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Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset 91影视 Explanations$ Math

OER 2018 Edition 路 902 pages

ISBN: 9781938168208

Chapter 13: Q. 36 (page 766)

A video game developer is testing a new game on three different groups. Each group represents a different target market for the game. The developer collects scores from a random sample from each group. The results are shown in the Table.
$\begin{array}{l} Group A & Group B & Group C \\ 101 & 151 & 101 \\ 108 & 149 & 109 \\ 98 & 160 & 198 \\ 107 & 112 & 186 \\ 111 & 126 & 160 \end{array}$
What are the $S S_{within}$ and $M S_{within}$ ?

Short Answer

Expert verified

The values of $S S_{within}$ and $M S_{within}$ are $9474$ and $789.5$ .

Step by step solution

01

Given Information

A video game developer is testing a new game on three different groups. Sample from each group is
$\begin{array}{l} Group A & Group B & Group C \\ 101 & 151 & 101 \\ 108 & 149 & 109 \\ 98 & 160 & 198 \\ 107 & 112 & 186 \\ 111 & 126 & 160 \end{array}$

02

Explanation

From our Table, we can calculate

$s_{1} = 525, s_{2} = 698, s_{3} = 754$

We now can calculate:

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

$S_{between} = \frac{s_{1}^{2}}{5} + \frac{s_{2}^{2}}{5} + \frac{s_{3}^{2}}{5} - \frac{{(s_{1} + s_{2} + s_{3})}^{2}}{15}$

where $n_{1} = n_{2} = n_{3} = 5$ and $n = n_{1} + n_{2} + n_{3} = 15$

So, we calculate

$\frac{(525)^{2}}{5} + \frac{(698)^{2}}{5} + \frac{(754)^{2}}{5} - \frac{(525 + 698 + 754)^{2}}{15}$

${SS}_{between} = 266.269 - 260568.6 = 5700.4$

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

$S_{total} = 275.743 - 260568.6$

$S_{total} = 15174.4$

03

Final Answer

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

${SS}_{within} = 9474$

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

${MS}_{within} = \frac{9474}{12} = 789.5$

Therefore,

$S S_{within} = 9474 M S_{within} = 789.5$

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Most popular questions from this chapter

Two coworkers commute from the same building. They are interested in whether or not there is any variation in the time it takes them to drive to work. They each record their times for $20$ commutes. The first worker鈥檚 times have a variance of $12.1$ . These coworkers' times have a variance of $16.9$ . The first worker thinks that he is more consistent with his commute times. Test the claim at the $10$ % level. Assume that commute times are normally distributed. What is the F statistic?

What is the $F -$ statistic?

What is the df for the numerator?

What happens to the curves as the degrees of freedom for the numerator and the denominator get larger?

An $F$ statistic can have what values?

See all solutions

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