Q.20 The chi-square statistic is(a) (... [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.20 (page 694)

The chi-square statistic is
(a) $\frac{(18 - 25)^{2}}{25} + \frac{(22 - 25)^{2}}{25} + \frac{(39 - 25)^{2}}{25} + \frac{(21 - 25)^{2}}{25}$
(b) $\frac{(25 - 18)^{2}}{18} + \frac{(25 - 22)^{2}}{22} + \frac{(25 - 39)^{2}}{39} + \frac{(25 - 21)^{2}}{21}$
(c) $\frac{(18 - 25)}{25} + \frac{(22 - 25)}{25} + \frac{(39 - 25)}{25} + \frac{(21 - 25)}{25}$
(d) $\frac{(18 - 25)^{2}}{100} + \frac{(22 - 25)^{2}}{100} + \frac{(39 - 25)^{2}}{100} + \frac{(21 - 25)^{2}}{100}$
(e) $\frac{(0.18 - 0.25)^{2}}{0.25} + \frac{(0.22 - 0.25)^{2}}{0.25} + \frac{(0.39 - 0.25)^{2}}{0.25} + \frac{(0.21 - 0.25)^{2}}{0.25}$

Short Answer

Expert verified

The correct answer is

(a) $\frac{(18 - 25)^{2}}{25} + \frac{(22 - 25)^{2}}{25} + \frac{(39 - 25)^{2}}{25} + \frac{(21 - 25)^{2}}{25}$

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 $4$ trees and counted the number in each quadrant. Here are their data:

Explanation

Quadratic	Count
$1$	$18$
$2$	22
$3$	$39$
$4$	$21$

The formula to compute the test statistic is

$蠂^{2} = 鈭� (O - E)^{2} / E$

Step 3:Calculation for test statistic

The calculation for test statistic could be done as:

Observed Value(O)	Expected value(E)
$18$	$0.25 (100) = 25$
$22$	$0.25 (100) = 25$
$39$	$0.25 (100) = 25$
$21$	$0.25 (100) = 25$

The test statistic is:

$蠂^{2} = 鈭� \frac{(O - E)^{2}}{E}$

$= \frac{(18 - 25)^{2}}{25} + \frac{(22 - 25)^{2}}{25} + \frac{(39 - 25)^{2}}{25} + \frac{(21 - 25)^{2}}{25}$

Thus, the test statistic is $\frac{(18 - 25)^{2}}{25} + \frac{(22 - 25)^{2}}{25} + \frac{(39 - 25)^{2}}{25} + \frac{(21 - 25)^{2}}{25}$

Thus, the correct option is (a).

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Short Answer

Step by step solution

Given information

Explanation

Step 3:Calculation for test statistic

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91影视

The chi-square statistic is(a) (18-25)225+(22-25)225+(39-25)225+(21-25)225(b) (25-18)218+(25-22)222+(25-39)239+(25-21)221(c) (18-25)25+(22-25)25+(39-25)25+(21-25)25(d)(18-25)2100+(22-25)2100+(39-25)2100+(21-25)2100(e)(0.18-0.25)20.25+(0.22-0.25)20.25+(0.39-0.25)20.25+(0.21-0.25)20.25

Short Answer

Step by step solution

Given information

Explanation

Step 3:Calculation for test statistic

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Applied Mathematics

Calculus

Probability and Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.