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# sampling distribution of mean

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1.
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 expenditures. Assume the population standard deviation for 2003 was \$1900.

Calculate the standard error of the mean amount of Medicare spending for a sample of fifty 2003 enrollees (to 2 decimals).

What is the probability the sample mean will be within +/- \$300 of the population mean (to 4 decimals)?

What is the probability the sample mean will be greater than \$7500 (to 4 decimals)?

If the consulting firm tells you the sample mean for the Medicare enrollees it interviewed was \$7500, would you question whether the firm followed correct simple random sampling procedures?

- Select your answer -Yes, because the probability of attaining that sample mean is very highYes, because the probability of attaining that sample mean is very lowNo, because the probability of attaining that sample mean is very highNo, because the probability of attaining that sample mean is very low

2. {Exercise 7.51}
A market research firm conducts telephone surveys with a 44% historical response rate. What is the probability that in a new sample of 400 telephone numbers, at least 150 individuals will cooperate and respond to the questions? In other words, what is the probability that the sample proportion will be at least 150/400 = .375?

Calculate the probability to 4 decimals.