A sociologist claims that marriage lowers the cumulative ave

A sociologist claims that marriage lowers the cumulative average of graduate students. If the cumulative average of 16 randomly selected married graduate students was 3.35 with a standard deviation of 0.3 and the cumulative average of 9 unmarried graduate students was 3.56 with a standard deviation of 0.5, do you agree with the sociologist’s claim at = 1%?

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   >=   0  
Ha:   u1 - u2   <   0  
At level of significance =    0.01          
As we can see, this is a    left   tailed test.      
Calculating the means of each group,              
              
X1 =    3.35          
X2 =    3.56          
              
Calculating the standard deviations of each group,              
              
s1 =    0.3          
s2 =    0.5          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    16          
n2 = sample size of group 2 =    9          
Thus, df = n1 + n2 - 2 =    23          
Also, sD =    0.182764268          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    -1.149021097          
              
where uD = hypothesized difference =    0          
              
Now, the critical value for t is              
              
tcrit =    -   2.499866739      
              
As |t| < 2.4999,   WE FAIL TO REJECT THE NULL HYPOTHESIS.          
              
Thus, we do not agree with the sociologist\'s claim: there is no significant evidence that marriage lowers the cumulative average of graduate students. [CONCLUSION]