An agent for professional football players claims that there is no difference between the earning
potential of safeties and linebackers in the NFL. Test the agents claim to a 0.05 significance level.
In order to run this test, you decide to use the easily accessible data of the 10 highest salaries in each
category.
1. Titans safety Kevin Byard: $14.1
million
2. Chiefs safety Tyrann Mathieu: $14
million
3. Redskins safety Landon Collins: $14
million
4. Ravens safety Earl Thomas: $13.75
million
5. Dolphins safety Reshad Jones: $12
million
6. Raiders safety Lamarcus Joyner: $10.5
million
7. Vikings safety Harrison Smith: $10.25
million
8. Patriots safety Devin McCourty: $9.5
million
9. Packers safety Adrian Amos: $9 million
10. Eagles safety Malcolm Jenkins: $8.75
million
1. Bears linebacker Khalil Mack:
$23.5 million
Safeties
X,=
S, =
2. Broncos linebacker Von Miller:
$19.1 million
3. Seahawks linebacker Bobby
Wagner: $18 million
4. Jets linebacker C.J. Mosley: $17
million
5. Packers linebacker Za'Darius
Smith: $16.5 million
6. Cardinals linebacker Chandler
Jones: $16.5 million
7. Texans linebacker Jadeveon
Clowney: $15.97 million
8. Falcons linebacker Deion Jones:
$14.25 million
9. Vikings linebacker Anthony Barr:
$13.5 million
10. 49ers linebacker Kwon Alexander:
$13.5 million
3. Prep work: Fill in the chart below. When calculating these values do not enter all the zeros for the
millions, instead use just the numeric value, and let the work millions take care of the numerous
zeros.
Linebackers
Xs=
Ss=
Ns=
XL=
SL=
nL=
4.
Test the claim that the standard deviations are different from each other.
5. Test the claim that Linebackers and safeties have essentially the same salaries. If the standard
deviations of your two samples are significantly different, do not pool. If the standard deviations of
your two samples are not significantly different, then pool.