- A random sample of 8 students is selected from a school database.
Each student's reaction time is measured at the start of the school day and again at the end of the school day. The reaction times, in milliseconds, are recorded below.
| Student | A | \(B\) | C | D | \(E\) | \(F\) | G | \(H\) |
| Reaction time at the start of the school day | 10.8 | 7.2 | 8.7 | 6.8 | 9.4 | 10.9 | 11.1 | 7.6 |
| Reaction time at the end of the school day | 10 | 6.1 | 8.8 | 5.7 | 8.7 | 8.1 | 9.8 | 6.8 |
- State one assumption that needs to be made in order to carry out a paired \(t\)-test.
(1)
The random variable \(R\) is the reaction time at the start of the school day minus the reaction time at the end of the school day. The mean of \(R\) is \(\mu\).
John uses a paired \(t\)-test to test the hypotheses
$$\mathrm { H } _ { 0 } : \mu = m \quad \mathrm { H } _ { 1 } : \mu \neq m$$
Given that \(\mathrm { H } _ { 0 }\) is rejected at the 5\% level of significance but accepted at the 1\% level of significance, - find the ranges of possible values for \(m\).