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
$12,000 \quad 3127.1720 .04$
$16,000 \quad 3140.9323 .63$
$20,000 \quad 3145.0018 .21$
$24,000 \quad 3143.0711 .44$ For this example, which of the following statements is correct?

Question

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
$12,000 \quad 3127.1720 .04$
$16,000 \quad 3140.9323 .63$
$20,000 \quad 3145.0018 .21$
$24,000 \quad 3143.0711 .44$ For this example, which of the following statements is correct?

Quizplus · Accepted Answer

The data were collected as part of an experiment, not an observational study, because the experimenters controlled the planting density. The assumption of equal variances (homogeneity of variance) cannot be assessed with the information provided, and ANOVA does not require equal sample sizes, though it is more robust to violations of this assumption when sample sizes are equal.

How Much Corn Should Be Planted Per Acre for a Farmer