The standard error of the slope coefficient in a simple linear regression is given by $s_b = \frac{s_e}{\sqrt{\sum (x_i - \bar{x})^2}}$. If a researcher increases the spread of the independent variable $x$ (increasing $\sum (x_i - \bar{x})^2$) while maintaining the same sample size and residual standard error $s_e$, how does this affect the confidence interval for the slope?