Febuary 2005, reports on the results achieved by Bank of America in improving cu

Question

Febuary 2005, reports on the results achieved by Bank of America in improving custoer satisfaction and customer loyalty by listing to the "voice of the customer." A key measue 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 cystiners wutg a resoibse if 9 or10 representing "customer delight." Find a 95 percent confindence 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 exceed.48, the historical proportion of customer delight for Bank of America?

Explanation / Answer

p = 195/350 z(95%) = 1.96 The interval goes from: p - z*sqrt(p*(1-p)/N) to p - z*sqrt(p*(1-p)/N) 195/350 - 1.96*sqrt(195/350*(1-195/350)/350) to 195/350 + 1.96*sqrt(195/350*(1-195/350)/350) With a calculator: 0.505 to 0.609 Yes, we are 95% confident that the proportion exceeds 48%, since the entire interval is over 0.48.

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