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

$χ^{2} = \sum (O - E)^{2} / E$

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:

$χ^{2} = \sum \frac{(O - E)^{2}}{E}$

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

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).

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

Calculus

Decision Maths

Logic and Functions

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

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

Calculus

Decision Maths

Logic and Functions

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.