Is there a random distribution of trees? The Wade Tract in Thomas County, Georgia, is an old-growth forest of longleaf pine trees (Pinus palustris) that has survived in a relatively undisturbed state since before the settlement of the area by Europeans.
Foresters who study these trees are interested in how the trees are distributed in the forest. Is there some sort of clustering, resulting in regions of the forest with more trees than others? Or are the tree locations random, resulting in no particular patterns?
Here is one way to examine this question. First, we divide the tract into four equal parts, or quadrants, in the east-west direction. Call the four parts, Q1 to Q4. Then we take a random sample of 100 trees and count the number of trees in each quadrant. Here are the data:
|
Quadrant
|
Q1
|
Q2
|
Q3
|
Q4
|
|
Count
|
18
|
22
|
39
|
21
|
(a) If the trees are randomly distributed, we expect to find 25 trees in each quadrant. Why? Explain your answer.
(b) We do not really expect to get exactly 25 trees in each quadrant. Why? Explain your answer.
(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.