Question: Physical Sciences Interstate Batteries guarantees their lawn tractor battery will last at least three years. To increase sales, the company is planning to offer a new replacement warranty, as long as 95% of all batteries do indeed last at least three years. A random sample of 200 customers was contacted, and 183 had batteries that lasted at least three years.

a. Is there any evidence to suggest the proportion of tractor batteries that last at least three years is less than 0.95? Use a = 0.05.

b. Find the p value associated with this hypothesis test.

c. Based on your results, would you recommend implementation of the new replacement warranty? Justify your answer.