4 The students in a large university department take a trial examination some time before the proper examination. A random sample of 60 students took both examinations during a particular course. 42 students passed the trial examination, 36 passed the proper examination and 13 failed both examinations.
- Copy and complete the following contingency table.
| Proper |
| \cline { 2 - 4 }
\multicolumn{1}{l}{} | Pass | Fail | Total | |
| \cline { 2 - 5 } | Pass | | | 42 |
| \cline { 2 - 5 }
Trial | Fail | | 13 | |
| \cline { 2 - 5 } | Total | 36 | | 60 |
- Carry out a test of independence at the \(\frac { 1 } { 2 } \%\) level of significance.