The results of a mathematics placement exam at two different

The results of a mathematics placement exam at two different campuses of Mercy College follow:

Mercy wants to know if there is a difference in the average math placement score at the two campuses.  What is the computed value of the test statistic?

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   =   0  
Ha:   u1 - u2   =/   0  
At level of significance =    0.05          
As we can see, this is a    2   tailed test.      
Calculating the means of each group,              
              
X1 =    33          
X2 =    31          
              
Calculating the standard deviations of each group,              
              
s1 =    8          
s2 =    7          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    330          
n2 = sample size of group 2 =    310          
Thus, df = n1 + n2 - 2 =    638          
Also, sD =    0.593299174          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    3.37098059 = 3.4 [ANSWER, OPTION D]