Formula used and other references to the textbook where appropriate. Working out

Question

Formula used and other references to the textbook where appropriate. Working out of the problem in step by step format.Final answer with correct units and phrased within the context of the problem -- that is, discuss what the final answer tells you in the context of the problem

1)A stockbroker at Critical Securities reported that the mean rate of return on a sample of 10 oil stocks was 12.6 percent with a standard deviation of 3.9 percent. The mean rate of return on a sample of 8 utility stocks was 10.9 percent with a standard deviation of 3.5 percent. At the .05 significance level, can we conclude that there is more variation in the oil stocks?

Explanation / Answer

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 F, as alpha =    0.05   ,      
alpha =    0.05          
df1 = n1 - 1 =    9         
df2 = n2 - 1 =    7          
F (crit) = 3.676674699            
              
Getting the test statistic, as              
s1 =    3.9          
s2 =    3.5          
              
Thus, F = s1^2/s2^2 =    1.241632653          
              
As F < 3.67667, then we fail to reject Ho.

There is no significant evidence that there is more variation in the oil stocks at 0.05 level. [CONCLUSION]

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