S4 June 2007 Q1

EdexcelOld spec9 marksIncludes hypothesis testingt-Tests & Further Tests

1. A medical student is investigating two methods of taking a person’s blood pressure. He takes a random sample of 10 people and measures their blood pressure using an arm cuff and a finger monitor. The table below shows the blood pressure for each person, measured by each method.

Person	A	B	C	D	E	F	G	H	I	J
Arm cuff	140	110	138	127	142	112	122	128	132	160
Finger monitor	154	112	156	152	142	104	126	132	144	180

(a) Use a paired \(t\)-test to determine, at the 10% level of significance, whether or not there is a difference in the mean blood pressure measured using the two methods. State your hypotheses clearly. (8)

(b) State an assumption about the underlying distribution of measured blood pressure required for this test. (1)

Mark scheme (a)

Scheme	Marks
\(d:\ 14\ \ 2\ \ 18\ \ 25\ \ 0\ \ -8\ \ 4\ \ 4\ \ 12\ \ 20\)	M1
\(\bar{d} = \pm 9.1 \qquad s_d = \sqrt{106.7} = 10.332..\) \(\left(\sum d = 91, \quad \sum x^2 = 1789\right)\)	A1 A1
\(\mathrm{H}_0 : \mu_d = 0 \qquad \mathrm{H}_1 : \mu_d \neq 0\)	B1
\(t = \pm\dfrac{9.1\sqrt{10}}{10.332} = \pm 2.785\) awrt \(\pm 2.78\) or 2.79	M1 A1
Critical value \(t_9 = \pm 1.833\)	B1
Significant. There is a difference between blood pressure measured by arm cuff and finger monitor.	A1
	(8)

Notes

One tail test loses the first B1. CV is 1.383 in this case. Can get 7/8