3 Because of the large number of students enrolled for a university geography course and the limited accommodation in the lecture theatre, the department provides a filmed lecture. Students are randomly assigned to two groups, one to attend the lecture theatre and the other the film. At the end of term the two groups are given the same examination. The geography professor wishes to test whether there is a difference in the performance of the two groups and selects the marks of two random samples of students, 6 from the group attending the lecture theatre and 7 from the group attending the films. The marks for the two samples, ordered for convenience, are shown below.

1. Stating a necessary assumption, carry out a suitable non-parametric test, at the \(10 \%\) significance level, for a difference between the median marks of the two groups.
2. State conditions under which a two-sample \(t\)-test could have been used.
3. Assuming that the tests in parts (i) and (ii) are both valid, state with a reason which test would be preferable.