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 compete with each other 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, and three acres were assigned at random to each of the planting densities. A summary of the data follows:
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$$\begin{array} { | l | l | l | } \hline \text { Plants (per acre) } & \bar { y } _ { i } & S _ { i } \\\hline 12,000 & 5 & 2.0 \\\hline 16,000 & 7 & 2.8 \\\hline 20,000 & 12 & 3.0 \\\hline 24,000 & 4 & 1.6 \\\hline\end{array}$$ Assume the data are four independent SRSs, one from each of the four populations of planting densities, and that the distribution of the yields is Normal.
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What would be an individual 95% Tukey confidence interval for a difference in the 12,000 and 24,000 planting densities?

A) -2000 ± (2.776) (2.42)
$$\left( \sqrt { \frac { 1 } { 3 } + \frac { 1 } { 3 } } \right)$$
B) 1 ± (2.776) (2.42)
$$\left( \sqrt { \frac { 1 } { 3 } + \frac { 1 } { 3 } } \right)$$
C) -12000 ± (2.306) (2.42)
$$\left( \sqrt { \frac { 1 } { 3 } + \frac { 1 } { 3 } } \right)$$
D) 1 ± (2.306) (2.42) $$\left( \sqrt { \frac { 1 } { 3 } + \frac { 1 } { 3 } } \right)$$