6. A tree is cut down and sawn into pieces. Half of the pieces are stored outside and half of the pieces are stored inside. After a year, a random sample of pieces is taken from each location and the hardness is measured. The hardness \(x\) units are summarised in the following table.
| | \(\Sigma x\) | \(\Sigma x ^ { 2 }\) |
| Stored outside | 20 | 2340 | 274050 |
| Stored inside | 37 | 4884 | 645282 |
- Show that unbiased estimates for the variance of the values of hardness for wood stored outside and for the wood stored inside are 14.2 and 16.5 , to 1 decimal place, respectively.
(2)
The hardness of wood stored outside and the hardness of wood stored inside can be assumed to be normally distributed with equal variances. - Calculate \(95 \%\) confidence limits for the difference in mean hardness between the wood that was stored outside and the wood that was stored inside.
(8) - Using your answer to part (b), comment on the means of the hardness of wood stored outside and inside. Give a reason for your answer.
(2)
(Total 12 marks)