A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. An SRS of 31 stores this year shows mean sales of 79 units of a small appliance, with a standard deviation of 14.6 units. During the same point in time last year, an SRS of 18 stores had mean sales of 91.41units, with standard deviation 11.9units. A decrease from 91.41 to 79 is a drop of about 16%.

a. Construct a 99% confidence interval estimate of the difference 12, where1 is the mean of this year's sales and2is the mean of last year's sales.

b. What is the margin of error?