QUANTITATIVE METHODS – DECEMBER 2016 Section II
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QUANTITATIVE METHODS – DECEMBER 2016
Section II
Case Studies
Case Study 1
The lending manager at a bank headquarters is looking at business loans approved at a particular branch in Edinburgh over the past two months. Some data have been collected on the size of loans and the ownership structures of the borrower companies as follows:
(Total 240 loans)
(i) Carry out an appropriate hypothesis test to determine whether the size of loan is independent of the type of borrower. (16 marks)
(ii) Write a report on your findings and comment on the relevance of the data collected. (9 marks) (Total 25 marks)
Case Study 2
The manager of a coffee shop is looking into taking out a major loan to refurbish the shop. The manager has been examining sales records and pricing information for cappuccino, latte and macchiato coffees over the last three years. You have been asked to help him analyse this data using price indices to try to understand the growth patterns observed. The base data that the manager has is as follows:
(i) Using Year 1 as the base year, calculate the following indices:
(a) Simple aggregate price indices for Year 2 and Year 3. (5 marks)
(b) Laspeyres price indices for Year 2 and Year 3. (6 marks)
(c) Paasche price indices for Year 2 and Year 3 (assuming that Year 3 is the current year). (6 marks)
(ii) Discuss the relevance of these indices for comparing the growth patterns, compare
the relative merits of each type of index, and suggest any other analyses that might help in putting a case to the Bank for additional funding. (8 marks)
(Total 25 marks)
Case Study 3
An insurance company is carrying out a survey in which members of the public are asked for their opinions on the service they have received. The survey is using three trained interviewers to carry out the interviews over the telephone. As part of the training, five of the interviews held by each interviewer were recorded. The time taken for each interview was measured and the data are shown in the table below.
(i) Carry out a one-way analysis of variance. Produce an appropriate summary table. (11 marks)
(ii) Test whether there is a significant difference in the mean lengths of interviews for the three interviewers. (6 marks)
(iii) Write a report on your findings. Indicate any other information you would require
about the data collected. Detail your recommendations for further research and analyses. (8 marks)
(Total 25 marks)
Case Study 4
Bruntsfield Stationers is a small independent paper shop that sells a lot of stationery to the local college students. The manager at Bruntsfield Stationers has been looking at his sales of fountain pens over the past 7 weeks. The following data are available:
(i) Calculate a 3-point moving average. Forecast the number of pens sold for Week 8. (6 marks)
(ii) Using the method of exponential smoothing with coefficient α = 0.3, calculate the
smoothed values. Forecast the number of pens sold in Week 8. (7 marks)
(iii) Compare the accuracy of the two methods using the mean square error. (7 marks)
(iv) Write a report on your findings and on the assumptions you have made. Discuss
the relevance of methods used and recommend possible improvements. (5 marks) (Total 25 marks)
TOTAL OF 100 MARKS
2023-07-04