Test scores of two independent samples of students from UNCG

Test scores of two independent samples of students from UNCG and A&T; on a national examination are given below. At a 0.05 level of significance, from the researcher\'s perspective, test to determine if the variance in score for A&T; is greater than the variance in score for UNCG.

Solution

Let

group 1 = At&T
group 2 = UNCG

Formulating the null and alternative hypotheses,              
              
Ho:   sigma1^2 / sigma2^2   <=   1  
Ha:    sigma1^2 / sigma2^2   >   1  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical chi^2, as alpha =    0.05   ,      
alpha =    0.05          
df1 = n1 - 1 =    3         
df2 = n2 - 1 =    3          
F (crit) = 9.276628153
            
              
Getting the test statistic, as              
s1 =    12.90994449          
s2 =    10.61445555          
              
Thus, F = s1^2/s2^2 =    1.479289941          
              
As F < 9.277, then we FAIL TO REJECT Ho.

Thus, there is no significant evidence that the variance in score for AT&T is greater than the variance in score in UNCG. [conclusion]