Assignment:
According to the current Collective Bargaining Agreement, the minimum salary for a Major League Baseball player will be $390,000 in 2008 and the maximum salary in 2008 will be $27.5 million per year after ten years (2007-11 Basic Agreement, 2007). $3.15 million was the average salary of the MLB's 855 players (Kendrick, 2008). The question is, does a baseball player's salary directly affect a team's ability to win baseball games? Our paper will test this hypothesis and give the reasons behind our findings.
In order to response the question of Major League Baseball players' salaries verses wins we will need to use a hypothesis to determine the answer. We will use a hypothesis of Ho: μ = player's salaries are equal to their performance statistics and Hi ≠ players with higher salaries do not have higher performance statistics.
Using the statistical data provided, we were able to construct two hypothesis statements that will be measured to see if salaries directly affect a team's ability to win baseball games (Lind, Marchall, & Wathen, 2008). To achieve this goal I have hypothesized that teams who have a high salary range will win more games than those teams that have players with lower salary ranges. The hypotheses to be tested are:
H0: (means of the games won are the same through out the salary scale)
H1: Not all the means are equal (at least one means is different then the others)
Data Format
ANOVA dependent variable and one factor which are seen below in table 1 and solution is seen in table 2.
Dependent variable:
Y= Total number of Wins
One Factor:
Factor A (salary of teams)
A1= $90,000,000 and over
A2= $89,999,999 to $69,000,000
A3=$68,999,999 to 48,999,999
A4=48,999,999 and below
Table 1
|
A1
90000000 +
|
A2
$89,999,999 to
$69,000,000
|
A3
$68,999,999 to
48,999,999
|
A4
48,999,998 and
Below
|
|
95
|
|
|
|
|
95
|
|
|
|
|
|
|
88
|
|
|
|
74
|
|
|
|
95
|
|
|
|
|
|
|
|
93
|
|
|
99
|
|
|
|
|
|
|
80
|
|
|
|
83
|
|
|
|
|
79
|
67
|
|
|
71
|
|
|
|
|
69
|
|
|
|
|
|
|
56
|
|
|
90
|
|
|
|
|
|
77
|
|
|
|
89
|
|
|
|
|
|
73
|
|
|
83
|
|
|
|
|
|
|
|
67
|
|
|
71
|
|
|
|
|
|
82
|
|
|
|
|
|
81
|
|
75
|
|
|
|
|
100
|
|
|
|
|
|
|
83
|
|
|
88
|
|
|
|
|
|
|
|
81
|
|
|
79
|
|
|
|
|
|
|
67
|
Table 2.
|
Factor
|
Mean
|
n
|
Std. Dev
|
|
A1
|
1=90.1
|
7
|
8.69
|
|
A2
|
2=80.3
|
8
|
11.09
|
|
A3
|
3=80.7
|
7
|
4.86
|
|
A4
|
4=74.0
|
8
|
11.75
|
|
Totals
|
81.0
|
30
|
10.83
|
|
ANOVA table
|
|
|
|
|
|
|
Source
|
SS
|
df
|
MS
|
F
|
p-value
|
|
Treatment
|
982.21
|
3
|
327.405
|
3.51
|
.0291
|
|
Error
|
2,421.79
|
26
|
93.146
|
|
|
|
Total
|
3,404.00
|
29
|
|
|
|