A doctor believes that a four-week exercise programme can reduce the resting heart rate of her patients. She takes a random sample of 7 patients and records their resting heart rate before the exercise programme and again after the exercise programme.
Patient
\(A\)
\(B\)
C
\(D\)
\(E\)
\(F\)
\(G\)
Resting heart rate before
65
68
77
79
80
88
92
Resting heart rate after
63
65
73
76
80
84
80
Using a \(5 \%\) level of significance, carry out an appropriate test of the doctor's belief. You should state your hypotheses, test statistic and critical value.
State the assumption made about the resting heart rates that was required to carry out the test.