Approved Answer THREE questions only. Question One a) A retail company has recently recruited an intern at its AB plc Head Office. She has discovered a pattern in demand showing a linear function: 80-(800+4P). By gathering information from one department, she has further discovered the Total Cost function of TC --30-1000 - 400. The Finance Director is excited about the new findings and would like to exploit the opportunity. The company are known to sell all it produces. 1) What is the profit function if P is the price and Q is the quantity demanded? (6 Marks) ii) Estimate the price and the quantity at breakeven and explain your answer. (10 Marks) m) Determine the profit when the quantity is 150. (3 Marks) b) The following information represents the quadratic equation which describes the relationship between the price and quantity of commodities sold. 24 P Q 18 3 20 2 4 Estimate the firm's demand function where - RO) for the given quadratic function P-Q+60+ (14.3 Marks) Total 33.3 Marks Terry21 CC ACCO Approved Question Two (a) A Quantitative Method module has been divided into four groups. During a recent online test in 2020, each group received an average score as follows: * 85, *2 = 78. *; -72, and X-82. What is the average score for the whole module if the number of students (n) in each group was as follows? 0) n-60, ng - 55, ny 58,7462 (3 marks) (ii) n = 50. n2 = 68, ng=65, 114 - 52 (3 marks) (b) 60 students recently took part in an aptitude test organized by a recruitment agency. Their grouped performance is given below: Performance Group Number of Students Above 90% 2 80% - 90% 8 70% - 80% 10 60% -70% 12 50% -60% 15 40% - 50% 9 30% - 40% 3 20% -30% 1 What is the mean performance of the students'? (8.3 marks) (i) Showing your steps, calculate the standard deviation of this grouped data and discuss the meaning of this statistic in the context of this data, (10 marks) (c) What are outliers in a dataset? How do you deal with outliers? (3 marks) (d) Explain three advantages of mean and three disadvantages of median (6 marks) Total 33.3 Marks Approved Question Three The table below provides the number of mergers and acquisitions made during each year for a ten-year period in the European Union. Year 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 Deals 1,017 1,039 609 872 708 763 896 724 681 567 Forecast the number of mergers and acquisitions in 2020 based on: a) 3-year moving average (6 Marks) b) Exponential smoothing with a=0.3 (7 Marks) e) Trend projection (16 Marks) d) On the basis of the analyses in parts (a) and (b), which method provides the better forecast? Explain. (4.3 Marks) Total 33.3 Marks Approved Question Four a) Describe Type I error and Type II error. What type of error do researchers usually control? (5 Marks) b) Suppose the average price of used BMW 1 series cars with 2010 registration is believed to be 5,250. A sample of 20 BMW 1 series cars listed on Autotrader.com with 2010 registration are given below: Price Mileage () 75K 5650 64K 7000 80k 5600 90k 4500 101k 3650 65k 5000 90k 4500 65k 5800 60k 6000 45k 7500 Price Mileage () 80k 5600 67k 6500 90K 4200 85k 4800 38k 8000 68k 6000 67k 6500 68k 6500 56k 5800 70k 5000 Assuming that the standard deviation is 500. Can it be concluded that the average price has increased using a 0.05 level of significance? (10 Marks) c) Suppose a sample of 36 supermarket managers revealed a mean salary of 36,800 with a standard deviation of 2,500. Construct the 95% confidence interval for the mean salary (10 Marks) d) In 2019, a random sample of 100 University of Greenwich students were surveyed and it was found that the proportion of students who travel home for Christmas is 0.60. Due to the COVID 19 situation, we hypothesise that only 55% student will travel home for Christmas in 2020. Test whether the proportion of students who travel home will decrease or not at the 1% level of significance. (8.3 Marks) Total 33.3 Marks