Q.19 An appropriate null hypothesis t... [FREE SOLUTION]

91影视

The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

Chapter 11: Q.19 (page 694)

An appropriate null hypothesis to test whether the trees in the forest are randomly distributed is
(a) $H_{0} : 渭 = 25$ , where $渭 =$ 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

Expert verified

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:

Explanation

The table is

Quadrant	Frequency
$1$	$18$
$2$	$22$
$3$	$39$
$4$	$21$

The proportion is computed as:

localid="1650552960795" $p_{i} = \frac{1}{4} = 0.25$

The null and alternative hypotheses are:

$H_{0} : p_{1} = 0.25$

$H_{0} : p_{2} = 0.25$

$H_{0} : p_{3} = 0.25$

localid="1650621296388" $H_{0} : p_{4} = 0.25$

$H_{a} :$ At least one of is different Thus, the correct option is (d).

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