9 The head teacher of a school believes that, on average, pupil absences on the days Monday, Tuesday, Wednesday, Thursday and Friday are in the ratio \(3 : 2 : 2 : 2 : 3\). The head teacher takes a random sample of 120 pupil absences. The results are as follows.
| Day of week | Monday | Tuesday | Wednesday | Thursday | Friday |
| Number of absences | 28 | 16 | 24 | 16 | 36 |
- Test at the \(5 \%\) significance level whether these results are consistent with the head teacher's belief.
A significance test at the \(5 \%\) level is also carried out on a second, independent, random sample of \(n\) pupil absences. All the numbers of absences are integers. The ratio of the numbers of absences for each day in this sample is identical to the ratio of the numbers of absences for each day in the original sample of size 120.
- Determine the smallest value of \(n\) for which the conclusion of this significance test is that the data are not consistent with the head teacher's belief.