An investor is trying to decide between 2 mutual funds Mutua

An investor is trying to decide between 2 mutual funds. Mutual fund #1 offers a

slightly higher return than mutual fund #2 so the investor decides that he will invest

in mutual fund #1 unless the risk of mutual fund #1 is significantly higher than the

risk of mutual fund #2. Using the standard deviation of 101 daily returns as a measure

of risk of the two mutual funds, the investor finds that the standard deviation of

mutual fund #1’s daily returns is .95 and the standard deviation of mutual fund #2’s

daily returns is .81. At the 10% level of significance, should the investor invest in

mutual fund #1 or #2?

Solution

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 =    0.1   ,      
alpha =    0.1          
df1 = n1 - 1 =    100         
df2 = n2 - 1 =    100          
F (crit) =    1.293439013         
              
Getting the test statistic, as              
s1 =    0.95          
s2 =    0.81          
              
Thus, F = s1^2/s2^2 =    1.375552507          
              
              
As F > F(crit), we REJECT THE NULL HYPOTHESIS.

There is significant evidence that the risk at fund #1 is greater than that of fund 2. [CONCLUSION]