Table gives the output for 8 years of an experimental farm that used each of 4 fertilizers. Assume that the outputs with each fertilizer are normally distributed with equal variance.
(a) Find the mean output for each fertilizer and the grand mean for all the years and for all four fertilizers.
(b) Estimate the population variance from the variance between the means or columns.
(c) Estimate the population variance from the variance withinthe samples or columns.
(d) Test the hypothesis that the population means are the same at the 5% level of signi?cance.
Table - Eight-Year Outputs with 4 Di?erent Fertilizers
|
Fertilizer 1
|
Fertilizer 2
|
Fertilizer 3
|
Fertilizer 4
|
|
51
|
47
|
57
|
50
|
|
47
|
50
|
48
|
61
|
|
56
|
58
|
52
|
57
|
|
52
|
61
|
60
|
65
|
|
57
|
51
|
61
|
58
|
|
59
|
48
|
57
|
53
|
|
58
|
59
|
51
|
61
|
|
60
|
50
|
46
|
59
|
|
440
|
424
|
432
|
464
|