A study was done on comparing the average earnings for colle

A study was done on comparing the average earnings for college graduates from Iowa compared to the average earnings of college graduates from Illinois. Based on the results below, can it be concluded that there is a difference in the mean earnings for Iowa and Illinois graduates at a .05 level of significance?

Iowa

Illinois

Sample Mean

$42187

$48792

Population Standard Deviation

$7913

$9812

Sample Size

40

40

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    two   tailed test.      
Calculating the means of each group,              
              
X1 =    42187          
X2 =    48792          
              
Calculating the standard deviations of each group,              
              
s1 =    7913          
s2 =    9812          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    40          
n2 = sample size of group 2 =    40          

Also, sD =    1993.056152          
              
Thus, the z statistic will be              
              
z = [X1 - X2 - uD]/sD =    -3.314005977          
              
where uD = hypothesized difference =    0          
              
Now, the critical value for z is              
              
zcrit =    +/-   1.96      
              
As |z| > 1.96,   WE REJECT THE NULL HYPOTHESIS.      

Thus, there is a significant difference in the mean earnings for Iowa and Illinois graduates at a .05 level of significance. [CONCLUSION]