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worksheet -Additional exercises for Confidence Intervals 1. In its October 7, 1991, issue, Fortune magazine reported on the rapid rise of fees and expenses charged by various types of mutual funds. As stated in the article “Ten years ago the stock funds tracked by Morningstar, a Chicago rating service, took out an average of 1.19% annually. Today the extract is 1.59%. The standard deviation did not change, it remained at 0.27 percent.” For this problem please work with the percentages as they are stated in the problem, i.e. do not change for example 1.59% to 0.0159 but use 1.59 in any necessary calculations. (a) Suppose the average annual expense for a random sample of 81 stock funds is 1.63 percent. Find a 98% confidence interval for the mean annual expense charged by all stock funds. (b) Provide an interpretation of the confidence interval within the context of the problem. 2. Hotel Managers. A study of the career paths of hotel general managers sent questionnaires to a simple random sample of 160 hotels. There were 114 responses. The average time these 114 general managers had spent with their current company was 11.8 years. You can take as fact that the standard deviation of years worked for a company by all GMs is 3.2 years. How large a sample of hotel managers would be needed to estimate the mean length of time spent with their company to within 1 year with 99% confidence?