- Tisam took a survey of students' favourite colours. The results are summarised in the table below.
| \multirow{2}{*}{} | Colour | |
| | Red | Blue | Green | Yellow | Black | Total |
| \multirow{3}{*}{Year group} | 1-5 | 34 | 15 | 14 | 22 | 3 | 88 |
| 6-9 | 23 | 32 | 12 | 9 | 8 | 84 |
| 10-12 | 5 | 28 | 19 | 8 | 8 | 68 |
| Total | 62 | 75 | 45 | 39 | 19 | 240 |
Tisam carries out a suitable test to see if there is any association between favourite colour and year group.
- Write down the hypotheses for a suitable test.
For her table, Tisam only needs to check one cell to show that none of the expected frequencies are less than 5
- Identify this cell, giving your reason.
- Calculate the expected frequency for this cell.
The test statistic for Tisam's test is 38.449
- Using a \(1 \%\) level of significance, complete the test.
You should state your critical value and conclusion clearly.