Question

I have two devices to check my blood pressure; one checks it at the wrist, and the other just above the elbow. I want to see if there is any difference in the two machines, so I check my blood pressure with both devices at the same time one morning. On the next five mornings, i repeat this check with both machines. The following table show the systolic reading at the elbow and wrist for these six days:

elbow	134	126	132	133	129	128
wrist	131	121	128	130	132	123

A) write symbolically the null and alternative hypotheses that would be used for this test.

b) if you are given an alpha level of significance of 0.05, specify an appropriate rejection region.
(hint: treat the above readings as "paired data")

c)calculate the value of the appropriate test statistic for this data.
(show the setup of the formula used in your calculation)

d) based upon the above calculations, would your decision be to reject the null hypothesis, or to fail to reject the null?

e) using significance level of 0.05, interpret your decision by circling the appropriate part of each of the bold phrases below

sample data does/does not provide "significant" evidence that the readings of these two devices are different/the same

f) verbalise what it would mean to make a type I error

g) if we had treated the readings from the two machines as independent of eachother, then calculate the value of the appropriate test statistic for this data. (show the setup of the formula used in your calculation)

Answer 1

Ans:

Let d=elbow -wrist

a)

b)df=6-1=5

critical value=tinv(0.05,5)=+/-2.571

Rejection region:

t<-2.571 or t>2.571

	1	2	3	4	5	6
elbow	134	126	132	133	129	128
wrist	131	121	128	130	132	123
d	3	5	4	3	-3	5
d-bar=	2.833
sd=	2.994

c)

Test statistic:

t=(2.833-0)/(2.994/sqrt(6))

t=2.318

d)Fail to reject the null hypothesis.

sample data does not provide "significant" evidence that the readings of these two devices are different.

f)when we conclude that means are different,but in fact,are same.