1 Technologists at a company that manufactures paint are trying to develop a new type of gloss paint with a shorter drying time than the current product. In order to test whether the drying time has been reduced, the technologists paint a square metre of each of the new and old paints on each of 10 different surfaces. The lengths of time, in hours, that each square metre takes to dry are as follows.
| Surface | A | B | C | D | E | F | G | H | I | J |
| Old paint | 16.6 | 17.0 | 16.5 | 15.6 | 16.3 | 16.5 | 16.4 | 15.9 | 16.3 | 16.1 |
| New paint | 15.9 | 16.3 | 16.3 | 15.9 | 15.5 | 16.6 | 16.1 | 16.0 | 16.2 | 15.6 |
- Explain why a paired sample is used in this context.
- The mean reduction in drying time is to be investigated. Why might a \(t\) test be appropriate in this context and what assumption needs to be made?
- Using a significance level of \(5 \%\), carry out a test to see if there appears to be any reduction in mean drying time.
- Find a 95\% confidence interval for the true mean reduction in drying time.