A marine biologist is investigating the growth rates of coral fragments using a new mineral supplement. Eight coral fragments are each split into two halves; one half is treated with the supplement, and the other serves as a control. The biologist claims that the mean growth of the treated fragments is more than 1.2 mm greater than the mean growth of the control fragments over a six-month period. The recorded growths (in mm) are shown in the table below:
| Fragment | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Control (CCC) | 12.4 | 15.1 | 11.8 | 14.2 | 13.5 | 12.9 | 14.8 | 13.0 |
| Treated (TTT) | 14.5 | 16.9 | 14.3 | 17.4 | 14.9 | 15.1 | 16.7 | 15.9 |
Assuming that the differences in growth are normally distributed, test the biologist's claim at the 1% significance level. State your hypotheses clearly and show your working.