Assignment 2 URBS 362 Winter 2023 - Submission Deadline: March 29, 2023 at 5:00 p.m. General Instructions This is a two-person assignment. Assignments from one-person teams are allowed. Three person teams are not accepted. Assignments are done on the student's own time. Calculations should be done by hand in order to provide practice for the exams. The assignments must be handed over in paper format in class or in the instructor's mail- box at the department. Answers can be typed (e.g., word processor) or handwritten. Please write clearly because words and numbers that cannot be read without difficulty will count as not written. Please submit only one assignment per team. Late reports will be subject to a 10% penalty per day for an unjustified late submission. For each question provide: a) A justification of the statistical test you selected. A reference to a one-tailed or a two-tailed test does not answer adequately to this question (0.5 points) b) The statistical hypotheses (null and alternative hypotheses). The mathematical no- tation is not accepted (0.5 points) c) The calculations and the results of the statistical test(s) (1.75 points) d) Your interpretation of the results of the statistical test(s). Specify if you accept or you reject the null hypothesis and give the practical implications. The level of significance (a) is 5% (or 0.05). (0.75 points) Each question is worth 3.5 points for a total of 7 points. The teaching assistant and course instructor do not provide help on the theory of the course. 1 Question 1 The price of housing on the Island of Montreal changes on a yearly basis. Your supervisor would like an update on the situation and has asked you to provide him with a comparison of the current price of condominiums in three boroughs. These boroughs and their corre- sponding abbreviations are Lachine (LAC), Outremont (OUT) and Rosemont/Petite-Patrie (RPP). The prices of condominiums are presented below as well as the boxplot of the observa- tions. Table 1: Price of Condominiums Borough Price (x 1,000$) LAC 403.6 LAC 503.6 LAC 562.9 LAC 452.3 OUT 559.2 OUT 616.0 OUT 507.2 OUT 728.4 RPP 652.5 RPP 511.2 RPP 447.5 RPP 586.0 2 400 Price (x 1,000$) 500 009 700 LAC OUT RPP Boroughs The next three tables provide calculations that can be used to answer the question. Table 2: First Set of Calculations Borough Mean price Variance of price LAC 480.6 4,680.6 OUT 602.7 8,997.3 RPP 549.3 7,938.1 Table 3: Second Set of Calculations Borough Mean price Overall mean (ix) (xi) LAC 480.6 544.2 -63.6 4,043.0 OUT 602.7 544.2 58.5 3,422.2 RPP 549.3 544.2 5.1 25.9 Sums 1,632.6 1,632.6 0.0 7,491.0 3 Table 4: Third Set of Calculations Borough Price Overall mean (xijx) (xij - x) LAC 403.6 544.2 -140.6 19,775.9 LAC 503.6 544.2 -40.6 1,645.8 LAC 562.9 544.2 18.7 350.9 LAC 452.3 544.2 -91.9 8,441.2 OUT 559.2 544.2 15.0 224.2 OUT 616.0 544.2 71.8 5,159.0 OUT 507.2 544.2 -37.0 1,368.9 OUT 728.4 544.2 184.2 33,928.6 RPP 652.5 544.2 108.3 11,732.8 RPP 511.2 544.2 -33.1 1,092.6 RPP 447.5 544.2 -96.7 9,348.2 RPP 586.0 544.2 41.8 1,744.2 Sums 6,530.5 6,530.5 0.0 94,812.1 Question 2 You are in charge of revitalizing an area in downtown Cullenville. Three urban architect firms present their concept to an evaluation committee. Which firm(s) have the highest rating? The rating of each of these projects is presented below as well as the boxplot of the ratings. Rating 30 35 40 45 50 Table 5: Ratings of Three Architectural Projects Jury Sitte Parker Rossi 1 40 30 48 2 42 45 49 3 30 38 44 4 37 32 53 30 Sitte Parker Rossi Project The next three tables provide calculations that can be used to answer these questions. Table 6: First Set of Calculations Project Mean rating Variance of rating Sitte 37.2 27.6 Parker 36.2 45.6 Rossi 48.5 13.7 5 Table 7: Second Set of Calculations Project Mean rating Overall mean rating (i x) | (i x) Sitte 37.25 40.67 -3.42 11.67 Parker 36.25 40.67 -4.42 19.51 Rossi 48.50 40.67 7.83 61.36 Sums 122.00 122.00 0.00 92.54 Table 8: Third Set of Calculations Project Rating Overall mean (xij - x) (xij - x) Sitte 40 40.67 -0.67 0.44 Sitte 42 40.67 1.33 1.78 Sitte 30 40.67 -10.67 113.78 Sitte 37 40.67 -3.67 13.44 Parker 30 40.67 -10.67 113.78 Parker 45 40.67 4.33 18.78 Parker 38 40.67 -2.67 7.11 Parker 32 40.67 -8.67 75.11 Rossi 48 40.67 7.33 53.78 Rossi 49 40.67 8.33 69.44 Rossi 44 40.67 3.33 11.11 Rossi 53 40.67 12.33 152.11 Sums 488 488.00 0.00 630.67