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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(1.9%, 2.8%)

(1.4%, 3.1%)

(1.9%, 3.5%)

(1.9%, 3.7%)

Explanation:

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.

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