Financial Risk Manager Part 1

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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.
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
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.

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.
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
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.

Comments (1)

Y YMar 19, 2026 3:50 PM

empty here

LeetQuiz .Mar 22, 2026 5:30 AM

Dear User, Thanks for your pointing out. The question uploaded by the user is missing the hypothesis table. Now we supplement by manually review the original question uploaded by the user, at the same time, I added it in the comment section for your reference.

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.

Choice Hypothesis Test statistic Decision
I. H₀: σ₁² ≤ σ₂² <br> H₁: σ₁² > σ₂² 1.2461 Earnings are statistically not significant from one another
II. H₀: σ₁² ≤ σ₂² <br> H₁: σ₁² > σ₂² 1.74 Earnings are statistically not significant from one another
III. H₀: σ₁² ≤ σ₂² <br> H₁: σ₁² ≤ σ₂² 1.2461 Earnings are statistically significant from one another
IV. H₀: σ₁² ≤ σ₂² <br> H₁: σ₁² < σ₂² 1.74 Earnings are statistically not significant from one another

Choice	Hypothesis	Test statistic	Decision
I.	H₀: σ₁² ≤ σ₂² <br> H₁: σ₁² > σ₂²	1.2461	Earnings are statistically not significant from one another
II.	H₀: σ₁² ≤ σ₂² <br> H₁: σ₁² > σ₂²	1.74	Earnings are statistically not significant from one another
III.	H₀: σ₁² ≤ σ₂² <br> H₁: σ₁² ≤ σ₂²	1.2461	Earnings are statistically significant from one another
IV.	H₀: σ₁² ≤ σ₂² <br> H₁: σ₁² < σ₂²	1.74	Earnings are statistically not significant from one another

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Last updated: March 22, 2026 at 05:30