4 A company has many factories. It is concerned about incidents of trespassing and, in the hope of reducing if not eliminating these, has embarked on a programme of installing new fencing.

1. Records for a random sample of 9 factories of the numbers of trespass incidents in typical weeks before and after installation of the new fencing are as follows.

   Factory	A	B	C	D	E	F	G	H	I
   Number before installation	8	12	6	4	14	22	4	13	14
   Number after installation	6	11	0	1	18	10	11	5	4

   Use a Wilcoxon test to examine at the \(5 \%\) level of significance whether it appears that, on the whole, the number of trespass incidents per week is lower after the installation of the new fencing than before.
2. Records are also available of the costs of damage from typical trespass incidents before and after the introduction of the new fencing for a random sample of 7 factories, as follows (in £).

   Factory	T	U	V	W	X	Y	Z
   Cost before installation	1215	95	546	467	2356	236	550
   Cost after installation	1268	110	578	480	2417	318	620

   Stating carefully the required distributional assumption, provide a two-sided \(99 \%\) confidence interval based on a \(t\) distribution for the population mean difference between costs of damage before and after installation of the new fencing. Explain why this confidence interval should not be based on the Normal distribution.