This economics question tests your understanding of economic models and analysis. The step-by-step answer below applies the relevant framework and explains the reasoning.
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Here are the solutions to the questions: 2b.i) Step 1: Identify the regression equation and the meaning of X. The regression equation is Y = 82 + 0.04X. X represents school funding in thousands of dollars per student. The school board proposes reallocating 1,000 per student. The question asks for the change if funding were given to 10 students. Step 2: Calculate the total change in funding (X). Total funding change = 1,000 per student × 10 students = \10,000. Since X is in thousands of dollars, X = (\10,000)/(\1,000/thousand) = 10. Step 3: Calculate the predicted change in graduation rate (Y). The change in Y is given by the slope multiplied by the change in X. Y = 0.04 × X Y = 0.04 × 10 Y = 0.4 The predicted graduation rate change is 0.4 percentage points. 2b.iii) To determine homogeneity, calculate the Coefficient of Variation (CV) for each school. A smaller CV indicates more homogeneous performance. The formula for CV is CV = Standard DeviationMean × 100\%. Step 1: Calculate CV for School A. Mean = 75, SD = 5 CV_A = (5)/(75) × 100\% = 0.0666... × 100\% ≈ 6.67\% Step 2: Calculate CV for School B. Mean = 70, SD = 12 CV_B = (12)/(70) × 100\% = 0.1714... × 100\% ≈ 17.14\% Step 3: Compare the CV values. Since CV_A (6.67\%) is less than CV_B (17.14\%), School A has more homogeneous performance. School A has the most homogeneous performance because its coefficient of variation is lower, indicating that its students' scores are less spread out relative to their mean score compared to School B. 3a.i) Step 1: Find the Z-score corresponding to the top 10% (90th percentile) for a normal distribution. For the top 10%, we need the score X such that P(Z > z) = 0.10, which means P(Z z) = 0.90. Using a standard normal distribution table or calculator, the Z-score for the 90th percentile is approximately z = 1.28. Step 2: Convert the Z-score back to a raw score using the formula X = + Z. Given = 75 and = 8. X = 75 + (1.28 × 8) X = 75 + 10.24 X = 85.24 The score that corresponds to an A- (top 10%) is 85.24. 3a.ii) Step 1: Determine the percentage of students who would fail. Failing is defined as the bottom 5%. Step 2: Calculate the number of students in a 100-person class. Number of failing students = 100 students × 0.05 = 5 students. In a 100-person class, 5 students would theoretically fail