4 An insurance company is investigating a new system designed to reduce the average time taken to process claim forms. The company has decided to use 10 experienced employees to process claims using the old system and the new system. Two procedures for comparing the systems are proposed.
Procedure \(A\) There are two sets of claim forms, set 1 and set 2. Each contains the same number of forms. Each employee processes set 1 on the old system and set 2 on the new system. The times taken are compared. Procedure \(B\) There is just one set of claim forms which each employee processes firstly on the old system and then on the new system. The times taken are compared.

1. State one weakness of each of these procedures. In fact a third procedure which avoids these two weaknesses is adopted. In this procedure each employee is given a randomly selected set of claim forms. Each set contains the same number of forms. The employees each process their set of claim forms on both systems. The times taken, in minutes, are shown in the table.

   Employee	1	2	3	4	5	6	7	8	9	10
   Old system	40.5	42.9	52.8	51.7	77.2	66.7	65.2	49.2	55.6	58.3
   New system	39.2	40.7	50.6	50.7	71.4	70.5	71.1	47.7	52.1	55.5

2. Carry out a paired \(t\) test at the \(5 \%\) level of significance to investigate whether the mean length of time taken to process a set of forms has reduced using the new system.
3. State fully the usual conditions for a paired \(t\) test.
4. Construct a \(99 \%\) confidence interval for the mean reduction in time taken to process a set of forms using the new system.