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Unformatted text preview: University of Durham EXAMINATION PAPER date May/June 2005 exam code MATH1711/01 description DATA ANALYSIS, MODELLING AND SIMULATION Time allowed: 3 hours Examination material provided: 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. ED01/2005 University of Durham Copyright continued 2 MATH1711/01 SECTION A 1. A study ( Biometrika (1942), vol 32, p.243) was carried out to study the effectiveness of a number of insecticides labelled A, B, C, D, E and F. Each insecticide was applied to 12 agricultural experimental units (small plots) of the same size and type. Subsequently a count was made of the number of insects (species Phlegethontius quinquemaculata ) remaining on each unit. The data and some summary statistics were as follows: Number of insects on plot x s A 10 7 20 14 14 12 14.50 4.72 10 23 17 20 14 13 B 11 17 21 11 16 14 15.33 4.27 17 17 19 21 7 13 C 1 7 2 3 1 2.08 1.98 2 1 3 1 4 D 3 5 12 6 4 3 4.92 2.50 5 5 5 5 2 4 E 3 5 3 5 3 6 3.50 1.73 1 1 3 2 6 4 F 11 9 15 22 15 16 16.67 6.21 13 10 26 26 24 13 (a) Explain the process of decomposing the data into overall mean, effects and residuals, giving a detailed illustration of the calculations for some of the data. (b) Showing your calculations, produce and interpret an effects and residuals plot. You may find it helpful to know that the quartiles and median of the residuals are 2, . 50 and 1 . 67. (c) Construct and interpret an analysis of variance table for the decomposition. (d) Assess the validity of the usual homogeneity assumption and if necessary decide what would be an appropriate transformation to be applied to the data. ED01/2005 University of Durham Copyright continued 3 MATH1711/01 2. In a study of warp breakage during the weaving of fabric ( Technometrics, 1982, p.63), 100 pieces of yarn were tested. The number of cycles of strain to breakage was recorded for each piece. The plots below are Gaussian quantile plots of respectively the number of cycles, the natural logarithm of the number of cycles and the square root of the number of cycles.root of the number of cycles....
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 Spring '11
 DrU.Picchini
 Math, Normal Distribution

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