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Answer: (1.9%, 3.7%)
## Explanation For a 90% 2-sided confidence interval with normally distributed returns, we use the formula: $$\beta_1 \pm Z_{\frac{\alpha}{2}} \times \text{se}(\beta_1)$$ Where: - $\beta_1 = 2.8\%$ (estimated slope coefficient) - $\text{se}(\beta_1) = 0.52\%$ (standard error) - $\alpha = 0.10$ (for 90% confidence) - $Z_{0.05} = 1.645$ (critical value from standard normal distribution) Calculation: $$2.8\% \pm 1.645 \times 0.52\% = 2.8\% \pm 0.8554\%$$ Lower bound: $2.8\% - 0.8554\% = 1.9446\% \approx 1.9\%$ Upper bound: $2.8\% + 0.8554\% = 3.6554\% \approx 3.7\%$ Therefore, the 90% confidence interval is approximately **(1.9%, 3.7%)**, which matches option D.
Author: Tanishq Prabhu
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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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