3 The management of a large chain of shops aims to reduce the level of absenteeism among its workforce by means of an incentive bonus scheme. In order to evaluate the effectiveness of the scheme, the management measures the percentage of working days lost before and after its introduction for each of a random sample of 11 shops. The results are shown below.
| Shop | A | B | C | D | E | F | G | H | I | J | K |
| \% days lost before | 3.5 | 5.0 | 3.5 | 3.2 | 4.5 | 4.9 | 4.1 | 6.0 | 6.8 | 8.1 | 6.0 |
| \% days lost after | 1.8 | 4.3 | 2.9 | 4.5 | 4.4 | 5.8 | 3.5 | 6.7 | 6.4 | 5.4 | 5.1 |
- The management decides to carry out a \(t\) test to investigate whether there has been a reduction in absenteeism.
- State clearly the hypotheses that should be used together with any necessary assumptions.
- Carry out the test using a \(5 \%\) significance level.
- Find a 95\% confidence interval for the true mean percentage of days lost after the introduction of the incentive scheme and state any assumption needed. The management has set a target that the mean percentage should be 3.5. Do you think this has been achieved? Explain your answer.