As part of an investigation, a random sample of 10 people had their heart rate, in beats per minute, measured whilst standing up and whilst lying down. The results are summarised below.
Person
1
2
3
4
5
6
7
8
9
10
Heart rate lying down
66
70
59
65
72
66
62
69
56
68
Heart rate standing up
75
76
63
67
80
75
65
74
63
75
State one assumption that needs to be made in order to carry out a paired \(t\)-test.
Test, at the \(5 \%\) level of significance, whether or not there is any evidence that standing up increases people's mean heart rate by more than 5 beats per minute. State your hypotheses clearly.