Question: An agricultural company is trying to decide which type of fertilizer to use on its crops. The company concerned with the average yield on its crops as well as the variance of their yields. In a sample of 41 different fields with using fertilizer A, the average crop yield per acre is 185 tons with a standard deviation of 35 tons. In a separate sample of 61 different fields using fertilizer B, the average crop yield is 175 tons with a standard deviation of 28 tons.

a) First, test the hypothesis (at the 1% level of significance) that there is no difference between the average yields using the different fertilizers. (15)

b) What is the p-value? (5)

c) Next, test the hypothesis (at the 10% level of significance) that variance of one of the yields is significantly larger than the other. (15)