A strain of sweet corn has been genetically modified with a gene from the bacterium Bacillus thuringiensis (Bt) to express the protein Cry1Ab, which is toxic to caterpillars that eat the leaves. Unfortunately, the pollen of transformed corn plants contains the toxin, too. Corn pollen dusts the leaves of other plants growing nearby, where it might have negative effects on non-pest caterpillars. You are hired to conduct a study to measure the effects on monarch butterfly caterpillars of ingesting Bt-modified pollen that has landed on the leaves of milkweed, a plant commonly growing in or near cornfields. You decide to use a completely randomized design to compare the effect of two treatments on monarch pupal weight. In one treatment, you place potted milkweed plants in plots of Bt-modified corn, where their leaves receive pollen carrying the toxin. In the other treatment, you place milkweed plants in plots with ordinary corn that has not been transformed with the Bt gene. You place a monarch larva on every milkweed plant. Previous studies have estimated that the standard deviation of pupal weight in monarch butterflies is about 0.25 g.

a. Suppose your goal at the end of the experiment is to calculate a 95%

confidence interval for the difference between treatments in mean monarch pupal weights. How many plots would you plan in each treatment if your goal was to produce a confidence interval for the difference in mean pupal weights between treatments having a total width of 0.4 g?

b. What sample size would you need if you decided that 0.4 was not precise enough, and that you wished to halve this interval to 0.2?

c. Imagine that your permits allow you to plant only five plots of Bttransformed corn, so that the only way you can increase the total sample size for the whole experiment is to increase the number of plots in the ordinary corn treatment. To achieve the same width of confidence interval as in part (a), would the total sample size needed (both treatments combined) likely be greater, smaller, or no different from that calculated in part (a)? Explain.

d. In designing the experiment, why would you not simply place all the milkweed plants for one treatment at random locations in a single large Bt-transformed corn field, and all the milkweed plants for the other treatment at random locations in a single large normal corn field?