The table below lists the number of games played in a yearly best-of-seven baseball championship series, along with the expected proportions for the number of games played with teams ofequal abilities. Use a 0.05 significance level to test the claim that the actual numbers of games fit the distribution indicated by the expected proportions.Games PlayedActual contests624547.18194.382Expected proportionho: me uuser veu reyuerés ayree wifi ue'expécieu prupofuunsH: At least one of the observed frequencies do not agree with the expected proportions.Calculate the test statistic, .y2 = (Round to three decimal places as needed.)

Given that: Games Played 4 5 6 7 Actual contests 18 19 24 38 Expected proportion 216 416 516…

Answered: The table below lists the number 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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Question

The table below lists the number of games played in a yearly best-of-seven baseball championship series, along with the expected proportions for the number of games played with teams of
equal abilities. Use a 0.05 significance level to test the claim that the actual numbers of games fit the distribution indicated by the expected proportions.
Games Played
Actual contests
6
24
5
4
7.
18
19
4.
38
2
Expected proportion
ho: me uuser veu reyuerés ayree wifi ue'expécieu prupofuuns
H: At least one of the observed frequencies do not agree with the expected proportions.
Calculate the test statistic, .
y2 = (Round to three decimal places as needed.)

Expert Solution

Step 1

Given that:

Games Played	4	5	6	7
Actual contests	18	19	24	38
Expected proportion	$\frac{2}{16}$	$\frac{4}{16}$	$\frac{5}{16}$	$\frac{5}{16}$

Significance level, $α = 0.05$

Step 2

State the null and alternative hypotheses:

$\begin{array}{rcl} H_{0} : T h e o b s e r v e d f r e q u e n c y a g r e e w i t h t h e e x p e c t e d p r o p o r t i o n s . \\ H_{1} : A t l e a s t o n e o f t h e o b s e r v e d f r e q u e n c i e s d o n o t a g r e e w i t h t h e e x p e c t e d p r o p o r t i o n s . \end{array}$

Find the total count:

$18 + 19 + 24 + 38 = 99$

Compute the expected frequencies by using the formula:

$E_{i} = n p_{i}$

Use table to find the expected frequency:

Actual Contests	Expected proportion	Expected frequency
18	$\frac{2}{16}$	$\frac{2}{16} \times 99 = 12.375$
19	$\frac{4}{16}$	$\frac{4}{16} \times 99 = 24.75$
24	$\frac{5}{16}$	$\frac{5}{16} \times 99 = 30.9375$
38	$\frac{5}{16}$	$\frac{5}{16} \times 99 = 30.9375$
$N = Σ f = 99$

Compute the test statistic:

$\begin{array}{rcl} χ^{2} & = & Σ \frac{{(O_{i} - E_{i})}^{2}}{E_{i}} \\ = & \frac{{(18 - 12.375)}^{2}}{12.375} + \frac{{(19 - 24.75)}^{2}}{24.75} + \frac{{(24 - 30.9375)}^{2}}{30.9375} + \frac{{(38 - 30.9375)}^{2}}{30.9375} \\ = & 7.0606 \\ ≅ & 7.061 \end{array}$