Question 1
The tonnage data for the last four years for ABC Shipping Company Limited is tabulated below.
- Using a 4-month moving average determine the projected tonnage moved for the last 3 months of 2022.
5marks
- Plot the data for all five years on a line graph and comment on trends and other significant features. 4marks
- The monthly forecast equation being used is: y= 1700+2t where t = 30 for January, t = 32 for February, t = 34 for March, etc. y= 402+3t where: t0 January of last year and y is the number of shipments. Determine the amounts of shipments for the first 6 months of the next year:
6marks
| 2022 | |
| Month | Number of tons of goods moved (,000) |
| January | 1600 |
| February | 1800 |
| March | 2400 |
| April | 1300 |
| May | 1200 |
| June | 1400 |
| July | 1800 |
| August | 900 |
| September | 1200 |
Question 2
The average values of the stocks of five companies listed on the local stock market over a 12 month period are given in the table below.
| Month | ARC Tools Ltd | Kim’s Pharmacy | Harold’s Catering | ABB Bank | Premier Roofs Ltd | Carol’s Foods Ltd |
| January | 7.1 | 12 | 11.1 | 24.3 | 28.5 | 58.2 |
| February | 8.8 | 13.2 | 19.5 | 23 | 56.9 | 56.3 |
| March | 5.5 | 15.8 | 26.3 | 22.8 | 76.4 | 56.4 |
| April | 12.4 | 10.4 | 15.2 | 29.4 | 45.2 | 67.5 |
| May | 15.5 | 13.5 | 16 | 26.5 | 36.4 | 50.3 |
| June | 1.8 | 14.2 | 18.4 | 25.3 | 54 | 48.4 |
| July | 4.2 | 14 | 35.6 | 29.7 | 81 | 54.3 |
| August | 2.3 | 13.6 | 58.4 | 27.3 | 72.8 | 45.2 |
| September | 12 | 18.4 | 21.5 | 20 | 90.6 | 40.6 |
| October | 12.9 | 10.7 | 38.2 | 20.9 | 88.4 | 38.4 |
| November | 8.7 | 12.8 | 4.6 | 11.4 | 90.5 | 35.2 |
| December | 2.1 | 13.4 | 19.2 | 25.1 | 69.2 | 50.6 |
- Determine the mean value of each stock for the 12 month period.
3marks
- Determine the coefficient of variation for each stock for the 12 month period. 5marks
- Use your results to advise a client who is risk averse.
3marks
- If one decided to take risks which are the two best stocks to invest in that are likely to give good returns. Give reasons for your answer.
4marks
Question 3
a) An Insurance company in trying to determine the level of premium to be charged to different shipping companies that are insured against damages. A survey was conducted on the company’s books and data was extracted for the past ten years. The data is summarized in the table below.
| Types of claims | |||||
| Type of Vessels | Marine Accidents | Fire | Injuries to Workers | Oil Spills | |
| Cruise Ships | 800 | 360 | 1400 | 700 | |
| Cargo ships | 1900 | 500 | 2500 | 400 | |
| Tankers | 1500 | 540 | 600 | 1200 | |
| Yachts | 800 | 360 | 400 | 200 | |
| Fishing Vessels | 6000 | 1200 | 2400 | 400 |
Test at the 5% level if the data indicate a relationship between the type of vessels insured and type of insurance claims submitted to the company. Explain your answer. (Figures are number of claims submitted)
10 marks
Question 4
The general manager at the local paint factory claimed that the volume of paint in each bucket sold by his company is 20 litres. Some customers disputed the general manager’s claim. You are assigned to test the general manager’s claim.
- Explain how you would conduct an experiment to test the claim.
3marks
- Another researcher selected 36 buckets of paints and found the mean volume to be 18.8 litres with a standard deviation of 0.5 litres. Construct a 95 % confidence interval for the mean volume of the paints. Also is there evidence at the 5% level of significance that the general manager’s claim is true? Explain your answer. 7marks
Question 5
Students are required to select one of the suggested projects below. Each project involves:
- Design of instruments for collecting data.
- Data Collection.
- Analysis of data.
- Presentation of data along with a narrative explaining the reasons for methods chosen, methodology, analysis, Literature review (where necessary) and an explanation of the results including possible usage and limitations.
- Appendix and references.
Suggested Projects
| 1. The impact of information technology on the throughput of goods at our local ports and its effect in lowering waiting time. |
| 2. Representation of CMU graduates in the maritime industry by sector and levels. |
| 3. Cruise shipping in Jamaica. An analysis of the number of persons visiting the island over the past 52 weeks. |
| 4. An analysis of waiting time at government offices in Jamaica and the loss of production time (in man hours). |
Students should complete in groups of 2. Marks are awarded for your report in the following areas: Achievement of the aims of the project, description of the background to the project, techniques used to gather data, Analysis and interpretation of data, conclusions drawn and the overall quality of the presentation of the report.
50 marks
