6 The deterioration of a certain drug over time was investigated as follows. The drug strength was measured in each of a random sample of 8 bottles containing the drug. These were stored for two years and the strengths were then re-measured. The original and final strengths, in suitable units, are shown in the following table.
| Bottle | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Original strength | 8.7 | 9.4 | 9.2 | 8.9 | 9.6 | 8.2 | 9.9 | 8.8 |
| Final strength | 8.1 | 9.0 | 9.0 | 8.8 | 9.3 | 8.0 | 9.5 | 8.5 |
- Stating any required assumption, test at the \(5 \%\) significance level whether the mean strength has decreased by more than 0.2 over the two years.
- Calculate a 95\% confidence interval for the mean reduction in strength over the two years.