Wk 4

Ch 8

Problem 44

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? 

Problem 48

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 Lincolnville 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?

Ch 9

Problem 56

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 66

Near the time of an election, a cable news service performs an opinion poll of 1,000 prob-able 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.

Problem 71

Refer to the Lincolnville School District bus data.

a. Develop a 95% confidence interval for the mean bus maintenance cost.

b. Develop a 95% confidence interval for the mean bus odometer miles.

c. Make a business memo to the state transportation official to report your results.

Case Study

Century National Bank Refer to the description of Century National Bank at the end of the Review of Chapters 1-4 on page 129. When Mr. Selig took over as president of Century several years ago, the use of debit cards was just beginning. He would like an update on the use of these cards. Develop a 95% confidence interval for the proportion of customers using these cards. On the basis of the confidence interval, is it reasonable to conclude that more than half of the customers use a debit card? Make a brief report interpreting the results.

Info needed for case

Century National Bank has offices in several cities in the Midwest and the southeastern part of the United States. Mr. Dan Selig, president and CEO, would like to know the characteristics of his checking account customers. What is the balance of a typical customer? How many other bank services do the checking account customers use? Do the customers use the ATM service and, if so, how often? What about debit cards? Who uses them, and how often are they used? To better understand the customers, Mr. Selig asked Ms. Wendy Lamberg, director of planning, to select a sample of customers and report. To begin, she has appointed a team from her staff. You are the head of the team and responsible for preparing the report. You select a random sample of 60 customers. In addition to the balance in each account at the end of last month, you determine (1) the number of ATM (automatic teller machine) transactions in the last month; (2) the number of other bank services (a savings account, a certificate of deposit, etc.) the customer uses; (3) whether the customer has a debit card (this is a bank service in which charges are made directly to the customer's account); and (4) whether or not interest is paid on the checking account. The sample includes customers from the branches in Cincinnati, Ohio; Atlanta, Georgia; Louisville, Kentucky; and Erie, Pennsylvania.