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The manager of a well-known bank is interested to know whether online banking is more popular amongst younger (under 40 years old) banking clients than amongst older (40 years and older) banking clients. In a random sample of 250 younger bank clients, 120 used online banking, and in a random sample of 300 older bank clients, 126 used online banking. a) Find and interpret a 99% confidence interval for the difference in the true proportion of younger and older bank clients that use online banking. (3) b) Is there a significant difference in the two population means, considering the confidence interval found in a)? (1)
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