Answer: [0.02054, 0.036466]

## Explanation The 95% confidence interval for the mean return is calculated using the formula: ``` CI = Mean return ± (t-critical × Standard error) ``` ### Step 1: Identify the parameters - Sample mean (μ) = 2.85% = 0.0285 - Sample standard deviation (σ) = 1.6% = 0.016 - Sample size (n) = 18 - Confidence level = 95% ### Step 2: Determine degrees of freedom and critical t-value - Degrees of freedom (df) = n - 1 = 18 - 1 = 17 - For a 95% confidence interval (two-tailed), we use α/2 = 0.025 - From the t-table: t₁₇,₀.₀₂₅ = 2.11 ### Step 3: Calculate standard error ``` Standard error = σ / √n = 0.016 / √18 = 0.016 / 4.2426 = 0.00377 ``` ### Step 4: Calculate margin of error ``` Margin of error = t-critical × Standard error = 2.11 × 0.00377 = 0.00796 ``` ### Step 5: Calculate confidence interval ``` Lower bound = 0.0285 - 0.00796 = 0.02054 Upper bound = 0.0285 + 0.00796 = 0.03646 ``` Therefore, the 95% confidence interval is [0.02054, 0.03646], which matches option D. **Key points:** - We use t-distribution because population variance is unknown - Degrees of freedom = n - 1 = 17 - For 95% confidence interval, we use α/2 = 0.025 (two-tailed) - The correct t-value from the table is 2.11

Author: Tanishq Prabhu