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. The given χ2test table gives many test statistics. The row we want to look at is labeled Pearson Chi-Square. Give the test statistic, the degrees of freedom, and the p-value. 2. At a significance level of .05, what can you conclude in the context of this problem?

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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. The given χ2test table gives many test statistics. The row we want to look at is labeled Pearson Chi-Square. Give the test statistic, the degrees of freedom, and the p-value.

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

 

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%
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
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