Explanation

To calculate the 95% confidence interval for the mean return, we use the formula:

Confidence Interval = Mean ± (t-statistic × Standard Error)

Step 1: Determine the correct t-statistic

• We have 12 months of data, so degrees of freedom = n - 1 = 12 - 1 = 11
• For a 95% confidence interval, we need a two-tailed test with α = 0.025 in each tail
• From the t-table, with df = 11 and α = 0.025, the t-statistic is 2.201

Step 2: Calculate the margin of error

Margin of Error = t-statistic × Standard Error = 2.201 × 2.70% = 5.9427%

Step 3: Calculate the confidence interval

Lower bound = -0.75% - 5.9427% = -6.6927% ≈ -6.69% Upper bound = -0.75% + 5.9427% = 5.1927% ≈ 5.19%

Therefore, the 95% confidence interval is -6.69% and 5.19%.

Why other options are incorrect:

• Option B (-6.63% and 5.13%): Uses t-statistic of 2.179 (df = 12 instead of 11)
• Option C (-5.60% and 4.10%): Uses t-statistic of 1.796 (incorrect α level)
• Option D (-5.56% and 4.06%): Uses t-statistic of 1.782 (incorrect α level)