Financial Risk Manager Part 1
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Justin Heinz, FRM, suspects that the earnings of the insurance industry are more divergent than those of the banking industry. In a bid to confirm his suspicion, Heinz collects data from a total of 31 insurance companies and establishes that the standard deviation of earnings across that industry is $4.8. Similarly, he collects data from 41 banks and establishes that the standard deviation of earnings across that industry is $4.3. Conduct a hypothesis test at the 5% level of significance to determine if the earnings of the insurance industry have a greater standard deviation than those of the banking industry.
Other
Community
NNikitesh
A
I
B
II
C
III
D
IV
Explanation:
Explanation:
This is an F-test for comparing two variances. The correct approach is:
-
Hypothesis formulation: Since we suspect the insurance industry earnings are MORE divergent (greater variance) than banking, we test:
- H₀: σ₁² ≤ σ₂² (insurance variance ≤ banking variance)
- H₁: σ₁² > σ₂² (insurance variance > banking variance) This is a right-tailed test.
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Test statistic calculation:
- s₁ = 4.8 (insurance standard deviation)
- s₂ = 4.3 (banking standard deviation)
- n₁ = 31 (insurance sample size)
- n₂ = 41 (banking sample size)
F-statistic = s₁² / s₂² = (4.8²) / (4.3²) = (23.04) / (18.49) = 1.2461
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Critical value and decision:
- Degrees of freedom: numerator df = n₁ - 1 = 30, denominator df = n₂ - 1 = 40
- At 5% significance level (α = 0.05), the critical F-value for F(30,40) is approximately 1.74
- Since calculated F (1.2461) < critical F (1.74), we fail to reject H₀
- Conclusion: Earnings are statistically not significantly different from one another
Matching with options:
- Option I has correct hypothesis (H₀: σ₁² ≤ σ₂² and H₁: σ₁² > σ₂²), correct test statistic (1.2461), and correct decision (not significant)
- Option II has correct hypothesis but wrong test statistic (1.74)
- Option III has wrong hypothesis (H₁: σ₁² ≤ σ₂²) and wrong decision
- Option IV has wrong hypothesis (H₁: σ₁² < σ₂²) and wrong test statistic
Therefore, Option I is correct.
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