6 A random sample of 80 students who had all studied Biology, Chemistry and Art at a college was each asked which they enjoyed most. The results, classified according to gender, are given in the table.
| Subject |
| \cline { 2 - 5 } | | Biology | Chemistry | Art |
| \cline { 2 - 5 }
Gender | Male | 13 | 4 | 11 |
| \cline { 2 - 5 } | Female | 37 | 8 | 7 |
| \cline { 2 - 5 } | | | | |
| \cline { 2 - 5 } |
It is required to carry out a test of independence between subject most enjoyed and gender at the \(2 \frac { 1 } { 2 } \%\) significance level.
- Calculate the expected values for the cells.
- Explain why it is necessary to combine cells, and choose a suitable combination.
- Carry out the test.