Vigilance Inc. provides secret shopping services to assist other companies in quality control. Vigilance has just been awarded a contract by Freshway Supermarkets to monitor the customer service experience at all its stores. To gather baseline data, Vigilance sent secret shoppers to pose as customers in 50 Freshway stores during an intensive 2-week period that the store managers were warned about, on the assumption that extra precautions would be taken to assure each store worked normally. Vigilance Inc. uses this data to create control charts for monitoring feedback from future ran- dom visits of secret shoppers. The data concerns a variety of customer ser- vice issues, but one measure that Freshway is particularly concerned about is the chain-wide number of misdirects. A misdirect occurs when the secret shopper asks an employee for help locating a particular item but is not personally escorted to that item, as per the store’s service standards. Across the entire chain, Vigilance secret shoppers recorded the following number of misdirects during the baseline evaluation period:

Questions

1. From the baseline data, what are the mean and the standard deviation of the natural variation in the daily proportion of misdirects that resulted from asking for help to locate an item?

Assume that in the future Vigilance intend store peat this procedure on random days, sending two secret shoppers to 50 stores, where each asks for directions once. Calculate the control limits for a p-chart to monitor the number of misdirects reported on those days, assuming that Vigilance always draws control charts with z = 3.0. Draw this chart and plot the existing baseline data on it.

Now assume that Vigilance would prefer to use a c-chart, because it may not always visit exactly 50 stores with two secret shoppers each during future sampling of the Freshway shopping experience. What would be the upper and the lower control limits on a c-chart that could be used to monitor misdirects?