A large retail lawn care dealer currently provides a two-year warranty on all lawn mowers sold at its stores. A new employee suggested that the dealer could save money by just not offering the warranty. To evaluate this suggestion, the dealer randomly decides whether or not to offer the warranty to the next 500 customers who enter the store and express an interest in purchasing a lawn mower. Out of the 250 customers offered the warranty, 91 purchased a mower, as compared to 53 of 250 not offered the warranty.

a) Place a 95% confidence interval using JMP on the difference in the proportion of customers purchasing lawn mowers with and without the warranty.

b) Test the research hypothesis that offering the warranty will increase the proportion of customers who will purchase a mower. Be 99% confident. What is the corresponding p-value?