An experiment was set up to compare the effect of different soil pH and calcium additives on the increase in trunk diameters for orange trees. Annual applications of elemental sulfur, gypsum, soda ash, and other ingredients were applied to provide pH value levels of 4, 5, 6, and 7. Three levels of a calcium supplement (100, 200, and 300 pounds per acre) were also applied. All factor-level combinations of these two variables were used in the experiment. At the end of a 2-year period, three diameters were examined at each factor-level combination. The data appear next.
Calcium
pH 100 200 300
5.2 7.4 6.3
4.0 5.9 7.0 6.7
6.3 7.6 6.1
7.1 7.4 7.3
5.0 7.4 7.3 7.5
7.5 7.1 7.2
7.6 7.6 7.2
6.0 7.2 7.5 7.3
7.4 7.8 7.0
7.2 7.4 6.8
7.0 7.5 7.0 6.6
7.2 6.9 6.4
a. Construct a profile plot. What do the data suggest?
b. Identify the treatment structure and the design structure.
c. Write an appropriate statistical model.
d. Using statistical software, perform an analysis of variance and test for interactions and main effects. Use .05.