An office manager has implemented an incentive plan that she thinks will reduce the mean time required to handle a customer complaint. The mean time for handling a complaint was 30 minutes prior to implementing the incentive plan. After the plan was in place for several months, a random sample of the records of 38 customers who had complaints revealed a mean time of 28.7 minutes with a standard deviation of 3.8 minutes.
a. Give a point estimate of the mean time required to handle a customer complaint.
b. What is the standard deviation of the point estimate given in (a)?
c. Construct a 95% confidence on the mean time to handle a complaint after implementing the plan. Interpret the confidence interval for the office manager.
d. Is there sufficient evidence that the incentive plan has reduced themean time to handlea complaint?