The following hypotheses are given A random sample of five o

The following hypotheses are given.

A random sample of five observations from the first population resulted in a standard
deviation of 12. A random sample of seven observations from the second population
showed a standard deviation of 7. At the .01 significance level, is there more variation in
the first population?

Solution

As we can see, this is a    right   tailed test.      
              
Thus, getting the critical chi^2, as alpha =    0.01   ,      
alpha =    0.01          
df1 = n1 - 1 =    4         
df2 = n2 - 1 =    6          
F (crit) =    9.14830103         
              
Getting the test statistic, as              
s1 =    12          
s2 =    7          
              
Thus, F = s1^2/s2^2 =    2.93877551          
              
As F < Fcrit, then we fail to reject the null hypothesis.

Thus, there is no significant evidence that there is more variation in the first population. [CONCLUSION]