QUANTITATIVE METHODS – APRIL 2022
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QUANTITATIVE METHODS – APRIL 2022
Case Study 1 Maximum Word Limit 1000 words
An online retailer has two adverts posted in different parts of a well-known social networking website, Advertisement X and Advertisement Y. An average of 3 “clicks” are generated by Advertisement X during the period Monday 10.00 to 10.05am UTC. There are on average 4 “clicks” generated by Advertisement Y during the same period.
(i) Calculate the probability that on a particular Monday, between 10.00 and 10.05 am:
(a) Advertisement X generates exactly 2 clicks. (2 marks)
(b) Advertisement X generates at least 5 clicks. (2 marks)
(c) Advertisement Y generates no more than 3 clicks. (2 marks)
(d) Advertisement X generates exactly three clicks and Advertisement Y exactly one click. (2 marks)
(e) At least 3 clicks are generated by the advertisements. (2 marks)
(ii) Describe the main characteristics of the distribution that you used in (i) above. (6 marks)
(iii) Explain why this distribution is important in management decision-making. Illustrate
your answer by giving three other examples of its use in business. (9 marks) (Total 25 marks)
Case Study 2 Maximum Word Limit 1000 words
Elite Foods provides catering for functions such as weddings, sporting events and conferences. At the end of each year, it reviews the cost of the standard items such as cutlery, glasses, jugs and linen that it has provided.
The company has collected data on the quantities and cost of some of the cutlery that has been purchased, and these are summarised in the table below.
(i) Using Year 1 as the base year, calculate the following indices:
(a) Simple aggregate price indices for Year 2 and Year 3. (3 marks)
(b) Laspeyres price indices for Year 2 and Year 3. (3 marks)
(c) Paasche price indices for Year 2 and Year 3 (assuming that Year 3 is the current year). (3 marks)
(ii) Discuss the relevance of these indices for comparing the costs of purchasing
the cutlery and compare the relative merits of each type of index. Use relevant examples to illustrate your answer. (16 marks)
(Total 25 marks)
Case Study 3 Maximum Word Limit 1000 words
A surgery has been running a campaign to inform patients about the dangers of obesity. It has chosen a random sample of patients who were diagnosed as clinically overweight and who had high blood pressure. The surgery has offered them individual counselling on diet and exercise. To measure the effectiveness of the campaign, these patients have been asked to have some routine measurements taken at the time of their initial counselling and six months later. Their blood pressure was measured at both visits.
The table below shows the blood pressure readings for ten patients.
(i) Carry out an appropriate hypothesis test to determine whether the average blood pressure after six months is significantly different from the level at the start of the project. (6 marks)
(ii) Carry out an appropriate hypothesis test to determine whether the average blood
pressure after six months is significantly lower than the level at the start of the project. (4 marks)
(iii) Write a report on your findings. Discuss any reservations you have about the data
and the hypotheses tests that have been used. Provide suggestions for improving the accuracy of future tests. (15 marks) (Total 25 marks)
Case Study 4 Maximum Word Limit 1000 words
A weekly farmer’s market runs in a city centre all year round. The aim is to offer local producers the chance to sell their produce direct to the customer. The market is popular with both consumers and producers alike.
A local jam producer has decided to rent a space at the market. She specialises in organically produced jam and has had a stall at the market for the last seven weeks. She has recorded the number of jars sold each week.
(i) Calculate a three-point moving average. Forecast the number of jars sold in Week 8. (3 marks)
(ii) Using the method of exponential smoothing with α = 0.4, calculate the smoothed values . Forecast the number of jars sold in Week 8. (3 marks)
(iii) Compare the accuracy of the two methods using the Mean Square Error. (4 marks)
(iv) Write a report on your findings and on the assumptions you have made. Discuss the
relevance of the methods you have used and recommend possible improvements. (15 marks) (Total 25 marks)
TOTAL OF 100 MARKS
2023-07-10