MATH171106

# MATH171106 - University of Durham EXAMINATION PAPER date...

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University of Durham EXAMINATION PAPER date May/June 2006 exam code MATH1711/01 description DATA ANALYSIS MODELLING AND SIMULATION Time allowed: 3 hours Examination material provided: Formula sheet Normal distribution table Graph paper Instructions: Credit will be given for the best SIX answers. All questions carry the same marks. Use a separate answer book for each Section. Approved electronic calculators may be used except where a question explicitly forbids it. ED01/2006 Durham University Copyright continued

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2 MATH1711/01 SECTION A 1. (i) For a set of data x 1 , . . . , x n , define the mean x and standard deviation s . Show that, under a change of units where each x i becomes a + bx i , the mean becomes a + b x and the standard deviation becomes | b | s . Hence, deduce the mean and standard deviation when data are converted to “standard” units. (ii) (a) Briefly discuss the risks involved in drawing conclusions from observational studies. (b) Briefly discuss the merits and disadvantages of stratified random sampling in comparison to simple random sampling. (c) Write a sentence or two to describe each of the following: controlled ex- periment, placebo, randomisation, quota sampling. 2. As part of a study reported in the Journal of Hazardous Materials (July 1995) the sorption rate (mole percentage) was measured for 32 hazardous organic solvents used to clean metal parts. Each solvent was also classified as being an aromatic, chloroalkane or ester. The data and some summary statistics were as follows: Sorption Rates n x s Aromatic 1 · 06 0 · 95 0 · 79 0 · 65 0 · 81 9 0.94 0.17 1 · 14 0 · 89 1 · 12 1 · 05 Chloroalkane 1 · 59 1 · 12 1 · 45 0 · 92 0 · 57 8 1.01 0.40 0 · 83 1 · 16 0 · 44 0 · 29 0 · 43 0 · 06 0 · 06 0 · 51 Ester 0 · 09 0 · 44 0 · 10 0 · 17 0 · 61 15 0.33 0.21 0 · 34 0 · 60 0 · 55 0 · 53 0 · 17
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