A 20-acre field is divided into l-acre plots, with the plots randomly assigned to one of four groups.

For each plot fertilizer is either applied (F) or not applied (NF). For each plot, water is either applied

(W) or not applied (NW). Thus, there are five plots for each of the four treatments: (F, W), (F, NW),

(NF, W), and (NF, NW). The crop yields in bushels per acre are shown below. Using a 5% level of significance, determine if the within-treatment variances are significantly different. If the null hypothesis of equal variances is accepted, test for a significant difference between group means. If the null hypothesis of equal means is rejected, use the Scheffé multiple range to determine if:

(a) the application of water causes a difference: (F, W) and (NF, W) vs. (F, NW) and (NF, NW);

(b) if the application of fertilizer causes a difference: (F, W) and (F, NW) vs. (NF, W) and (NF, NW);

(c) if both fertilizer and water have a significant effect on crop yield: (F, W) vs. (F, NW), (NF, W), and

(NF, NW).

(F, W) (F, NW) (NF, W) (NF, NW)

114 102 103 93 132 114 109 104 109 92 111 86 116 106 96 91 108 90 100 82