Problem
A banana grower has three fertilizers from which to choose. He would like to determine which fertilizer produces banana trees with the largest yield (measured in pounds of bananas produced). The banana grower has noticed that there is a difference in the average yields of the banana trees depending on which side of the farm they are planted (South Side, North Side, West Side, or East Side), therefore, a randomized block design is used in the study. Because of the variation in yields among the areas on the farm, the farmer has decided to randomly select three trees within each area and then randomly assign the fertilizers to the trees. After harvesting the bananas, he calculates the yields of the trees within each of the areas. Can the banana grower conclude that there is a significant difference among the average yields of the banana trees for the three fertilizers? The results are as follows.
|
Side of Farm
|
Fertilizer A
|
Fertilizer B
|
Fertilizer C
|
|
South Side
|
4848
|
4646
|
5858
|
|
North Side
|
5353
|
4343
|
5252
|
|
West Side
|
5454
|
4242
|
5151
|
|
East Side
|
4545
|
4141
|
5252
|