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: 44, 53, 54, 48, 88, 59, 68, 52, 54, 57. The values for group B are: 66, 61, 57, 61, 26, 72, 58, 52, 58, 63.

Answer Choices:

A. 1.668

B. 0.057

C. 0.541

D. 0.592

Solution

Calculating the means of each group,              
              
X1 =    57.7          
X2 =    57.4          
              
Calculating the standard deviations of each group,              
              
s1 =    12.42801495          
s2 =    12.29453356          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    10          
n2 = sample size of group 2 =    10          
Thus, df = n1 + n2 - 2 =    18          
Also, sD =    5.52821048          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    0.057   [ANSWER, B]