Question: Crop yields are influenced by “soil pH”. “Soil pH” of 6 (slightly acid) is usually considered optimum. The intensive use of Nitrogen fertilizers reduces “soil pH” and thus crop yields. Lime application on the soil can increase soil pH, thus solving the problem.

In order to make Lime worth using, “soil pH” should be lower than 5.5. You have been hired by a company planning to install a “Lime Distribution Center” to supply Lime to farmers in East Central Illinois. You were asked to evaluate the feasibility of such investment.

First you decided to statistically evaluate “Soil pH” across East Central Illinois. In order to do that, you randomly collected a large data set (N=150) from three different “soil conditions” (n₁=n₂=n₃=50): Control (soils that never received Nitrogen fertilization nor lime), Nitrogen (soils that received only Nitrogen), and Nitrogen-Lime (soils that received Nitrogen and lime). After taking a look at the SAS output, answer the following questions.

Dependent Variable: pH

Sum of

Source DF Squares Mean Square F Value Pr > F

Condition 2 1.14827139 0.57413569 4.81 0.0095

Error 147 17.55448232 0.11941825

Corrected Total 149 18.70275371

R-Square Coeff Var Root MSE pH Mean

0.061396 5.783664 0.345569 5.974923

Least Significant Difference 0.1366

Means with the same letter are not significantly different.

t Grouping Mean N condition

A 6.04130 50 Nitrogen-Lime

A 6.03217 50 Control

B 5.85130 50 Nitrogen

a) Although the “Sum of Squares Error” is large and “The Coefficient of the determination” is small, the null Hypothesis of Condition being equal is rejected. Why do you think this happened?

b) Review the LSD output and make inferences about the soil conditions. Be meaningful.

c) Would you recommend installing a Lime distribution facility in Central Illinois? Why?