Financial Risk Manager Part 1
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An organization estimates that the effect of increasing the number of qualified Financial Risk Managers hired by 1 will improve the stock's annual return by 2.8% with a standard error of 0.52%. Construct a 90% 2-sided confidence interval for the size of the slope coefficient, assuming the stock's returns are normally distributed.
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NNikitesh
A
(1.9%, 2.8%)
B
(1.4%, 3.1%)
C
(1.9%, 3.5%)
D
(1.9%, 3.7%)
Explanation:
The 90% confidence interval for the slope coefficient is calculated using the formula: β₁ ± Z_{α/2} * se(β₁).
Calculation:
- β₁ (slope coefficient) = 2.8%
- se(β₁) (standard error) = 0.52%
- For a 90% 2-sided confidence interval, α = 0.10, so α/2 = 0.05
- Z_{0.05} = 1.645 (critical value from standard normal distribution)
Margin of error: 1.645 × 0.52% = 0.8554%
Confidence interval: 2.8% ± 0.8554% = (1.9446%, 3.6554%)
Rounding: (1.9%, 3.7%) which matches option D.
Why other options are incorrect:
- A (1.9%, 2.8%): Too narrow, doesn't account for the full margin of error
- B (1.4%, 3.1%): Incorrect margin of error calculation
- C (1.9%, 3.5%): Slightly too narrow, likely from using a different critical value or rounding error
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