In the 2015 AFC Championship game, there was a charge the New England Patriots deflated their footballs for an advantage. The balls should be inflated to between 12.5 and 13.5 pounds per square inch. The measurements were 11.50, 10.85, 11.15, 10.70, 11.10, 11.60, 11.85, 11.10, 10.95, 10.50, and 10.90 psi (pounds per square inch).

a. Test the hypothesis that the population mean is less than 12.5 psi using a significance level of 0.05. State clearly whether the Patriots’ balls are deflated or not. Assume the conditions for a hypothesis test are satisfied.

b. Use the data to construct a 95% confidence interval for the mean psi for the Patriots’ footballs. How does this confidence interval support your conclusion in part a?