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 SBP is associated with higher Cd levels. Below are the SBP and Cd measurements for a sample a participants. What can the researcher conclude with an α of 0.01?

SBP	Cd
169 161 115 113 182 126 179 127 148 160 140	56.6 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--- na Correlation Slope Chi-Square
Compute the statistic selected above:

b) Compute the appropriate test statistic(s) 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

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 = 2.821

b) The value of test statistic = 1.945

Decision : Fail to reject H0

c) Effect size = r² = 0.5441² = 0.296, medium effect

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