- A medical student is investigating whether there is a difference in a person's blood pressure when sitting down and after standing up. She takes a random sample of 12 people and measures their blood pressure, in mmHg , when sitting down and after standing up.
The results are shown below.
| Person | A | \(B\) | C | D | \(E\) | F | \(G\) | \(H\) | I | \(J\) | \(K\) | \(L\) |
| Sitting down | 135 | 146 | 138 | 146 | 141 | 158 | 136 | 135 | 146 | 161 | 119 | 151 |
| Standing up | 131 | 147 | 132 | 140 | 138 | 160 | 127 | 136 | 142 | 154 | 130 | 144 |
The student decides to carry out a paired \(t\)-test to investigate whether, on average, the blood pressure of a person when sitting down is more than their blood pressure after standing up.
- State clearly the hypotheses that should be used and any necessary assumption that needs to be made.
- Carry out the test at the \(1 \%\) level of significance.
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