In calculating 95 Percentage confidence interval forum1 um2

In calculating 95 Percentage confidence interval forum1 - um2; the difference between the means of two normally distributed populations, summary\' statistics from two independent samples are: m = 60,x = l80,s^21 n = 45 y = 160, and s^22 = 900. Then, the lower limit of the confidence interval is:

Solution

  
Calculating the means of each group,              
              
X1 =    180          
X2 =    160          
              
Calculating the standard deviations of each group,              
              
s1 =    18.97366596          
s2 =    30          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    60          
n2 = sample size of group 2 =    45          
Thus, df = n1 + n2 - 2 =    103          

Also, sD =    5.099019514          
              
      
              
For the   0.95   confidence level, then      
              
alpha/2 = (1 - confidence level)/2 =    0.025          
t(alpha/2) =    1.959963985          
              
lower bound = [X1 - X2] - t(alpha/2) * sD =    10.0061054   [OPTION C]