To construct a 90% two-sided confidence interval for a normally distributed parameter, we use the formula: Confidence Interval = $\text{Estimate} \pm Z_{\alpha/2} \times \text{Standard Error}$

For a 90% confidence level, the significance level $\alpha$ is 10%, meaning $5%$is in each tail. The critical Z-value for a one-sided `$5`%$tail ($Z_{0.05}$) is approximately 1.645.

Given:

• Estimate (slope coefficient) = 0.3%
• Standard Error = 0.12%

Calculating the bounds:

• Lower Bound = $0.3% - 1.645 \times 0.12% = 0.3% - 0.1974% = 0.1026%$
• Upper Bound = $0.3% + 1.645 \times 0.12% = 0.3% + 0.1974% = 0.4974%$

Rounding the bounds to three decimal places yields (0.103%, 0.497%).