- Secondary schools in a region conduct ability testing at the start of Year 7 and the start of Year 8. Each year a regional education officer randomly selects 240 Year 7 students and 240 Year 8 students from across the region. The results for last year are summarised in the table below.
| \cline { 2 - 3 }
\multicolumn{1}{c|}{} | Mean score | Variance of scores |
| Year 7 | 101 | 38 |
| Year 8 | 103 | 42 |
The regional education officer claims that there is no difference between the mean scores of these two year groups.
- Test the regional education officer's claim at the \(1 \%\) significance level. You should state your hypotheses, test statistic and critical value clearly.
- Explain the significance of the Central Limit Theorem in part (a).