Din Tai Fung, Taiwan, specializes in xiaolongbao

(steamed dumplings) and Chinese cuisine. It has a number of clients that use their process for producing exotic Huaiyang dinners for customers in the United Kingdom. The operating cost for the franchised process has a fixed cost of £1,000 per week plus £5 for every unit produced. Recently, a number of restaurant owners using the process stated that the cost model is no longer valid and, in fact, the weekly costs are higher.

Your job is to determine if there is strong evidence to support the owners’ claim. To do so, you obtain a random sample of n = 50 restaurants and determine their costs. You also find that the number of units produced in each restaurant is normally distributed with a mean of m = 403 and a variance s2 = 650. The random sample mean 1n = 502 for weekly costs was £3,055. Prepare and implement an analysis to determine if there is strong evidence to conclude that costs are greater than those predicted by the cost model.