- 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 | | |
- 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.
- State clearly an assumption you have made to enable you to carry out the test in part (a).
- 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.
- Write down what you can conclude about the effect of music on a student's performance during the test.