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 on-line after making a visit to a retail store yielded a mean savings of $ 58 and a standard deviation of $ 55.

a. Is there evidence that the population mean savings for all show-roomers who purchased a consumer electronics item is different from $ 50? (Use a 0.05 level of significance.)

b. Determine the p-value and interpret its meaning.