Two companies that manufacture batteries for electronics products have submitted their products to an independent testing agency. The agency tested 200 of each company’s batteries and recorded the length of time the batteries lasted before failure. The following results were determined:

a. Based on these data, determine the 95% confidence interval to estimate the difference in average life of the batteries for the two companies. Do these data indicate that one company’s batteries will outlast the other company’s batteries on average? Explain.
b. Suppose the manufacturers of each of these batteries wished to warranty their batteries. One small company to which they both ship batteries receives shipments of 200 batteries weekly. If the average length of time to failure of the batteries is less than a specified number, the manufacturer will refund the company’s purchase price of that set of batteries. What value should each manufacturer set if they wish to refund money on at most 5% of the shipments?