2. An engineer decided to investigate whether or not the strength of rope was affected by water. A random sample of 9 pieces of rope was taken and each piece was cut in half. One half of each piece was soaked in water over night, and then each piece of rope was tested to find its strength. The results, in coded units, are given in the table below
| Rope no. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| Dry rope | 9.7 | 8.5 | 6.3 | 8.3 | 7.2 | 5.4 | 6.8 | 8.1 | 5.9 |
| Wet rope | 9.1 | 9.5 | 8.2 | 9.7 | 8.5 | 4.9 | 8.4 | 8.7 | 7.7 |
Assuming that the strength of rope follows a normal distribution, test whether or not there is any difference between the mean strengths of dry and wet rope. State your hypotheses clearly and use a \(1 \%\) level of significance.
(8 marks)