A marketing researcher wants to estimate the mean savings ($) realized by shoppers who showroom. Showrooming is the practice of inspecting products in retail stores and then purchasing the products online at a lower price. A random sample of 100 shoppers who recently purchased a consumer electronics item online after making a visit to a retail store yielded a mean savings of $ 58 and a standard deviation of $ 55. 

a. Construct a 95% confidence interval estimate for the mean savings for all showroomers who purchased a consumer electronics item. 

b. Suppose the owners of a consumer electronics retailer wants to ­estimate the total value of lost sales attributed to the ne X_t 1,000 showroomers that enter their retail store. How are the results in (a) useful in assisting the consumer electronics retailer in their estimation?