The x? test statistic for a goodness of fit follows where f, is the observed frequency for category i, e, is theexpected frequency for category i, and k is the number of categories. The appropriate x? has k - 1 degrees offreedom.x² =(f, - e)?%3Di = 1The observed and expected frequencies are summarized in the table below.ExpectedFrequencySquaredDifferenceSquared DifferenceDivided by ExpectedObservedDifferenceCategoryFrequencyfj - ej(f - e,)?Frequencye3,600A(-60)? :208020 - 80 = -60= 3,60080B8080100403,60090The sum of the final column will be the x test statistic. Thus, the test statistic is x?=There are k = 3 categories, so the degrees of freedom is k - 1Enter an exact number.

The complete table is, Category Observed fij Expected eij Difference fij-eij Squared…

Answered: The x2 test statistic for a goodness of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The x? test statistic for a goodness of fit follows where f, is the observed frequency for category i, e, is the
expected frequency for category i, and k is the number of categories. The appropriate x? has k - 1 degrees of
freedom.
x² =
(f, - e)?
%3D
i = 1
The observed and expected frequencies are summarized in the table below.
Expected
Frequency
Squared
Difference
Squared Difference
Divided by Expected
Observed
Difference
Category
Frequency
fj - ej
(f - e,)?
Frequency
e
3,600
A
(-60)? :
20
80
20 - 80 = -60
= 3,600
80
B
80
80
100
40
3,600
90
The sum of the final column will be the x test statistic. Thus, the test statistic is x?
=
There are k = 3 categories, so the degrees of freedom is k - 1
Enter an exact number.

Expert Solution

Step 1

The complete table is,

Category	Observed $f_{i j}$	Expected $e_{i j}$	Difference $f_{i j} - e_{i j}$	Squared Difference ${(f_{i j} - e_{i j})}^{2}$	Squared Difference Divided by Expected Frequency $\frac{{(f_{i j} - e_{i j})}^{2}}{f_{i j}}$
A	20	80	-60	${(- 60)}^{2} = 3, 600$	$\frac{3600}{80} = 45$
B	80	80	0	${(0)}^{2} = 0$	0
C	100	40	$100 - 40 = 60$	${(60)}^{2} = 3, 600$	$\frac{3600}{40} = 90$

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