Chapter 11: Q.19 (page 694)

An appropriate null hypothesis to test whether the trees in the forest are randomly distributed is
(a) $H_{0} : μ = 25$ , where $μ =$ the mean number of trees in each quadrant.
(b) $H_{0} : p = 0.25$ , where $p =$ the proportion of all trees in the forest that are in Quadrant $1 .$
(c) $H_{0} : n_{1} = n_{2} = n_{3} = n_{4} = 25$ , where $n_{i}$ is the number of trees from the sample in Quadrant $i$ .
(d) $H_{0} : p_{1} = p_{2} = p_{3} = p_{4} = 0.25$ , where $p_{i}$ is the actual proportion of trees in the forest that are in Quadrant $i$ .
(e) $H_{0} : {\hat{p}}_{1} = {\hat{p}}_{2} = {\hat{p}}_{3} = {\hat{p}}_{4} = 0.25$ , where ${\hat{p}}_{i}$ is the proportion of trees in the sample that are in Quadrant $i .$

Short Answer

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Correct Answer is

(d) $H_{0} : p_{1} = p_{2} = p_{3} = p_{4} = 0.25$ , where $p_{i}$ is the actual proportion of trees in the forest that are in Quadrant $i$ .

Step by step solution

Given information

Given in the question that, Researchers wondered whether the trees in a longleaf pine forest in Georgia are randomly distributed. To find out, they divided the forest into four equal quadrants. Then the researchers took a random sample of 100 trees and counted the number in each quadrant. Here are their data: