Assignment:
Americans have become increasingly concerned about the rising cost of Medicare. In 1990, the average annual Medicare spending per enrollee was $3267; in 2003, the average annual Medicare spending per enrollee was $6883 (Money, Fall 2003). Suppose you hired a consulting firm to take a sample of fifty 2003 Medicare enrollees to further investigate the nature of expenditure. Assume the population standard deviation for 2003 was $2000.
a. Show the sampling distribution of the mean amount of Medicare spending for a sample of fifty 2003 enrollees.
b. Determine the probability the sample mean will be within ±$300 of the population mean.
c. Determine the probability the sample mean will be greater than $7500. If the consulting firm tells you the sample mean for the Medicare enrollees they interviewed was $7500, would you question whether they followed correct simple random sampling procedures? Why or why not?
Provide complete and step by step solution for the question and show calculations and use formulas.