A large number of students are split into two groups $A$ and $B$. The students sit the same test but under different conditions. Group A has music playing in the room during the test, and group B has no music playing during the test. Small samples are then taken from each group and their marks recorded. The marks are normally distributed.

The marks are as follows:
Sample from Group $A$: 42, 40, 35, 37, 34, 43, 42, 44, 49
Sample from Group $B$: 40, 44, 38, 47, 38, 37, 33

\begin{enumerate}[label=(\alph*)]
\item Stating your hypotheses clearly, and using a 10\% level of significance, test whether or not there is evidence of a difference between the variances of the marks of the two groups.
[8]

\item State clearly an assumption you have made to enable you to carry out the test in part (a).
[1]

\item Use a two tailed test, with a 5\% level of significance, to determine if the playing of music during the test has made any difference in the mean marks of the two groups. State your hypotheses clearly.
[7]

\item Write down what you can conclude about the effect of music on a student's performance during the test.
[1]
\end{enumerate}

\hfill \mbox{\textit{Edexcel S4  Q2 [17]}}