Two ride-sharing companies are competing for business in a large city. To help customers compare the companies, a data scientist selects a random sample of 40 completed rides from each of the two companies. From each sample, he computes the mean amount of time that passed between when the request for a pickup was placed and when the customer was picked up. Company A took, on average, 18 minutes to pick up customers with a standard deviation of 4 minutes. Company B took, on average, 12 minutes to pick up customers with a standard deviation of 10 minutes.

(a) Construct and interpret a 98% confidence interval for the difference in mean response time for these two ride-sharing companies.

(b) The results of the study are particularly meaningful to customers if one company is found to be significantly different from the other company regarding response time. Based upon the 98% confidence interval, is there reason to believe that the two ride-sharing companies have different mean response times? Explain.