# Case study: century national bank

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. Sleig 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 an attached Excel file named Banking-2003.

The Century National Bank has offices in several cities the Midwest and the southeastern part of the United States. Mr. Dan Sleig, 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 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. Sleig 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 services (a savings account, a certificate of deposit, etc.) the customer uses; (3) whether the customer has a debit card; 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.

Case Questions:

1. Develop a graph and a table that shows descriptive statistics (central tendency measures and dispersion measures) of the checking balances.

2. When Mr. Sleig took over as president of Century several years ago, the use of debit cards was just beginning. He would like an update of 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? Interpret the results.

3. With many other options available, customers no longer let their money sit in a checking account. For many years the mean checking balance has been \$1,600. Does the sample data indicate that the mean account balance has declined from this value?

4. Recent years have also seen an increase in the use of ATM machines. When Mr. Sleig took over the bank, the mean number of transactions per month per customer was 8; now he believes it has increased to more than 10. In fact, the advertising agency that prepares TV commercials for Century would like to use this on the new commercial being designed. Is there sufficient evidence to conclude that the mean number of transactions per customer is more than 10 per month? Could the advertising agency say the mean is more than 9 per month?

5. The bank has branch offices in four different cities mentioned earlier. Mr. Sleig would like to know if there is a difference in the mean checking account balances among the four branches. If there are differences, between which branches do these differences occur?

6. Mr. Sleig is also interested in the ATMs. Is there a difference in the ATM use among the branches? Also do customers who have debit cards tend to use ATMs differently from those who don’t have debit cards? Is there a difference in ATM use by those with checking accounts that pay interest versus those that do not?

7. At a 0.05 significance level, is there a relationship between the location of the branch and whether the customer has a debit card?

8. Using checking account as the dependent variable and using the number of ATM transactions, the number of other services used, whether the individual has a debit card, and whether interest is paid on the particular account as independent variables, write a report indicating which of the variables seem related to the account balance and how well they explain the variation in account balances. Should all of the independent variables be used in the analysis or can some be dropped? Did you notice any indications to multicollinearity, heteroscedasticity

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