The average monthly return of a bond portfolio is 1% with a standard deviation of 4%. On the other hand the average monthly return of a stock portfolio is 2% with standard deviation of 6%. Each portfolio is measured on a period of 24 months. Test if the variance of the stock portfolio is higher at 5% significance level.
Data:
n1 = 24
n2 = 24
s1^2 = 6^2 = 36
s2^2 = 4^2 = 16
Hypotheses:
Ho: σ1^2 = σ2^2
Ha: σ1^2 > σ2^2
Decision Rule:
α = 0.05
Numerator DOF = 24 - 1 = 23
Denominator DOF = 24 - 1 = 23
Critical F- score = 2.014425
Reject Ho if F > 2.014425
Test Statistic:
F = s1^2 / s2^2 = 36/16 = 2.25
p- value = 0.028823
Decision (in terms of the hypotheses):
Since 2.25 > 2.0144 we reject Ho and accept Ha
Conclusion (in terms of the problem):
There is sufficient evidence that the variance of the stock portfolio is higher.
The average monthly return of a bond portfolio is 1% with a standard deviation of 4%. On the othe...
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