Need Help: MATH238 COURSEWORK (Statistics)


MATH238 COURSEWORK (Statistics)

To be submitted to the Faculty Office by 13:00 on Monday 7th November 2016. You should work on this coursework in self-selected groups of three students, however if you prefer to work in a pair or individually then it is okay to do this. Students who work in a group for the coursework should only submit one piece of work, clearly labelled with all of their ID numbers. You should type set your coursework using Word. Your submission must consist of no more than 4 sides of A4 pages, with font of size 12. You should give due consideration to your personal time management to ensure that coursework is submitted in plenty of time prior to the deadline. Note that plagiarism will be treated according to University regulations. Please see http://www.plymouth.ac.uk/student-life/your-studies/essential-information/regulations/plagiarism This coursework is worth 30% of the overall coursework mark for this module, so it is worth 10.5% of the overall module mark. This assessment is designed to test your ability to:  Produce graphical displays of data  Calculate appropriate statistical quantities for a data set  Use regression analysis Your work will be assessed according to the following criteria:  Presentation of graphical displays  Correct application of statistical methods  Correct conclusions  Clear and concise presentation of your solutions Coursework set on Tuesday 18th October 2016. 1. One of the characteristics of bitumen for road mixes is its Softening Point Temperature (oC). According to BS EN 12591:2009, the preferred bitumen grade for use in highways in the UK should be between 38oC and 47oC. A sample of 34 shipments of bitumen delivered to a highway building site has been examined and their Softening Point Temperature recorded below. 46.4 45.6 44.9 42.2 45.9 44.1 44.2 48.5 42.2 44.0 43.7 43.6 45.8 44.0 47.9 45.5 46.8 42.4 46.0 45.9 44.3 44.2 44.8 43.0 46.4 49.9 47.6 44.0 41.9 45.5 44.0 43.9 46.6 42.8 (a) Using Excel, create a histogram of this data, with the classes (41.55, 42.75], (42.75, 43.95], …. . (b) Calculate appropriate measures of location and spread for the data. State why you have chosen to use these. (c) Construct a 95% confidence interval for the true mean of the Softening Point Temperature. In your workings, use the precision of at least 2 decimal places. (d) The manufacturer of the sampled bitumen claims that their bitumen has Softening Point Temperature of 45oC. Based on the collected data, is there any evidence, at the 95% confidence level, to dispute the manufacturer’s claim? (e) How large the sample of softening point temperatures would need to be in order for the maximum margin of error to be 0.5 oC, at the 95% confidence level. (20 marks) (Over…) 2. The table below gives the net profits, in thousands of pounds, of a small engineering company during the first 10 years that it has been in business. Year, x Net profit, y (£000) 1 33.5 2 46.3 3 49.6 4 56 5 74.6 6 89.5 7 118.5 8 142.5 9 195.8 10 248.1 (a) Use Excel to obtain a good regression model for this data, taking the net profit as the response variable and year as the explanatory variable. You should include and briefly discuss:  a scatter plot  initial use of trendlines to assess the possible models  the proportion of variation explained by your model  tests that the coefficients are significant  analysis of the residuals  the equation for the Net Profit in terms of the Year (b) Use your regression model to estimate the net profit: (i) in year 11 and (ii) in year 15. Comment on the reliability of the results you obtain. (30 marks)

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