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 needs to know if there is a relationship between SBP and Cd. Below are the SBP and Cd measurements for a sample a participants. What can the researcher conclude with α = 0.05?

SBP	Cd
169 161 115 113 182 126 179 127 148 160 140	55.9 55.7 55.7 55.5 55.9 55.8 55.8 55.5 55.7 55.8 55.6

a) What is the appropriate statistic?
---Select one--- (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 one--- (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 one--- (na, trivial effect, small effect, medium effect, large effect)  

d) Make an interpretation based on the results.

a. There was a significant positive relationship between systolic blood pressure and cadmium levels.

b. There was a significant negative relationship between systolic blood pressure and cadmium levels.

c. There was no significant relationship between systolic blood pressure and cadmium levels.

Answer 1

Let denotes the true correlation coefficient between SBP and Cd measurements.

To test whether higher SBP is associated with higher Cd levels, i.e. to test whether there is a positive correlation,

a) The appropriate statistic - Correlation

Here,

critical value = 1.833

The value of test statistic = -2.824

Effect size = r² = -.0.6854² = 0.4698

d) B.There was a significant negative relationship between systolic blood pressure and cadmium levels.