Question

The blood pressure measurements of a single patient were taken by twelve different medical students and the results are listed below. Answer parts ​a-c.

systolic​ (x)	138	132	141	119	123	120	127	129	125	143	142	138
diastolic​ (y)	92	91	99	84	88	82	83	84	82	96	104	97

a. Find the value of the linear correlation coefficient r.

b. Find the critical values of r from the table showing the critical values for the Pearson correlation coefficient using

alpha=0.05

c. Is there sufficient evidence to conclude that there is a linear correlation between the two​ variables?

Answer 1

Solution:

	X	Y	XY	X^2	Y^2
	138	92	12696	19044	8464
	132	91	12012	17424	8281
	141	99	13959	19881	9801
	119	84	9996	14161	7056
	123	88	10824	15129	7744
	120	82	9840	14400	6724
	127	83	10541	16129	6889
	129	84	10836	16641	7056
	125	82	10250	15625	6724
	143	96	13728	20449	9216
	142	104	14768	20164	10816
	138	97	13386	19044	9409
SUM	1577	1082	142836	208091	98180

Putting values , we get

r = 0.8878

b)

n = 12

df = n - 2 = 12 - 2 = 10

= 0.05

Using the critical value table for Pearson correlation coefficient, (two tailed )

Critical value are  0.576

c)

r = 0.8878

| r | = | 0.8878| = 0.8878

r >  0.576

reject H₀

significance correlation.

YES , there is sufficient evidence to conclude that there is a linear correlation between the two​ variables.