Although there were some changes in the roster from 2009, Red Sox maintained man
ID: 3434708 • Letter: A
Question
Although there were some changes in the roster from 2009, Red Sox maintained many players, despite adding John Lackey for a sizable 18.7 million dollar contract. Were the average salaries of the Red Sox players remaining in the lineup affected as a result of this move? Use the data below the lists the 2009 and 2010 salaries (in millions of $) to construct an appropriate hypothesis test at the 0.05 significance level.
Player
2009 Salary
2010 Salary
Josh Beckett
11.1
12.1
J Drew
14.0
14.0
Jacoby Ellsbury
0.45
0.49
Jon Lester
1.0
3.7
Mike Lowell
14.5
14.5
Daisuke Matsuzaka
8.3
8.3
Hideki Okajimi
1.7
2.7
David Ortiz
13.0
13.0
Jonathan Papelbon
6.2
9.3
Dustin Pedroia
1.7
3.7
Jason Varitek
5.0
3.0
Tim Wakefield
4.0
3.5
Kevin Youkilis
6.2
9.3
Player
2009 Salary
2010 Salary
Josh Beckett
11.1
12.1
J Drew
14.0
14.0
Jacoby Ellsbury
0.45
0.49
Jon Lester
1.0
3.7
Mike Lowell
14.5
14.5
Daisuke Matsuzaka
8.3
8.3
Hideki Okajimi
1.7
2.7
David Ortiz
13.0
13.0
Jonathan Papelbon
6.2
9.3
Dustin Pedroia
1.7
3.7
Jason Varitek
5.0
3.0
Tim Wakefield
4.0
3.5
Kevin Youkilis
6.2
9.3
Explanation / Answer
We use paired t test to do it because it tests the same subjects twice.
Let mu_d be the mean difference between 2009 Salary and 2010 Salary
The test hypothesis:
Null hypothesis: mu_d=0
Alternative hypothesis: mu_d not equal to 0
The test statistic is
t= mean difference/(s/vn)
=-0.80308/(1.53779/sqrt(13))
=-1.88
The degree of freedom =n-1=13-1=12
It is a two-tailed test.
So the p-value= 2*P(t with df=12 <-1.88) =0.0846 (from student t table)
Since the p-value is larger than 0.05, we do not reject the null hypothesis.
So we can not conclude that the average salaries of the Red Sox players were remaining in the lineup affected as a result of this move
6.70385 mean 2009 Salary 7.50692 mean 2010 Salary -0.80308 mean difference (2009 Salary - 2010 Salary) 1.53779 std. dev. 0.42651 std. error 13 n 12 dfRelated Questions
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