Question

In: Statistics and Probability

A medical researcher wants to begin a clinical trial that involves systolic blood pressure (SBP) and...

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.

Solutions

Expert Solution

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.


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