In: Statistics and Probability
3) An experiment was performed where HEK 293 cells expressing TLR5 was treated with flagellin and the following absorbance readings were measured at 655 nm.
No treatment: 0.232, 0.247, 0.239
Flagellin treatment: 0.355, 0.377, 0.350
What is the P-value as calculated by T-test? Assume 2-tails and equal variance among the groups.
Ho :   µ1 - µ2 =   0  
           
   
Ha :   µ1-µ2 ╪   0  
           
   
          
           
   
  
Sample #1   ---->   1  
           
   
mean of sample 1,    x̅1=   0.239  
           
   
standard deviation of sample 1,   s1 =   
0.0075          
       
size of sample 1,    n1=   3  
           
   
          
           
   
Sample #2   ---->   2  
           
   
mean of sample 2,    x̅2=   0.361  
           
   
standard deviation of sample 2,   s2 =   
0.0144          
       
size of sample 2,    n2=   3  
           
   
          
           
   
difference in sample means =    x̅1-x̅2 =   
0.2393   -   0.4   =  
-0.121  
          
           
   
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 -
1)s2²]/(n1+n2-2)) =    0.0115  
           
   
std error , SE =    Sp*√(1/n1+1/n2) =   
0.0094          
       
          
           
   
t-statistic = ((x̅1-x̅2)-µd)/SE = (  
-0.1213   -   0   ) /   
0.01   =   -12.97
          
           
   
Degree of freedom, DF=   n1+n2-2 =   
4          
       
p-value =       
0.0002   (excel function: =T.DIST.2T(t stat,df)
)