Fidelity Magellan is a large cap growth mutual fund and Fide

Fidelity Magellan is a large cap growth mutual fund and Fidelity Small Cap Stock is a small cap growth mutual fund (Morningstar Funds 500, 2006). The standard deviation for both funds was computed based on a sample of size 26. For Fidelity Magellan, the sample stan- dard deviation is 8.89%; for Fidelity Small Cap Stock, the sample standard deviation is 13.03%. Financial analysts often use the standard deviation as a measure of risk. Use = .05 as the level of significance.

What is the P-Value ?

Solution

Let

sigma1 = standard deviation of fidelity magellan
sigma2 = standard deviation of fidelity small cap

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    two   tailed test.      
              
Thus, getting the critical chi^2, as alpha =    0.05   ,      
alpha/2 =    0.025          
df1 = n1 - 1 =    25         
df2 = n2 - 1 =    25          
F (crit) =    0.448369753   and   2.230302095  
              
Getting the test statistic, as              
s1 =    8.89          
s2 =    13.03          
              
Thus, F = s1^2/s2^2 =    0.465494646          
              
As F is between the two critical values, we FAIL TO REJECT THE NULL HYPOTHESIS.              

Getting the P value,

P = 0.06141138 [ANSWER, TWO TAILED AREA]

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In case they needed a one tailed area, we divide this by 2,

P = 0.030705692 [and we reject the null hypothesis.]