8 After contracting a particular disease, patients from a hospital are advised to have their blood tested monthly for a year. In order to test whether patients comply with this advice the hospital management commissioned a survey of 100 patients. A hospital statistician selected the patients randomly from records and asked the patients whether or not they had complied with the advice. The results classified by gender are as follows.
| Gender | |
| \cline { 2 - 4 } | | Female | Male |
| \cline { 2 - 4 }
Comply | Yes | 34 | 30 |
| \cline { 2 - 4 } | No | 11 | 25 |
| \cline { 2 - 4 } | | | |
| \cline { 2 - 4 } |
- Test at the \(5 \%\) significance level whether compliance with the advice is independent of gender.
- A manager believed that a greater proportion of female patients than male patients comply with the advice. Carry out an appropriate test of proportions at the \(10 \%\) significance level.