- A Head of Department at a large university believes that gender is independent of the grade obtained by students on a Business Foundation course. A random sample was taken of 200 male students and 160 female students who had studied the course.
The results are summarised below.
| \cline { 3 - 4 }
\multicolumn{2}{c|}{} | Male | Female |
| \multirow{3}{*}{Grade} | Distinction | \(18.5 \%\) | \(27.5 \%\) |
| \cline { 2 - 4 } | Merit | \(63.5 \%\) | \(60.0 \%\) |
| \cline { 2 - 4 } | Unsatisfactory | \(18.0 \%\) | \(12.5 \%\) |
Stating your hypotheses clearly, test the Head of Department's belief using a 5\% level of significance. Show your working clearly.