Researchers suspect that Variety A tomato plants have a different average yield than Varicty B tomato plants. To find out, researchers randomly select 10 Variety A and 10 Variety B tomato plants. Then the researchers divide in half each of 10 small plots of land in different locations. For each plot, a coin toss determines which half of the plot gets a Variety A plant; a Variety B plant goes in the other half. After harvest, they compare the yield in pounds for the plants at each location. The 10 differences (Variety A - Variety B) in yield are recorded. A graph of the differences looks roughly symmetric and unimodal with no outliers. The mean difference is Xᴀ-ʙ = 0.34 and the standard deviation of the differences is Xᴀ-ʙ = 0.83. Let μᴀ-ʙ = the true mean difference (Variety A - Variety B) in yield for tomato plants of these two varieties. Which of the following is the best reason to use a one-sample t interval for a mean difference rather than a two-sample : interval for a difference in means to analyze these data?
A. This is an experiment with randomly assigned treatments.
B. The sample size is less than 30 for both treatments.
C. The response variable, yield of tomatoes, is quantitative.
D. The number of plots is the same for Variety A and Variety B plants.
E. Each plot is given both varieties of tomato plant.