EXAMPLE 8.5 Planning a Sample of Customers

Your company has received complaints about its customer support service. You intend to hire a consulting company to carry out a sample survey of customers. Before contacting the consultant, you want some idea of the sample size you will have to pay for. One critical question is the degree of satisfaction with your customer service, measured on a 5-point scale. You want to estimate the proportion of your customers who are satisfied (that is, who choose either “satisfied” or “very satisfied,” the two highest levels on the 5-point scale).

You want to estimate with 95% confidence and a margin of error less than or equal to 3%, or 0.03. For planning purposes, you are willing to use . To find the sample size required,

Round up to get . (Always round up. Rounding down would give a margin of error slightly greater than 0.03.)

Similarly, for a 2.5% margin of error, we have (after rounding up)

and for a 2% margin of error,