Question

3) Five different second-year medical students took blood pressure measurements of the same patient
and the results are listed below. The goal of this research project is to determine if the diastolic BP and
patients systolic BP are correlated. The following data are for five BP readings.

Systolic Diastolic
138 84
135 88
122 81
130 86
140 91

a. Provide a scatterplot of the data below. Label and put numbers along the axes.
b. Calculate and interpret the sample correlation coefficient. Show all handwritten steps.
c. Test at the 10% significance level where there is a true positive correlation between diastolic BP
and patients systolic BP. Show all handwritten steps.

Answer 1

b) Correlation coefficient with step

N =    Number of Pair	=	5
	Systolic(Xi)	Diastolic(Yi)	Xi*Xi	Yi*Yi	Xi*Yi
	138	84	19044	7056	11592
	135	88	18225	7744	11880
	122	81	14884	6561	9882
	130	86	16900	7396	11180
	140	91	19600	8281	12740
Total	665	430	88653	37038	57274

Mean   =	X̄or X-bar =	Σ x	=	665	=	133.000
N	5
Mean   =	Yor Y-bar =	Σ Y	=	430	=	86.000
N	5

Variance of X =	σx^2   =	Σ x*x	- (X-bar)^2	=	88653	- 133*133	=	41.60
N	5
Variance of X =	41.6

Variance of Y   =	σy^2   =	Σ y*y	- (Y-bar)^2	=	37038	- 86*86	=	11.60
N	5
Variance of Y =	11.6

Correlation Coeffiicient (r)	=	n*(Σ Xi*Yi)    - (Σ Xi) *(Σ Yi)
	=	5*57274 - 665*430
	SQRT(5*88653 - 665*665)	* SQRT(5*37038 - 430*430)
	=	0.76477489

Correlation Coeffiicient (r)	=	0.764774893
There is positive correlation between variable as correlation is > 0

c) to do correlation test