How Much Corn Should Be Planted Per Acre for a Farmer

Multiple Choice

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.
$$\begin{array} { | c | c c l | } \hline \text { Plants (per acre) } & \text { Yield (bushels per acre) } \\\hline 12,000 & 150.1 & 113.0 & 118.4 \\\hline 16,000 & 166.9 & 120.7 & 135.2 \\\hline 20,000 & 165.3 & 130.1 & 139.6 \\\hline 24,000 & 134.7 & 138.4 & 156.1 \\\hline\end{array}$$ 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.

$$\begin{array}{l}\text { One-Way ANOVA: Yield Versus Density }\\\\\begin{array} { l r r r r r } \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \\\text { Density } & & 589 & & & \\\text { Error } & & & 356 & & \\\text { Total } & & & & &\end{array}\\\\\begin{array} { l c r r } \text { Density } & \mathrm { N } & \text { Mean } & \text { StDev } \\12,000 & 3 & 127.17 & 20.04 \\16,000 & 3 & 140.93 & 23.63 \\20,000 & 3 & 145.00 & 18.21 \\24,000 & 3 & 143.07 & 11.44\end{array}\end{array}$$
What is the degrees of freedom for the density (i.e., between-group) component?

A) 2
B) 3
C) 8
D) 11