9.55 Is there a random distribution of trees? In Example 6.1 (page 342), we examined data concerning the longleaf pine trees in the Wade Tract and concluded that the distribution of trees in the tract was not random. Here is another way to examine the same question. First, we divide the tract into four equal parts, or quadrants, in the east–west direction. Call the four parts through . Then we take a random sample of 100 trees and count the number of trees in each quadrant. Here are the data:

QuadrantQ1Q2Q3Q4
Count18223921

  1. (a) If the trees are randomly distributed, we expect to find 25 trees in each quadrant. Why? Explain your answer.

  2. (b) We do not really expect to get exactly 25 trees in each quadrant. Why? Explain your answer.

  3. (c) Perform the goodness-of-fit test for these data to determine if these trees are randomly scattered. Write a short report giving the details of your analysis and your conclusion.