A large retail lawn care dealer currently provides a 2- 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 50 customers who enter the store and express an interest in purchasing a lawnmower. Out of the 25 customers offered the warranty, 10 purchased a mower as compared to 4 of 25 not offered the warranty.
a. Place a 95% confidence interval on π1 – π2, the difference in the proportions of customers purchasing lawnmowers 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. Use a = .05.
c. Are the conditions for using a large- sample test to answer the question in part (b) satisfied? If not, apply an exact procedure.
d. Based on your results from parts (a) and (b), should the dealer offer the warranty?