Question

6.124a During the National Football League’s 2014 AFC championship game, officials measured the air pressure on 11 of the game footballs being used by the New England Patriots.  They found that the balls had an average air pressure of 11.1 psi, with a standard deviation of 0.40 psi.

            

1. Assuming this is a representative sample of all footballs used by the Patriots in the 2014 season, perform the appropriate test to determine if the average air pressure in footballs used by the Patriots was significantly less than the allowable limit of 12.5 psi.  There is no extreme skewness or outliers in the data, so it is appropriate to use the t-distribution.

Answer 1

Solution:

We are given that:

n = Sample Size = 11

Sample Mean =

s = Sample standard deviation = 0.40

We have to test if the average air pressure in footballs used by the Patriots was significantly less than the allowable limit of 12.5 psi.

We use following steps:

Step 1) State null hypothesis H0 and alternative hypothesis H1:

Vs

Step 2) Find t test statistic:

Step 3) Find t critical value:

Look in t table for df = n - 1 = 11 -1 = 10 and one tail area = 0.05

From t table we get: t critical value = 1.812

Since this is left tailed test , t critical is negative

thus t critical = -1.812

Step 4) Decision rule:

Reject null hypothesis H0, if t test statistic value < t critical value = -1.812 , otherwise we fail to reject H0

Since  t test statistic value -11.608 < t critical value = -1.812 , we reject null hypothesis H0.

Step 5) Conclusion:

There is sufficient evidence to conclude that: the average air pressure in footballs used by the Patriots was significantly less than the allowable limit of 12.5 psi.