Past Exam Paper Essay
The question paper consists of 8 printed page, each of which is identified by the Code Number LUBS5000M Statistical Tables Graph Paper LUBS5000M UNIVERSITY OF LEEDS January 2010 Examination for the degree of MA Accounting and Finance MSc Banking and Finance MSc International Finance MSc Management MSc International Business QUANTITATIVE METHODS Time allowed 3 hours Answer ALL questions - Past Exam Paper Essay introduction. Section A (answer ALL questions) Section A carries 20% of the overall marks. 1. It is possible to find the inter-quartile range of a set of data by plotting an ogive and reading off the appropriate values.
A. B. True False 2. Two events A and B are not mutually exclusive. This means A. B. C. D. Whether A occurs does not affect the probability that B occurs A and B can occur together The probability of A is one minus the probability of B. A and B cannot occur together P. T. O. LUBS5000M 3. The following information is calculated from a grouped frequency table, fx= 391 fx2 = 4181. What is the standard deviation of x? A. B. C. D. 8. 71 4. 74 22. 47 cannot be calculated from the above information f = 50 4. A random sample of 150 people is asked whether they smoke or not and 30 per cent say that they do.
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What is the 95% confidence interval for the percentage of the population who say they smoke? A. B. C. D. 22. 67% to 37. 33% 25% to 35% 27. 50% to 32. 50% 20. 35% to 39. 65% 5. The start of an exponential smoothing process with an alpha of 0. 2 is as follows: Period Actual Forecast 1 1020 2 940 1020 3 920 1004 4 950 What will be the forecast for period 4? A. B. C. D. 1020. 8 966. 8 875. 4 987. 2 6. A life insurance salesman sells on average 2. 5 life insurances policies per week. What is the probability that he will sell some policies in a given week? A. B. C. D. 0. 9179 0. 7627 0. 9750 0. 0821 P.
T. O. LUBS5000M 7. Assuming that the salesman in question 6 works a five day week what would be the probability that he sells one policy each day? A. B. C. D. 0. 2044 0. 3033 0. 3935 0. 9179 8. You wish to introduce into a wage regression model a qualitative variable with 2 categories, public sector / private sector, to capture the impact of working in the public sector on wage levels. What is the correct way to do this? A. It can’t be done. B. Include two dummy variables, each coded 0/1, the first where 1 = public sector, 0 = private sector, the second where 1 = private sector, 0 = public sector.
C. Include one dummy variable, in which 1 = public sector, 0 = private sector. D. Include one dummy variable, in which 1 = private sector, 0 = public sector. 9. Hospital records show that of patients suffering from a certain disease, 45% make a full recovery. What is the probability that of 6 randomly selected patients, 4 will make a full recovery? A. B. C. D. 0. 2553 0. 0410 0. 6151 0. 1861 10. All other things being equal (working on the same sample) for a lower level of confidence we will get a narrower confidence interval? A. True B. False P. T. O. LUBS5000M
Section B (answer ALL questions) Section B carries 20% of the overall marks. 1. Use your knowledge of sampling and specifically the standard error of the sample mean to explain why many national market research and political opinion surveys contain 500 to 1000 respondents, no more and no less? (5 marks) 2. What is meant by a correlation coefficient and how we can test whether a correlation coefficient is statistically significant or not? (5 marks) 3. Data on the salaries of two occupations – financial management and solicitors and lawyers is outlined below.
Financial Management (Salary) ? 79,545 ? 65,254 ? 22,876 Solicitors and Lawyers (Salary) ? 51,579 ? 43,469 ? 16,232 Mean Mode Standard deviation Explain each of the statistical terms and describe what conclusions you can draw about the comparative salaries of both occupations? (5 marks) 4. Outline the different sampling methods that can be used to draw a representative sample of observations from its population and give examples of when each method is appropriate. (5 marks) P. T. O. LUBS5000M Section C (answer ALL questions) Section C carries 60% of the overall marks. 1.
