Assume that you have a sample of n1 8 with the sample mean

Assume that you have a sample of n1 = 8, with the sample mean Xbar1 = 42, and a sample standard deviation S1 = 4, and you have an independent sample of n2 = 15 from another population, with a sample mean Xbar2 = 34, and a sample standard deviation S2= 5. What is the value of the pooled variance t-stat test statistic for testing H0: µ1 = µ2

Solution

  
Calculating the means of each group,              
              
X1 =    42          
X2 =    34          
              
Calculating the standard deviations of each group,              
              
s1 =    4          
s2 =    5          
              
Thus, the pooled standard deviation is given by              
              
S = sqrt[((n1 - 1)s1^2 + (n2 - 1)(s2^2))/(n1 + n2 - 2)]               
              
As n1 =    8   , n2 =    15  
              
Then              
              
S =    4.69041576          
              
Thus, the standard error of the difference is              
              
Sd = S sqrt (1/n1 + 1/n2) =    2.053452378          
              
As ud = the hypothesized difference between means =    0   , then      
              
t = [X1 - X2 - ud]/Sd =    3.895878028   [ANSWER]