Chapter 9, Problem 45SE

Deflated Footballs? Patriots 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). $\left(\text{Source: http:// online}\text{.wsj}\text{.com/public/resources/documents/Deflategate}\text{.pdf}\right)$

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.

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?