Chapter Work Statistics (4)

All directions and questions are in the word document, excel sheet has references for questions.

Complete the problems below from the textbook. You will need to use the “Lincolnville School District Bus Data” and the “Century National Bank Data” files for this assignment.

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1. Chapter 8 – Problem 44

2. Chapter 8 – Problem 48

3. Chapter 9 – Problem 56

4. Chapter 9 – Problem 66

5. Chapter 9 – Problem 71

6. Chapter 9 Case A – Century National Bank

For problems requiring computations, please ensure that your Excel file includes the associated cell computations and/or statistics output. This information is needed in order to receive full credit on these problems.

Submit output in one Excel file.

 

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?

d. What is the likelihood the sample mean is greater than $3.92?

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?

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?

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.

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

Century National Bank: Refer to the description of Century National Bank (below marked reference) 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 reason-able to conclude that more than half of the customers use a debit card? Write a brief report interpreting the results.

REFERENCE:

This information listed below is to help guide the Century National Bank information listed above. You do not need to complete the questions below **Just a reference** also use the excel sheet for the data**

A(Century National Bank Review page 129 use this information to answer the question above) The following case will appear in subsequent review sections. Assume that you work in the Planning Department of the Century National Bank and report to Ms. Lamberg. You will need to do some data analysis and prepare a short written report. Remember, Mr. Selig is the president of the bank, so you will want to ensure that your report is complete and accurate. A copy of the data appears in Appendix A.6 (Attached in excel). 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 ac-count customers use? Do the customers use the ATM ser-vice 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 prepare a 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 ser-vices (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. 1. Develop a graph or table that portrays the checking balances. What is the balance of a typical customer? Do many customers have more than $2,000 in their accounts? Does it appear that there is a difference in the distribution of the accounts among the four branches? Around what value do the account balances tend to cluster? 2. Determine the mean and median of the checking ac-count balances. Compare the mean and the median balances for the four branches. Is there a difference among the branches? Be sure to explain the difference between the mean and the median in your report. 3. Determine the range and the standard deviation of the checking account balances. What do the first and third quartiles show? Determine the coefficient of skewness and indicate what it shows. Because Mr. Selig does not deal with statistics daily, include a brief description and interpretation of the standard deviation and other measures.