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4. The department of HR at the University of Michigan wants to estimate the amount of...

4. The department of HR at the University of Michigan wants to estimate the amount of an annual healthcare premium needed for an Assistant Professor as part of a new recruiting program. In a sample of 50 Assistant Professors, they found that the average yearly premium needed is $16,000 with a standard deviation of $3,500. (a) What is the population mean? What is the best estimate of the population mean? (b) Develop an 90% confidence interval for the population mean. (c) Assuming a 99% level of confidence, how large of a sample is required with an acceptable error of $400?

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