A sports scientist is investigating whether wearing a new design of compression socks affects the post-workout blood lactate levels of athletes. She conducts an experiment using a sample of 12 runners. Each runner's blood lactate levels (measured in mmol/L\text{mmol/L}mmol/L) are recorded following a high-intensity treadmill run under two conditions: first, using normal athletic socks, and second, using the new compression socks. The data for each participant is presented in the table below.
| Athlete | Normal Socks (A) | Compression Socks (B) |
|---|---|---|
| a | 5.2 | 4.0 |
| b | 6.4 | 6.4 |
| c | 4.8 | 5.4 |
| d | 7.1 | 6.3 |
| e | 5.9 | 5.1 |
| f | 6.6 | 6.6 |
| g | 8.0 | 6.5 |
| h | 4.3 | 4.5 |
| i | 5.5 | 4.4 |
| j | 6.2 | 5.6 |
| k | 7.3 | 7.5 |
| l | 6.8 | 5.4 |
Using the Wilcoxon Signed-Ranks test, calculate the value of TTT. Use the formula where T T\,T is the sum of ranks of the differences with the least frequent sign.
