- A random sample of 8 people were given a new drug designed to help people sleep.
In a two-week period the drug was given for one week and a placebo (a tablet that contained no drug) was given for one week.
In the first week 4 people, selected at random, were given the drug and the other 4 people were given the placebo. Those who were given the drug in the first week were given the placebo in the second week. Those who were given the placebo in the first week were given the drug in the second week.
The mean numbers of hours of sleep per night for each of the people are shown in the table.
| Person | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) |
| Hours of sleep with drug | 10.8 | 7.2 | 8.7 | 6.8 | 9.4 | 10.9 | 11.1 | 7.6 |
| Hours of sleep with placebo | 10.0 | 6.5 | 9.0 | 5.6 | 8.7 | 8.0 | 9.8 | 6.8 |
- State one assumption that needs to be made in order to carry out a paired \(t\)-test.
- Stating your hypotheses clearly, test, at the \(1 \%\) level of significance, whether or not the drug increases the mean number of hours of sleep per night by more than 10 minutes. State the critical value for this test.