Question 1 :

Following political pressure from residents of the Canterbury Borough, funding is now available to install a noise barrier. Different approaches can be taken to install the barrier. The choice of the approach is important because it can lead to different proportions of gaps in the barrier. Previous studies have shown a link between the percentage of area occupied by gaps and the reduction in noise level. Using the data provided with the question, a) please confirm if such a relationship exists. In case of a significant relationship, b) what is the decrease in decibels if we have a percentage of gaps of five percent?

Flaw Data and Calculations on Percentage Gap and Noise Reduction (in dB) Reading Percentage (p) Noise reduction (n) (p 13) (p 1'32 (12 71) (n )2 (p fJ)(n 1'1) A 25.00 0 17.90 320.56 -8.43 71.04 -150.91 B 13.00 3 5.90 34.86 -5.43 29.47 -32.05 C 6.00 6 -1.10 1.20 -2.43 5.90 2.66 D 3.00 9 -4.10 16.77 0.57 0.33 -2.34 E 1.50 11 -5.60 31.31 2.57 6.61 -14.39 F 0.78 14 -6.32 39.89 5.57 31.04 -35.19 G 0.39 16 -6.71 44.97 7.57 57.33 -50.77 Sums 49.67 59 0.00 489.57 0.00 201.71 -282.99 Value of Condominiums in Four Boroughs (x $1,000) Borough Price LAC 362.33 LAC 342.94 LAC 243.64 LAC 403.58 RPP 347.52 RPP 522.53 RPP 351.15 RPP 485.97 VER 275.81 VER 132.97 VER 435.63 VER 459.73 OUT 559.18 OUT 716.04 OUT 828.41 OUT 507.21The next two tables provide calculations that can be used to answer the question. First Set of Calculations Borough Mean price Overall mean (i,- 5c) (3?,- 3'02 LAC 338.12 435.92 -97.79 9563.09 FiPF' 652.71 435.92 216.79 46999.18 VEFi 426.79 435.92 -9.12 83.19 OUT 326.03 435.92 -109.88 12073.79 Sums 1743.66 1743.66 0.00 68719.26 Second Set of Calculations Borough Price Overall mean (xj - x) (xij - x)2 LAC 362.33 435.92 -73.58 5414.36 LAC 342.94 435.92 -92.97 8644.22 LAC 243.64 435.92 -192.27 36969.41 LAC 403.58 435.92 -32.33 1045.44 RPP 347.52 435.92 -88.39 7813.20 RPP 522.53 435.92 86.61 7501.58 RPP 351.15 435.92 -84.76 7184.31 RPP 485.97 435.92 50.06 2505.67 VER 275.81 435.92 -160.10 25633.39 VER 132.97 435.92 -302.94 91775.26 VER 435.63 435.92 -0.29 0.08 VER 459.73 435.92 23.81 566.95 OUT 559.18 435.92 123.27 15194.68 OUT 716.04 435.92 280.12 78467.04 OUT 828.41 435.92 392.49 154048.94 OUT 507.21 435.92 71.29 5082.93 Sums 6974.64 6974.64 0.00 447847.47