6 A survey is carried out in an attempt to determine whether the salary achieved by the age of 30 is associated with having had a university education.
The results of this survey are given in the table.
| Salary < £30000 | Salary \(\boldsymbol { \geq }\) £30000 | Total |
| University education | 52 | 78 | 130 |
| No university education | 63 | 57 | 120 |
| Total | 115 | 135 | 250 |
- Use a \(\chi ^ { 2 }\) test, at the \(10 \%\) level of significance, to determine whether the salary achieved by the age of 30 is associated with having had a university education.
- What do you understand by a Type I error in this context?