Financial Risk Manager Part 1
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A random sample of 50 FRM exam candidates was found to have an average IQ of 125. The standard deviation among candidates is known (approximately 20). Assuming that IQs follow a normal distribution, carry out a statistical test (5% significance level) to determine whether the average IQ of FRM candidates is greater than 120. Compute the test statistic and give a conclusion.
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A
Test statistic: 1.768; Reject H₀
B
Test statistic: 2.828; Reject H₀
C
Test statistic: 1.768; Fail to reject H₀
D
Test statistic: 1.0606; Fail to reject H₀
Explanation:
Explanation
Hypothesis Formulation
- H₀: μ = 120 (null hypothesis - average IQ is 120)
- H₁: μ > 120 (alternative hypothesis - average IQ is greater than 120)
- This is a one-tailed test since we're testing for an increase only
Test Statistic Calculation
Given:
- Sample mean (x̄) = 125
- Population mean (μ) = 120
- Population standard deviation (σ) = 20
- Sample size (n) = 50
Test statistic formula:
Calculation:
Decision Making
Critical Value Approach:
- For 5% significance level (one-tailed), critical z-value = 1.6449
- Since 1.768 > 1.6449, we reject H₀
P-value Approach:
- P(Z > 1.768) = 1 - P(Z < 1.768) = 1 - 0.96147 = 0.03853 (3.853%)
- Since p-value (0.03853) < significance level (0.05), we reject H₀
Conclusion
There is sufficient statistical evidence at the 5% significance level to conclude that the average IQ of FRM candidates is greater than 120.
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