1. The manager of a department store is thinking about establishinga new billing system for the store’s credit customers. After a thorough financial analysis, she determines that the new system will be cost-effective only if the mean monthly account is greater than R70. A random sample of 200 monthly accounts is drawn, for which the sample mean account is R74. The manager knows that the accounts are normally distributed, with a standard deviation of R30. Is there enough evidence at the 5% significance level to conclude that the new system will be cost effective? (Remember to use the 4-step process.)2. 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)MathStatistics and Probability STK 113
