Download A stockbroker at critical securities reported that the

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 with a standard deviation of 3.5 percent .
At .05 significance level can we conclude that there is more variation in the oil stocks?
Let  12 and  22 be the variances of the return of oil and utility stocks respectively.
Here we want to test the null hypothesis H0:  12 =  22 against the alternative hypothesis
H1:  12 >  22 .
Let s1 and s2 be the sample standard deviation of the return of oil and utility stocks
respectively.
The test statistic for testing H0 is
F
s12
s22
F( n1 1,n2 1) , the F distribution with (n1  1, n2  1) degrees of freedom.
From the given data,
n1 = 10, n2 = 8, s1 = 3.9, s2 = 3.5
Thus the calculated value of F 
3.92
= 1.2416
3.52
Since the significance level is 0.05, using the F distribution with (n2  1, n1  1) = (9, 7)
degrees of freedom, we get the critical value = 3.667
Thus the critical region of the test is F > 3.667
That is we reject the null hypothesis if F > 3.667.
Here, F = 1.2416 < 3.667
So we fail to reject the null hypothesis Ho. Thus at .05 significance level we cannot
conclude that there is more variation in the oil stocks
P-value approach
Using the F distribution with (n2  1, n1  1) = (9, 7) degrees of freedom, we get the P-value
as
P-value = P[ F > 1.2416] = 0. 3964
Since the level of significance  = 0.05, we reject the null hypothesis H 0 if
the P-value < 0.05.
Here the P-value = 0. 3964 > 0.05
So we do not reject the null hypothesis Ho. Thus at .05 significance level we cannot
conclude that there is more variation in the oil stocks