7.112 Planning a study to compare tree size. In Exercise 7.79 (page 459), DBH data for longleaf pine trees in two parts of the Wade Tract are compared. Suppose that you are planning a similar study in which you will measure the diameters of longleaf pine trees. Based on Exercise 7.79, you are willing to assume that the standard deviation for both halves is 20 cm. Suppose that a difference in mean DBH of 10 cm or more would be important to detect. You will use a t statistic and a two-sided alternative for the comparison.

1. (a) Find the power if you randomly sample 20 trees from each area to be compared.

2. (b) Repeat the calculations for 60 trees in each sample.

3. (c) If you had to choose between the 20 and 60 trees per sample, which would you choose? Give reasons for your answer.