posted by Steve on .
Quality Progress, February 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?
Use a proportional confidence interval formula.
CI95 = p + or - 1.96(√pq/n)
...where p = 195/350 (convert to a decimal), q = 1 - p, n = 350, and + or - 1.96 represents the 95% interval using a z-table.
I'll let you take it from here.