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. ------------------------------ You also wonder if having a high batting average affects the salary of baseball players. You classify all 370 baseball players as having a high batting average if it is over .300. 1. What is the conditional distribution of high salary when looking only at those who have high batting averages? 2. What is the marginal distribution of high salary? 3. Give the four expected counts.

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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.

------------------------------

You also wonder if having a high batting average affects the salary of baseball players. You classify all 370 baseball players as having a high batting average if it is over .300.

1. What is the conditional distribution of high salary when looking only at those who have high batting averages?

2. What is the marginal distribution of high salary?

3. Give the four expected counts.

Chi-Square Tests
Asymptotic
Significance (2- Exact Sig. (2-
sided)
Exact Sig. (1-
sided)
Value
df
sided)
Pearson Chi-Square
12.501°
1
.000
Continuity Correctionb
11.152
.001
Likelihood Ratio
11.223
1
.001
Fisher's Exact Test
.001
.001
Linear-by-Linear
Association
12.464
1
.000
N of Valid Cases
337
a. O cells (0.0%) have expected count less than 5. The minimum expected count is 9.99.
b. Computed only for a 2x2 table
Transcribed Image Text:Chi-Square Tests Asymptotic Significance (2- Exact Sig. (2- sided) Exact Sig. (1- sided) Value df sided) Pearson Chi-Square 12.501° 1 .000 Continuity Correctionb 11.152 .001 Likelihood Ratio 11.223 1 .001 Fisher's Exact Test .001 .001 Linear-by-Linear Association 12.464 1 .000 N of Valid Cases 337 a. O cells (0.0%) have expected count less than 5. The minimum expected count is 9.99. b. Computed only for a 2x2 table
Case Processing Summary
Cases
Valid
Missing
Total
N
Percent
N Percent
N
Percent
High Salary * HighBatting
0.0%
337
100.0%
337
100.0%
High Salary * HighBatting Crosstabulation
HighBatting
Below Average
Batting
High Batting
Average
Total
High Salary Normal Salary Count
228
18
246
Expected Count
219.0
27.0
246.0
% within HighBatting
76.0%
48.6%
73.0%
High Salary
Count
72
19
91
Expected Count
81.0
10.0
91.0
% within HighBatting
24.0%
51.4%
27.0%
Total
Count
300
37
337
Expected Count
300.0
37.0
337.0
% within HighBatting
100.0%
100.0%
100.0%
Transcribed Image Text:Case Processing Summary Cases Valid Missing Total N Percent N Percent N Percent High Salary * HighBatting 0.0% 337 100.0% 337 100.0% High Salary * HighBatting Crosstabulation HighBatting Below Average Batting High Batting Average Total High Salary Normal Salary Count 228 18 246 Expected Count 219.0 27.0 246.0 % within HighBatting 76.0% 48.6% 73.0% High Salary Count 72 19 91 Expected Count 81.0 10.0 91.0 % within HighBatting 24.0% 51.4% 27.0% Total Count 300 37 337 Expected Count 300.0 37.0 337.0 % within HighBatting 100.0% 100.0% 100.0%
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