Quality Progress, Feburary 2005, reports on the results achieved by Bank of America in improving customer satisfaction and customer loyalty by listening to the "voice of the customer". A key measure of customer satisfaction is the response on a scale from 1 to 10 to the question: "Considering all the business you do with Bank of America, what is your overall satisfaction with Bank of America?"
Suppose that a random sample of 350 current customers results in 195 customers with a response of 9 or 10 representing "customer delight". Find a 95 percent confidence interval for the true proportion of all current Bank of America customers who would respond with a 9 or 10. Are we 95 percent confident that this proportion exceeds .48, the historical proportion of customer delight for Bank of America?
When a poll or survey is conducted, and we can assume we have a simple random sample from a large population, we can calculate confidence intervals using the standard error. The formula for standard error is Sqrt[p(1-p)/n], where p is the percent of people giving a certain answer (in this case rating service 9 or 10) ...