4 Julie, a driving instructor, believes that the first-time performances of her students in their driving tests are associated with their ages.
Julie's records of her students' first-time performances in their driving tests are shown in the table.
| Age | Pass | Fail |
| \(\mathbf { 1 7 } - \mathbf { 1 8 }\) | 28 | 20 |
| \(\mathbf { 1 9 } - \mathbf { 3 0 }\) | 2 | 14 |
| \(\mathbf { 3 1 } - \mathbf { 3 9 }\) | 12 | 33 |
| \(\mathbf { 4 0 } - \mathbf { 6 0 }\) | 6 | 5 |
- Use a \(\chi ^ { 2 }\) test at the \(1 \%\) level of significance to investigate Julie's belief.
- Interpret your result in part (a) as it relates to the 17-18 age group.