1. **State the problem:** We need to find the standard deviation of the differences in depression scores between caffeine and placebo conditions for 11 subjects. 2. **Calculate the differences:** For each subject, subtract the caffeine depression score from the placebo depression score to get the difference $d_i$. $$d = [16-5, 23-5, 5-4, 7-3, 14-8, 24-5, 6-0, 3-0, 15-2, 12-11, 0-1] = [11, 18, 1, 4, 6, 19, 6, 3, 13, 1, -1]$$ 3. **Find the mean of the differences:** $$\bar{d} = \frac{1}{n} \sum_{i=1}^{n} d_i = \frac{11 + 18 + 1 + 4 + 6 + 19 + 6 + 3 + 13 + 1 - 1}{11} = \frac{81}{11} \approx 7.364$$ 4. **Calculate the squared deviations from the mean:** $$ (d_i - \bar{d})^2 = [(11-7.364)^2, (18-7.364)^2, (1-7.364)^2, (4-7.364)^2, (6-7.364)^2, (19-7.364)^2, (6-7.364)^2, (3-7.364)^2, (13-7.364)^2, (1-7.364)^2, (-1-7.364)^2] $$ $$ = [13.28, 113.17, 40.44, 11.31, 1.86, 134.02, 1.86, 19.15, 31.72, 40.44, 70.92]$$ 5. **Sum the squared deviations:** $$\sum (d_i - \bar{d})^2 = 13.28 + 113.17 + 40.44 + 11.31 + 1.86 + 134.02 + 1.86 + 19.15 + 31.72 + 40.44 + 70.92 = 477.17$$ 6. **Calculate the sample variance:** $$s^2 = \frac{\sum (d_i - \bar{d})^2}{n-1} = \frac{477.17}{10} = 47.717$$ 7. **Calculate the standard deviation:** $$s = \sqrt{47.717} \approx 6.91$$ **Final answer:** The standard deviation of the differences is approximately **6.91**.