You manage a chain of supermarkets and care about maintaining minimum standards of customer satisfaction. In the past you occasionally surveyed customer satisfaction on a scale of 1–10, 10 being good.
As manager, you have set a minimum target for all stores in the chain: the mean satisfaction level of customers should be at least 7.5. To monitor this you intend to regularly survey customers across the chain and compare each store with this benchmark. One typical set of results for “Store X” is displayed in the chart below, which summarizes responses of 100 customers for a single survey last year, prior to the recent changes.
The sample mean for these data is 7.11, below the 7.5 target. If it was just one customer who responded 7, you would presumably not infer that Store X was underperforming. If there were 1000 customers in the survey you would probably be convinced. So the size of the survey is important. This survey involved 100 customers. How accurate is the 7.11?
The accuracy matters because you are going to be doing this many, many times. There are more than 80 stores in the chain and you are going to be surveying each store every month. This means around 1000 store surveys will be carried out during the year. If you send out the management consultants to every store that “fails,” you could spend a ...