance level.
c. Test the hypothesis that the use of fertilizers (any one of the 3) has a positive effect on corn crops. Define the model, specify the hypothesis to be tested, the test used and your conclusion at the 5% significance level.
d. Based on a multiple regression decide what fertilizer has the greatest effect on corn yield.