In: Math
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.
Solution:
Given:
Sample Size = n = 11
Sample Mean =
Sample standard deviation = s = 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.
Step 1) State H0 and 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
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:
Since we have rejected H0, 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.