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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To compute simultaneous rather than individual Tukey confidence intervals, which of the following must be adjusted?

A) The critical value
B) The degrees of freedom
C) Both the critical value and the degrees of freedom
D) Neither the critical value nor the degrees of freedom