Natures Way Ltd is a small health food specialist that is trying to break into the highly competitive breakfast cereal market. In order to boost its sales it is undertaking a nationwide advertising campaign and is promoting its product by giving customers a 10% discount on the purchase price of their breakfast cereal. In order to assess the impact of this campaign the company has commissioned some research based on evidence from across the UK. The resulting ordinary least squares model indicates the following relationship between the sales of its breakfast cereal and three core drivers of sales revenue: Sales 33. 5 + 25. Advert (13. 5) (5. 3) Standard errors in brackets. Analysis of Variance Regression Residual Total Sum of Squares 17000 3410 20410 F 18. 3 Significance F 0. 000 = + 31. 2 Prom (12. 2) – 1. 10 Comp (0. 49) where: Sales = Sales of breakfast cereal (? millions) Advert = Advertising expenditure (? millions) Prom = Cost of promotions campaign (? millions) Comp = Sales of competitors (? millions) (a) Discuss the statistical evidence in relation to: (i) which variables are statistically significant at the 5% level and which are no, (ii) how well the regression model fits, (iii) a test of the hypothesis that R Squared = 0.
In each case explain which ‘test’ you are using, and what it is testing for. (10 marks) (b) Give a written interpretation of each of the coefficient estimates. (3 marks) P. T. O. LUBS5000M (c) What would be the level of sales if advertising expenditure was ? 0. 5 million, promotion cost ? 0. 5 million and competitor sales had fallen to ? 2 million? (3 marks) (d) What is omitted variable bias and what are its consequences for OLS regression? (4marks) (20 marks in total). 2. During the current credit crunch the Ridings Bank has experienced a highly volatile market for its mortgage products.
As it stands it has been able to survive without the need to close any of its branch network and all redundancies have been on a voluntary basis. However, this situation is no longer sustainable and they have asked you to investigate the future demand for their mortgage products and make recommendations as to their future strategy. To help you carry out this analysis they have provided you with the following information on the number of mortgages loan agreements over the last three years (see table below).
Number of Mortgage Loan Agreements Year 2007 2008 2009 Period 1 2 3 1 2 3 1 2 3 Number of Mortgage Loans (000’s) 131 200 92 101 170 71 86 152 59 P. T. O. LUBS5000M (a) Distinguish between the additive and multiplicative models in time series analysis. (2 marks) (b) Plot the loan figures and appropriate trend line on the graph paper and identify from the graph the choice of model for working out the seasonal component. (4 marks) (c) Finish the calculations that are required to produce the forecasts for the next 3 periods (2010(1), 2010(2), 2010(3)). 8 marks) (d) What recommendations would you make to the company regarding their future strategy? (4 marks) (e) Explain how you can quantify the suitability of the chosen model over the alternative one? (2 marks) (20 marks in total) 3 (a) In hypothesis testing there are two broad groups of tests – parametric and nonparametric. When do we use parametric tests and when are non-parametric tests appropriate? (2 marks) (b) Explain how the choice of parametric test depends on the size of the sample as well as the number of samples. 3 marks) (c) Economists are interested in the impact of the current recessionary environment on business ‘failures’ and whether these are concentrated in certain industry sectors. You have been asked to analyse this data to determine whether there is any statistical relationship (at the 5% level) between industry sector and business ‘failures’ and to explain your results in terms that would be comprehensible to someone with little knowledge of statistics. P. T. O. LUBS5000M Manufacturing Receivership Going Concern Total 12 38 50 Industry Sector Retail Construction 14 56 70 34 46 80 Total 60 140 200 (6 marks) d) The makers of an electric car claim that it can do 186 miles per charge-up. A sample of 9 electric cars was selected and each one driven until the car ran out of power. The sample showed that the cars travelled on average 179 miles with a standard deviation of 10 miles. At the 1% level of significance is there evidence to suggest that the car makers have overstated their claim? (3 marks) (e) An insurance company is reviewing is current policy rates. When originally setting the rates they believed that the average claim would be ? 900 but they are concerned that the true mean is higher than this and they are losing money.
On the basis of a random sample of 121 claims they find a sample mean of ? 975 with a standard deviation of ? 300. At the 1% level of significance test whether the insurance company will be losing money? (3 marks) (f) In the past a library predicted that 85% of people returning books do so on time. However, there is a growing perception that this figure is incorrect. A random sample of 500 customers indicates that 390 of them return their books on time. Does this suggest that the return rate is significantly different from 85%? (at the 2% level of significance) (3 marks) (20 marks in total). END