Quality Progress, February 2005, reports on the results achieved by Bank of America in improving customer satisfaction and customer loyalty b 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 result 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?

Answer 1

Find a confidence interval formula using proportions. Convert your proportions to decimals for ease in calculation. Use + or - 1.96 for the interval in the formula to represent 95 percent confidence (this is found using a z-table). You should be able to draw your conclusions from there.