Q.22 What is the F statistic?聽... [FREE SOLUTION]

91影视

Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset 91影视 Explanations$ Math

OER 2018 Edition 路 902 pages

ISBN: 9781938168208

Chapter 13: Q.22 (page 766)

What is the $F$ statistic?

Short Answer

Expert verified

The value of $F - s t a t i s t i c = 10.404$ .

Step by step solution

Given Information

Team 1	Team 2	Team 3	Team 4
1	2	0	3
2	3	0	4
0	2	1	4
3	4	1	3
2	4	0	2

Calculate the F statistics

To find the value of $F$ -statistic:

From our Table, we can calculate

s_{1} = 8, s_{2} = 15, s_{3} = 2, s_{4} = 16

We now can calculate:

{SS}_{between} = 鈭� [\frac{{(s_{j})}^{2}}{n_{j}}] - \frac{{(鈭� s_{j})}^{2}}{n}

$S S_{between} = \frac{s_{1}^{2}}{5} + \frac{s_{2}^{2}}{5} + \frac{s_{3}^{2}}{5} + \frac{s_{4}^{2}}{5} - \frac{{(s_{1} + s_{2} + s_{3} + s_{4})}^{2}}{20}$

$where n_{1} = n_{2} = n_{3} = n_{4} = 5 and n = n_{1} + n_{2} + n_{3} + n_{4} = 20$

We calculate,

$\frac{(8)^{2}}{5} + \frac{(15)^{2}}{5} + \frac{(2)^{2}}{5} + \frac{(16)^{2}}{5} - \frac{(8 + 15 + 2 + 16)^{2}}{20}$

Calculate the sum of squares within the group

${SS}_{between} = 109, 8 - 84.05 = 25.75$

$S_{total} = 鈭� x^{2} - \frac{{(鈭� x)}^{2}}{n}$

$S_{total} = 123 - 84.05$

$S_{total} = 38.95$

${SS}_{within} = {SS}_{total} - {SS}_{between}$

${SS}_{within} = 13.2$

Calculate the mean of square

We calculate $M S_{between}$ like:

$M S_{between} = \frac{S S_{between}}{k - 1}, where k = 4$

${MS}_{between} = \frac{25.75}{3} = 8.58333$

We calculate $M S_{within}$ like:

$M S_{within} = \frac{S S_{within}}{n - k}$

${MS}_{within} = \frac{13.2}{16} = 0.825$

Now, we can find $F -$ statistic:

F = \frac{M S_{between}}{M S_{within}} = \frac{8.58333}{0.825}

$F = 10.404$

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91影视

What is the $F$ statistic?

Short Answer

Step by step solution

Given Information

Calculate the F statistics

Calculate the sum of squares within the group

Calculate the mean of square

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