Question 1 - A-Level Maths

In a trial for a new cough medicine, a random sample of 8 healthy patients were given steadily increasing doses of a pepper extract until they started coughing. The level of pepper that triggered the coughing was recorded. Each patient completed the trial after taking a standard cough medicine and, at a later time, after taking the new medicine. The results are given in the table below.

	Level of pepper extract that triggers coughing
Patient	\(A\)	\(B\)	\(C\)	\(D\)	\(E\)	\(F\)	\(G\)	\(H\)
Standard medicine	46	12	18	31	23	16	27	9
New medicine	53	16	13	49	11	34	38	22

Using a suitable test, at the \(5 \%\) level of significance, state whether or not, on the basis of this trial, you would recommend using the new medicine. State your hypotheses clearly.
State an assumption needed to carry out this test.