We are interested in looking at the effect of a baseball player’s free-agent status on their salary. We look at 337 baseball players and categorize them as either having a high salary (above 2 million) or not, and as either being free agents or not. 1. Verify the expected counts using the equation: expected = row total x column total / (divided by) table total 2. At a significance level of .05, what can you conclude in the context of this problem? 3. Verify the χ2 test statistic using: X2 = ∑ (observed - expected) 2 /(divided by) expected.

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
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Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
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We are interested in looking at the effect of a baseball player’s free-agent status on their salary. We look at 337 baseball players and categorize them as either having a high salary (above 2 million) or not, and as either being free agents or not.

1. Verify the expected counts using the equation: expected = row total x column total / (divided by) table total

2. At a significance level of .05, what can you conclude in the context of this problem?

3. Verify the χ2 test statistic using: X2 = ∑ (observed - expected) /(divided by) expected.

High Salary * Free Agent Crosstabulation
Free Agent
Not Free Agent Free Agent
Total
High Salary Normal Salary Count
185
61
246
Expected Count
148.2
97.8
246.0
% within Free Agent
91.1%
45.5%
73.0%
High Salary
Count
18
73
91
Expected Count
54.8
36.2
91.0
% within Free Agent
8.9%
54.5%
27.0%
Total
Count
203
134
337
Expected Count
203.0
134.0
337.0
% within Free Agent
100.0%
100.0%
100.0%
Chi-Square Tests
Asymptotic
Significance (2- Exact Sig. (2-
sided)
Exact Sig. (1-
sided)
Value
df
sided)
Pearson Chi-Square
85.190°
1
.000
Continuity Correctionb
82.891
.000
1
Likelihood Ratio
86.872
1
.000
Fisher's Exact Test
.000
.000
Linear-by-Linear
Association
84.937
1
.000
N of Valid Cases
a. O cells (0.0%) have expected count less than 5. The minimum expected count is 36.18.
337
b. Computed only for a 2x2 table
Transcribed Image Text:High Salary * Free Agent Crosstabulation Free Agent Not Free Agent Free Agent Total High Salary Normal Salary Count 185 61 246 Expected Count 148.2 97.8 246.0 % within Free Agent 91.1% 45.5% 73.0% High Salary Count 18 73 91 Expected Count 54.8 36.2 91.0 % within Free Agent 8.9% 54.5% 27.0% Total Count 203 134 337 Expected Count 203.0 134.0 337.0 % within Free Agent 100.0% 100.0% 100.0% Chi-Square Tests Asymptotic Significance (2- Exact Sig. (2- sided) Exact Sig. (1- sided) Value df sided) Pearson Chi-Square 85.190° 1 .000 Continuity Correctionb 82.891 .000 1 Likelihood Ratio 86.872 1 .000 Fisher's Exact Test .000 .000 Linear-by-Linear Association 84.937 1 .000 N of Valid Cases a. O cells (0.0%) have expected count less than 5. The minimum expected count is 36.18. 337 b. Computed only for a 2x2 table
Crosstabs
Case Processing Summary
Cases
Valid
Missing
Total
N
Percent
N
Percent
N
Percent
High Salary * Free Agent
337
100.0%
0.0%
337
100.0%
Transcribed Image Text:Crosstabs Case Processing Summary Cases Valid Missing Total N Percent N Percent N Percent High Salary * Free Agent 337 100.0% 0.0% 337 100.0%
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