A clinical trial evaluates a new compound designed to improv

A clinical trial evaluates a new compound designed to improve wound healing in trauma patients. The new compound is compared against a placebo. After treatment for 5 days with the new compound or placebo, the extent of wound healing is measured and the data is shown in the table below. Is there a difference in the extent of wound healing by treatment. Run the appropriate test at a 5% level of significance.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   <=   0  
Ha:   u1 - u2   >   0  
At level of significance =    0.05          
As we can see, this is a    right   tailed test.      
Calculating the means of each group,              
              
X1 =    31.25          
X2 =    31.25          
              
Calculating the standard deviations of each group,              
              
s1 =    11.44188213          
s2 =    14.95270321          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    4          
n2 = sample size of group 2 =    4          
Thus, df = n1 + n2 - 2 =    6          
Also, sD =    9.414085192          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    0          
              
where uD = hypothesized difference =    0          
              
Now, the critical value for t is              
              
tcrit =    +   1.943180281      
              
Thus, comparing t and tcrit, we decide to   WE FAIL TO REJECT THE NULL HYPOTHESIS.          
              
Also, using p values,              
              
p =    0.5          
              
Comparing this to the significance level,    WE FAIL TO REJECT THE NULL HYPOTHESIS.          

Thus, we have no significant evidence at 0.05 level that there is a greater wound healing in the new compound than in the placebo. [conclusion]