10.107 An interesting and practical use of the test comes about in the testing for segregation of species of plants or animals. Suppose that two species of plants, A and B, are growing on a test plot.To assess whether or not the species tend to segregate, n plants are randomly sampled from the plot, and the species of each sampled plant and the species of its nearest neighbor are recorded. The recorded. The data are then arranged in a table as follows:

If a and d are large relative to b and

c, we would be inclined to say that the species tend to segregate. (Most of A’s neighbors and of type A, and most of B’s neighbors are of type B). If b and c are large compared to a and

d, we would say that the species tend to be overly mixed. In either of these cases (segregation or overmixing), a test should yield a large value, and the hypothesis of random mixing would be rejected. For each of the following cases, test the hypothesis of random mixing (or, equivalently, the hypothesis that the species of a sampled plants is independent of the species of its nearest neighbor). Use in each case.

a a 20, b 4, c = 8, d = 18 ba 4, b 20, c = 18, d = 8 ca 20, b = 4, c = 18, d = 8

Transcribed Image Text:

Sample Plant A Nearest Neighbour A B a b B C d n