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Answer: (1.9%, 3.7%)
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
Author: Nikitesh Somanthe
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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.
A
(1.9%, 2.8%)
B
(1.4%, 3.1%)
C
(1.9%, 3.5%)
D
(1.9%, 3.7%)
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