Question

Use the most recent NFL season for your data. For each team, find the quarterback rating for the number one quarterback. Test the claim that the mean quarterback rating for a number one quarterback is more than 80.

Answer 1

We have the data regarding the most recent NFL season quarterback ratings. The data is as follows:

122.5	96.8	88.7	82.4	79.2	74.6
110.6	92.9	87.1	81.1	79.1	72.9
105.6	92.2	85.7	80.9	78.2	72.4
102.5	90.7	84.9	80.5	77.8	70.5
97.2	90.1	84.5	80.4	74.6	70.1

 

From the data we have,

Sample size n = 30

Sample mean X̅ = 86.22

Standard deviation x = 12.36

 

Here we have to test that the average quarterback ratings is greater than 80.

 

The null and alternative hypotheses are shown below.

H0: µ = 80

vs

H1: µ > 80

 

Here the alternative hypothesis H1: µ > 80 is the claim.

 

Level of significance α = 0.05.

 

The given level of significance is 0.05 and at the 29 degrees of freedom the test is right-tailed then the critical value is t = 1.70.

 

To find the test statistics value we have the test statistics as,

t = (X̅ - µ)/(s/√n)

 

By substituting the value we get

t = (86.22 – 80)/(12.36/√30)

   = 2.77

The calculated value is 2.77 which lies in the critical region we reject the null hypothesis. This was shown in the below graph.

 

As the null hypothesis is rejected there is enough evidence to support the claim that the average quarterback rating is greater than 80.

As the null hypothesis is rejected there is enough evidence to support the claim that the average quarterback rating is greater than 80.