How Much Corn Should Be Planted Per Acre for a Farmer

How much corn should be planted per acre for a farmer to get the highest yield? Too few plants will give a low yield, while too many plants will result in plants competing for moisture and nutrients, resulting in a lower yield. Four levels of planting density are to be studied: 12,000, 16,000, 20,000, and 24,000 plants per acre. The experimenters had 12 acres available for the study; 3 acres were assigned at random to each of the planting densities. The data follow.
$$\begin{array} { | c | ccc | } \hline \text { Plants (per acre) } & \text { Yield (bushels per acre) } \\\hline 12,000 & 150.1 & 113.0 & 118.4 \\\hline 16,000 & 166.9 & 120.7 & 135.2 \\\hline 20,000 & 165.3 & 130.1 & 139.6 \\\hline 24,000 & 134.7 & 138.4 & 156.1 \\\hline\end{array}$$ Assume the data can be considered four independent SRSs, one from each of the four populations of planting densities, and that the distribution of the yields is Normal. A partial ANOVA table produced by Minitab follows, along with the means and standard deviations of the yields for the four groups.
One-Way ANOVA: Yield Versus Density
Source DF SS MS F P
Density 589
Error $\quad 356$
Total
Density      N Mean StDev
$12,000 \quad 3127.1720 .04$
$16,000 \quad 3140.9323 .63$
$20,000 \quad 3145.0018 .21$
$24,000 \quad 3143.0711 .44$ What is the sum of squares for the error component?

A) 196
B) 356
C) 589
D) 2848