Question

1. Suppose a researcher is interested in the effectiveness of a new anti-hypertensive medication in a population of clinical trial participants with high blood pressure. In this particular study, the researchers decide to use each participant as their own control, offering the participants the study drug either preceding or proceeding a control period involving best standard of care. Assume the following sample of participants enrolled in the study represents an appropriate approximation to the normal distribution.

Participant	Systolic blood pressure (mmHG) Best Standard of Care	Systolic blood pressure (mmHG) With new drug treatment
A	154	122
B	143	123
C	161	119
D	138	117

1. What type of t-test would you use here?
2. Carry out an appropriate t test investigating the effectiveness of the medication on systolic blood pressure with 95% confidence (.05 level). Be sure to include each of the four steps of hypothesis testing.

Answer 1

a) paired t test

b)

sample size ,    n =    4          
Degree of freedom, DF=   n - 1 =    3   and α =    0.05  
t-critical value =    t α/2,df =    3.1824   [excel function: =t.inv.2t(α/2,df) ]      
                  
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    10.3722          
                  
std error , SE = Sd / √n =    10.3722   / √   4   =   5.1861
margin of error, E = t*SE =    3.1824   *   5.1861   =   16.5045
                  
mean of difference ,    D̅ =   28.750          
confidence interval is                   
Interval Lower Limit= D̅ - E =   28.750   -   16.5045   =   12.2455
Interval Upper Limit= D̅ + E =   28.750   +   16.5045   =   45.2545
                  
so, confidence interval is (   12.25   < µd <   45.25   )