This case study has been developed from an original case study in the Course Textbook (Database in Appendix A)

Summary of Learning Outcomes:

LO 1. Analyze the probability of given business outcomes using fundamental probability concepts for discrete and continuous probability distributions.

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LO 2. Apply concepts of sampling and the Central Limit Theorem in obtaining information that will facilitate the analysis of appropriate business issues.

LO 3. Compute the probability of given business outcomes by building one and two tailed confidence intervals for Z and t probability distributions.

Case Study Overview

You work in the Planning Department of Union National Bank and report to Ms. Maryam. Union National Bank has offices in several locations.

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Ms. Maryam would like to know the characteristics of her checking account customers. You will do a data analysis and prepare a written report to summarize your findings. You will use AED as the common currency of the data. The complete data is also provided in the project excel workbook.

To purpose of the report that you will write is to try to answer a number of questions concerning bank customers such as:

i. What is the balance of a typical customer?

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ii. How many other bank services do the checking account customers use?

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iii. Do the customers use the ATM service and, if so, how often?

iv. How about debit cards? Who uses them and how often are they used?

As you are the head of the research team you select a random sample of 60 customers to answer the above questions. In addition to the balance in each account at the end of last month you determine:

1. The number of ATM transactions in the last month

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2. The number of other bank services (a saving 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)

4. Whether or not interest is paid on the checking account

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The sample data you have collected includes customers from the branches in Dubai (1); Abu Dhabi (2); RAK (3); and Sharjah (4).

Tasks:

Your tasks should be written up in a short but professionally presented report for Ms. Maryam. This report should include your results, answers to the questions in the tasks and, where required, an explanation or your additional comments on the data results and findings.

Please ensure that your report clearly identifies the Tasks that you are addressing.

Task A:

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Develop a graph and table that shows the data of the checking balances. What is the balance of a typical customer? What percentage of customers has more than AED 2,000 in their accounts? Around what value do the account balances tend to cluster?

Task B:

Determine and compare the mean, median, mode, range and the standard deviation of the checking account balances. Make meaningful comments on findings.

Task C:

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Create a discrete probability distribution of the data the number of other bank services used . What is the probability that a selected customer uses less than 5 other bank services? What is the probability that a selected customer uses 3 or more other bank services?

Task D:

Develop a 95% confidence interval for the mean balance of all their customers. Assume that the population standard deviation is AED 575. Comment on the result.

Develop a 99% confidence interval for the proportion of customers using a debt card for their account. On the basis of this confidence interval, is it reasonable to conclude that more than half of the customers use a debit card? Explain your findings.

Task E:

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Create a contingency table using columns for the four Emirates. For the two rows use the number of ATM transactions that are less than or equal to 10 and more than 10 per month.

Calculate the probability that a customer will bank in Abu Dhabi or has more than 10 ATM transactions.

Calculate the probability that a customer will bank in Sharjah and has 10 or fewer ATM transactions.

Calculate the probability that a selected customer from RAK given that they make more than 10 transactions.

Correct statistical calculation of the data and interpretation as explained in their report.

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Each task will be awarded a maximum of 15 marks (Total Marks = 75). Students should use the excel data to calculate the results as required by the questions. This can be achieved using excel functions or Megastat. Students should provide a written answer where requested. Written answers should relate to course concepts and theories. The report should clearly state which task is being addressed.

Professional presentation and supporting information

Students should submit their homework in a professional format and will be given credit for this along with any correctly formatted and labeled tables, charts, formulas and data included to support their answers (Total 25 marks)

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