1 As part of an investigation into the starting salaries of graduates in a European country, the following information was collected.
| \multirow{2}{*}{} | | Starting salary (€) |
| Sample size | Sample mean | Sample standard deviation |
| Science graduates | 175 | 19268 | 7321 |
| Arts graduates | 225 | 17896 | 8205 |
- Stating a necessary assumption about the samples, construct a \(98 \%\) confidence interval for the difference between the mean starting salary of science graduates and that of arts graduates.
- What can be concluded from your confidence interval?