3. An archaeologist is studying the compression strength of bricks at some ancient European sites. He took random samples from two sites \(A\) and \(B\) and recorded the compression strength of these bricks in appropriate units. The results are summarised below.
| Site | Sample size \(( n )\) | Sample mean \(( \bar { x } )\) | Standard deviation \(( s )\) |
| \(A\) | 7 | 8.43 | 4.24 |
| \(B\) | 13 | 14.31 | 4.37 |
It can be assumed that the compression strength of bricks is normally distributed.
- Test, at the \(2 \%\) level of significance, whether or not there is evidence of a difference in the variances of compression strength of the bricks between these two sites. State your hypotheses clearly.
(5)
Site \(A\) is older than site \(B\) and the archaeologist claims that the mean compression strength of the bricks was greater at the younger site. - Stating your hypotheses clearly and using a \(1 \%\) level of significance, test the archaeologist's claim.
- Explain briefly the importance of the test in part (a) to the test in part (b).