7 The numbers of students taking A levels in three subjects at a school were classified by the year in which they entered the school as follows.
| \cline { 2 - 5 }
\multicolumn{1}{c|}{} | Subject | Mathematics | English | Physics |
| \multirow{3}{*}{} | Year 7 | 17 | 16 | 7 |
| \cline { 2 - 5 } | Year 12 | 13 | 2 | 5 |
The Head of the school carries out a significance test at the \(10 \%\) level to test whether subjects taken are independent of year of entry.
- Show that in carrying out the test it is necessary to combine columns.
- Suggest a reason why it is more sensible to combine the columns for Mathematics and Physics than the columns for Physics and English.
- Carry out the test.
- State which cell gives the largest contribution to the test statistic.
- Interpret your answer to part (iv).