Answer: [-0.00811, 0.10811]

**Explanation:** To calculate the 95% confidence interval for the mean when the population variance is unknown, we use the t-distribution. **Step 1: Identify the parameters** - Sample mean (x̄) = 5% = 0.05 - Sample standard deviation (s) = 15% = 0.15 - Sample size (n) = 28 - Degrees of freedom (df) = n - 1 = 28 - 1 = 27 - Confidence level = 95% **Step 2: Determine the critical t-value** For a 95% confidence interval with two tails, we need t_{27,0.025} = 2.05 (from the provided table) **Step 3: Calculate the standard error** Standard error (SE) = s / √n = 0.15 / √28 ≈ 0.15 / 5.2915 ≈ 0.02835 **Step 4: Calculate the margin of error** Margin of error = t-value × SE = 2.05 × 0.02835 ≈ 0.05811 **Step 5: Construct the confidence interval** CI = x̄ ± margin of error = 0.05 ± 0.05811 = [-0.00811, 0.10811] **Why other options are incorrect:** - **A [0.00181, 0.0989]**: Uses incorrect critical value or calculation - **B [-0.0084, 0.1084]**: Uses approximate calculation - **D [0.02135, 0.07835]**: Uses z-value (1.96) instead of t-value, or incorrect standard error calculation **Key Concept:** When population variance is unknown and sample size is relatively small (n < 30), we use the t-distribution rather than the normal distribution to construct confidence intervals.

Author: Nikitesh Somanthe