The manager of a chain of fast-food restaurants believes that the proportion of customers who are served within 2 minutes of placing their order is greater during lunch hours than during dinner hours. To investigate, he selects a random sample of 35 customers who placed an order during lunch hours and a random sample of 75 customers who placed an order during dinner hours. The manager finds that 71.4% of the customers were served within 2 minutes during the lunch hours and 66.7% of the customers were served within 2 minutes during the dinner hours. (a) Construct and interpret a 99% confidence interval for the difference in the proportion of the population of all dinner customers and all lunch customers who are served within 2 minutes.

(b) Does the confidence interval constructed in part (a) give the manager reason to believe that the proportion of customers who are served within 2 minutes of placing their order is greater during lunch hours than during dinner hours?