Chapter 9, Problem 46SE

Deflated Footballs? Colts In the 2015 AFC Championship game, there was a charge the New England Patriots deflated their footballs for an advantage. The Patriots’ opponents during the championship game were the Indianapolis Colts. Measurements of the Colts footballs were taken. The balls should be inflated to between $12.5$ and $13.5$ pounds per square inch (psi). The measurements were $12.70,12.75,12.50,12.55,12.35,12.30,12.95,\text{ and }12.15$ psi. (Source: http://online.wsj.com/public/resources/documents/ Deflategate.pdf)

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

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