Find the two sample z test value comparing the mean of group

Find the two sample z test value comparing the mean of group A with that of group B (A-B). The values for group A are: 54, 34, 40, 46, 34, 60, 72, 38, 44, 52, 35. The values for group B are: 32, 44, 35, 43, 60, 52, 58, 51, 44, 47.

Answer choices are:

A. 0.634

B. 0.58

C. 1.801

D. -0.074

Solution

  
Calculating the means of each group,              
              
X1 =    46.27272727          
X2 =    46.6          
              
Calculating the standard deviations of each group,              
              
s1 =    12.1827001          
s2 =    9.02096324          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    11          
n2 = sample size of group 2 =    10          
Thus, df = n1 + n2 - 2 =    19          
Also, sD =    4.650842909          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    -0.074 [ANSWER, D]