Question Four [11 marks] An analyst who works for the hedge fund Angel Partners has been asked to assess the benefits of investing in a large group of unlisted agricultural biotechnology companies. They have been asked to estimate both the average investment return and the standard deviation of these returns. In the past it was assumed that for the population of biotechnology companies , the average return was 15% with standard deviation of 7%. Management thinks that this may not still be the case as the industry has matured due to developments in both scientific processes governing discovery and commercialization of new products. The analyst plans to obtain a point estimate and a 90% interval estimate of the mean and the standard deviation from a new sample of companies. Using this information answer the following questions. Super Sch (a) If the analyst wants to have an error bound of 2% when they obtain the required interval estimate how large a sample should they take. [2 marks] (b) Using the information you have been given and the result from part (a) what is the sampling distribution of the mean in this situation. [1 mark] (c) Using the sampling distribution from part (b) of this question obtain the value for which 90% of all possible samples will have a larger value for the sample mean. [2 marks] (d) The analyst takes the sample and obtains the sample estimates for the mean = 7% and the standard deviation s = 5%. Find the 90% interval estimate of the population mean and state how we interpret this result. [3 marks] [3 marks] 0B 5/6 (e) Using the information from parts (a) and (d) of this question obtain the 980% interval estimate of the variance. Briefly explain how we would interpret this interval estimate of o2. [3 marks] Total marks : 11=2+1+2+3+3 END OF THE MID-SEMESTER TEST QUESTIONS TOTAL MARKS 40 = 13+5+11+11