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. What is the conditional distribution of the variable High Salary when looking only at those who are free agents? 2. What is the conditional distribution of the variable High Salarywhen looking only at those who are not free agents? 3. What is the marginal distribution of High Salary

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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. What is the conditional distribution of the variable High Salary when looking only at those who are free agents?

2. What is the conditional distribution of the variable High Salarywhen looking only at those who are not free agents?

3. What is the marginal distribution of High Salary?

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%
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
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