Problem 1: An economist uses the price of a gallon of milk as a measure of inflation. She finds that the average price is $3.82 per gallon and the population standard deviation is $0.33. You decide to sample 40 convenience stores, collect their prices for a gallon of milk, and compute the mean price for the sample.
a. What is the standard error of the mean in this experiment?
b. What is the probability that the sample mean is between $3.78 and $3.86?
c. What is the probability that the difference between the sample mean and the population mean is less than $0.01?
d. What is the likelihood the sample mean is greater than $3.92?
Problem 2: Refer to the Lincolnville School District bus data. Information provided by manufacturers of school buses suggests the mean maintenance cost per year is $4,400 per bus with a standard deviation of $1,000. Compute the mean maintenance cost for the Lin-colnville buses. Does the Lincolnville data seem to be in line with that reported by the manufacturer? Specifically, what is the probability of Lincolnville's mean annual maintenance cost, or greater, given the manufacturer's data?
Problem 3: Families USA, a monthly magazine that discusses issues related to health and health costs, surveyed 20 of its subscribers. It found that the annual health insurance premiums for a family with coverage through an employer averaged $10,979. The standard deviation of the sample was $1,000.
a. Based on this sample information, develop a 90% confidence interval for the population mean yearly premium.
b. How large a sample is needed to find the population mean within $250 at 99% confidence?
Problem 4: Near the time of an election, a cable news service performs an opinion poll of 1,000 probable voters. It shows that the Republican contender has an advantage of 52% to 48%.
a. Develop a 95% confidence interval for the proportion favoring the Republican candidate.
b. Estimate the probability that the Democratic candidate is actually leading.
c. Repeat the above analysis based on a sample of 3,000 probable voters.
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