Chapter 11.3, Problem 11.22E

A tire company is considering switching to a new type of adhesive designed to improve tire reliability in high-temperature and overload conditions. In laboratory “torture” tests with temperatures and loads 90% higher than the maximum normally encountered in the field, 15 tires constructed with the new adhesive run an average of 65 miles before failure, with a standard deviation of 14 miles. For 18 tires constructed with the conventional adhesive, the mean mileage before failure was 53 miles, with a standard deviation of 22 miles. Assuming normal populations and using the 0.05 level of significance, can we conclude that the new adhesive is superior to the old under such test conditions? What is the most accurate statement that could be made about the p-value for this test?