Question

A medical researcher wants to begin a clinical trial that involves systolic blood pressure (SBP) and cadmium (Cd) levels. However, before starting the study, the researcher wants to confirm that higher SPB is associated with lower Cd levels. Below are the SBP and Cd measurements for a sample a participants. What can the researcher conclude with an α of 0.10?

SBP	Cd
169 183 115 113 182 126 179 127 148 160 140	55.5 55.7 55.8 55.9 55.5 55.7 55.6 55.9 55.8 55.7 55.8

a) What is the appropriate statistic?
---Select--- na Correlation Slope Chi-Square
Compute the statistic selected in a):

b) Obtain/compute the appropriate values to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
effect size =  ;   ---Select--- na trivial effect small effect medium effect large effect

d) Make an interpretation based on the results.

There was a significant positive relationship between systolic blood pressure and cadmium levels.There was a significant negative relationship between systolic blood pressure and cadmium levels.    There was no significant relationship between systolic blood pressure and cadmium levels.

Answer 1

	SBP (X)	Cd (Y)	X2	Y2	XY
	169	55.5	28561	3080.25	9379.5
	183	55.7	33489	3102.49	10193.1
	115	55.8	13225	3113.64	6417
	113	55.9	12769	3124.81	6316.7
	182	55.5	33124	3080.25	10101
	126	55.7	15876	3102.49	7018.2
	179	55.6	32041	3091.36	9952.4
	127	55.9	16129	3124.81	7099.3
	148	55.8	21904	3113.64	8258.4
	160	55.7	25600	3102.49	8912
	140	55.8	19600	3113.64	7812
Sum	1642	612.9	252318	34149.87	91459.6

n=	12
r	0.856304

=((B14*F13)-(B13*C13))/(((B14*D13)-B13^2)*((B14*E13)-C13^2))^0.5

a) Correlation is the appropriate statistic

b) H0: ρ = 0

H1: ρ ≠ 0 where ρ is the correlation coefficient

degrees of freedom = n-2 = 12-2 = 10

Test statistic = (0.856304*(12-2)^0.5) / (1-0.856304^2)^0.5 = 5.24

Critical value (from excel function) = TDIST(0.10,10,2) = 0.92

Since critical value < test statistic, we reject null hypothesis.

c) r=0.856

This means that x and y are positively correlated, so higher SPB are associated with higher cd levels.

The effect is large.

Effect size = Positive

Magnitude = 0.856 or 85.6%

d) Since null hypothesis was rejected in part (b), ρ ≠ 0 and r is positive, therefore, there was a significant positive relationship between systolic blood pressure and cadmium levels.