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Quantitative Methods Exam Paper

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BA Business Management and
BA Business Management with Industrial Experience

YEAR 2 SESSION 2008/09

DECEMBER DIET

C58QT

QUANTITATIVE METHODS

Date: December 2008 Time: 2 Hours

EXAMINERS:

INSTRUCTIONS TO CANDIDATES

Answer THREE QUESTIONS from FOUR – Each Question is worth 20 marks

NUMBER OF SECTIONS: 1

NUMBER OF PAGES: 5 (including Front Cover)

TO BE SUPPLIED: Formula Sheet, Graph Paper, Statistical Tables

Answer THREE questions.
Each question is worth 20 marks

Question 1

A finance company is concerned about the time that employees spend surfing the WWW. The company has taken a random sample of 40 employees and has automatically recorded the time each employee has spent surfing on the last Friday in March. The times (recorded in minutes) are summarised in the table below.

|23 |11 |54 |35 |21 |15 |33 |13 |
|17 |56 |12 |90 |5 |32 |15 |67 |
|17 |12 |120 |34 |128 |5 |76 |34 |
|130 |45 |67 |106 |19 |69 |37 |94 |
|10 |25 |31 |57 |28 |100 |32 |80 |

Table: surfing duration (minutes) on the last Friday in March for a random sample of 40 employees.

(i) Calculate the five-number summary for the data; (5 marks)

(ii) Draw a boxplot; (5 marks)

(iii) Classify the data into a frequency table, using intervals 0 to 9, 10 to 19 etc; (5 marks)

(iv) Write a report on your findings and indicate any additional information you would require. (5 marks)

(Total 20 marks)

Question 2 Overleaf/..

Question 2

The quality control department of a Borders knitwear company employs a rigorous process of testing each of 3 components before final assembly of the garment.

The probability that component A will pass inspection is 0.35, the probability that component B will pass inspection is 0.47 and the probability that component C will pass inspection is 0.58. The probability that both components A and B will pass inspection is 0.25, the probability that both components B and C will pass inspection is 0.35, and the probability that both components C and A will pass inspection is 0.28. The probability that all three components will pass inspection is 0.19.

(i) Draw a Venn diagram and mark the probability corresponding to each component, (3 marks)

and from that find the probability that:

(ii) none of the components will pass inspection; (3 marks)

(iii) component B will pass but not component A; (4 marks)

(iv) at least two of the components will pass inspection; (4 marks)

(v) component A or component C (or both) will pass inspection; (4 marks)

(vi) Explain why Venn diagrams are a useful method of displaying probabilities. (2 marks)

(Total 20 marks)

Question 3 Overleaf/..

Question 3

The following table shows the price and consumption of engine oil for a local haulage firm.

|Type of engine oil |Price (£) per litre |Consumption (litres) |
| | |2006 |2007 |2005 |2006 |2007 |
| |2005 | | | | | |
|Castrol GTX |1.94 |2.10 |2.24 |225 |275 |237 |
|Magnatec |1.48 |1.52 |1.58 |250 |220 |190 |
|Synthetic |1.14 |1.10 |1.08 |230 |320 |400 |

Table: Price and consumption of engine oil, 2005 to 2007

Calculate, using 2005 as a base year:

i) Laspeyres price index for 2006 and 2007; (8 marks)

ii) Paasche price indices for 2006 and 2007, assuming that 2007 is the current year; (8 marks)

iii) Fisher’s price indices for 2006 and 2007, assuming that 2007 is the current year; (2 marks)

iv) Explain why Fisher’s index is described as being the ‘ideal' index. (2 marks)

(Total 20 marks)

Question 4 Overleaf/..

Question 4

The table below shows the number of Scottish higher education students in 2005/6 and 2006/7

|College/University |HE Students 2005/6 |HE Students 2006/7 |
|The University of Aberdeen |13,760 |14,025 |
|University of Abertay Dundee |4,125 |4,180 |
|Bell College |4,720 |5,280 |
|The University of Dundee |18,610 |18,225 |
|Edinburgh College of Art |1,705 |1,710 |
|The University of Edinburgh |23,715 |24,225 |
|Glasgow Caledonian University |17,045 |17,450 |
|Glasgow School of Art |1,555 |1,685 |
|The University of Glasgow |23,590 |25,300 |
|Heriot-Watt University |10,225 |10,560 |
|Napier University |14,850 |14,540 |
|The University of Paisley |13,035 |14,270 |
|Queen Margaret University College, Edinburgh |5,390 |5,280 |
|The Robert Gordon University |12,790 |12,985 |
|The Royal Scottish Academy of Music and Drama |680 |690 |
|The University of St Andrews |8,645 |8,965 |
|Scottish Agricultural College |745 |805 |
|The University of Stirling |8,935 |10,510 |
|The University of Strathclyde |25,105 |26,000 |
|UHI Millennium Institute |6,600 |6,855 |
|Total |215,830 |223,530 |
| | | |
| | | |
|Source: Higher Education Statistics Agency | | |

(i) Write a report summarising the main features of the data. Include any tables, graphs and statistics that may be appropriate. (20 marks)

(Total 20 marks)

END OF PAPER

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