- A psychologist claims to have developed a technique to improve a person's memory.
A random sample of 8 people are each given the same list of words to memorise and recall.
Each person then receives memory training from the psychologist. After the training, each person is given the same list of new words to memorise and recall.
The table shows the percentage of words recalled by each person before and after the training.
| Person | A | \(B\) | C | \(D\) | E | \(F\) | G | \(H\) |
| Percentage of words recalled before training | 24 | 33 | 33 | 39 | 30 | 38 | 32 | 34 |
| Percentage of words recalled after training | 28 | 30 | 37 | 41 | 32 | 44 | 35 | 34 |
- State why a paired \(t\)-test is suitable for these data.
- State an assumption that needs to be made in order to carry out a paired \(t\)-test in this case.
- Test, at the \(5 \%\) level of significance, whether or not there is evidence of an increase in the percentage of words recalled after receiving the psychologist's training. State your hypotheses, test statistic and critical value used for this test.