6 Fiona, a lecturer in a school of engineering, believes that there is an association between the class of degree obtained by her students and the grades that they had achieved in A-level Mathematics.
In order to investigate her belief, she collected the relevant data on the performances of a random sample of 200 recent graduates who had achieved grades A or B in A-level Mathematics. These data are tabulated below.
| \multirow{2}{*}{} | Class of degree | |
| | 1 | 2(i) | 2(ii) | 3 | Total |
| \multirow{2}{*}{A-level grade} | A | 20 | 36 | 22 | 2 | 80 |
| B | 9 | 55 | 48 | 8 | 120 |
| Total | 29 | 91 | 70 | 10 | 200 |
- Conduct a \(\chi ^ { 2 }\) test, at the \(1 \%\) level of significance, to determine whether Fiona's belief is justified.
- Make two comments on the degree performance of those students in this sample who achieved a grade B in A-level Mathematics.