Problem 1:
The mean television viewing time for Americans is 15 hours per week (Money, November 2003). Suppose a sample of 40 Americans is taken to further investigate viewing habits. Assume the population standard deviation for weekly viewing time is o = 3 hours.
a. What is probability the sample mean will be within 1 hour of the population mean (to 4 decimals)?
b. What is the probability the sample mean will be within 45 minutes of the population mean (to 4 decimals)?
Problem 2:
The Democrat and Chronicle reported that 25% of the flights arriving at the San Diego airport during the first five months of 2001 were late (Democrat and Chronicle, July 23, 2001). Assume the population proportion is p = .25.
a. Calculate o (p) with a sample size of 1000 flights (to 4 decimals).
b. What is the probability that the sample proportion will be within +/-.03 of the population proportion if a sample of size 1000 is selected (to 4 decimals)?
c. What is the probability that the sample proportion will be within +/-0.3 of the population proportion if a sample of size 500 is selected (to 4 decimals)?
Problem 3:
The president of Doerman Distributors, Inc., believes that 30% of the firm's orders come from first-time customers. A simple random sample of 100 orders will be used to estimate the proportion of first-time customers.
a. What is the probability that the sample proportion will be between .20 and .40 (to 4 decimals)?
b. What is the probability that the sample proportion will be between .25 and .35 (to 4 decimals)?
Problem 4:
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 $2200.
a. Calculate the standard error of the mean amount of Medicare spending for a sample of fifty 2003 enrollees (to 2 decimals).
b. What is the probability the sample mean will be within +/-$300 of the population mean (to 2 decimals).
c. What is the probability the sample mean will be greater than $7500 (to 4 decimals)?