7. Two groups of students take the same examination. A random sample of students is taken from each of the groups. The marks of the 9 students from Group 1 are as follows $$\begin{array} { l l l l l l l l l } 30 & 29 & 35 & 27 & 23 & 33 & 33 & 35 & 28 \end{array}$$ The marks, \(x\), of the 7 students from Group 2 gave the following statistics $$\bar { x } = 31.29 \quad s ^ { 2 } = 12.9$$ A test is to be carried out to see whether or not there is a difference between the mean marks of the two groups of students. You may assume that the samples are taken from normally distributed populations and that they are independent.

1. State one other assumption that must be made in order to apply this test and show that this assumption is reasonable by testing it at a \(10 \%\) level of significance. State your hypotheses clearly.
2. Stating your hypotheses clearly, test, using a significance level of \(5 \%\), whether or not there is a difference between the mean marks of the two groups of students.