5. Seven pipes of equal length are selected at random. Each pipe is cut in half. One piece of each pipe is coated with protective paint and the other is left uncoated. All of the pieces of pipe are buried to the same depth in various soils for 6 months.
The table gives the percentage area of the pieces of pipe in the various soils that are subject to corrosion.
| Soil | A | B | C | D | E | F | G |
| 39 | 40 | 43 | 32 | 42 | 33 | 36 |
| \% Corrosion | | uncoated pipe |
| 41 | 36 | 61 | 48 | 42 | 48 | 45 |
- Stating your hypotheses clearly and using a \(5 \%\) significance level, carry out a paired \(t\)-test to assess whether or not there is a difference between the mean percentage of corrosion on the coated pipes and the mean percentage of corrosion on the uncoated pipes.
- State an assumption that has been made in order to carry out this test.
- Comment on the validity of this assumption.
- State what difference would be made to the conclusion in part (a) if the test had been to determine whether or not the percentage of corrosion on the uncoated pipes was higher than the mean percentage of corrosion on the coated pipes. Justify your answer.