I'm inferring that you're not happy with the basic "look" because you would like the subscripts of \sigma
to be less far away, i.e, they should be snugged up to the left. If this is the concern, just write \sigma_{\!\beta_1}
, \sigma_{\!\beta_1}
, etc.
You may also want to settle on a standard size for the fraction terms. In your screenshot \frac
(or \dfrac
) appears to be employed for the left-hand material, whereas \tfrac
appears to be used for the material to the right of \Rightarrow
. I would choose one or the other look, but not mix 'em up in one and the same equation. Speaking for myself, I prefer \frac
look (with larger parentheses) to the \tfrac
look (with smaller parentheses).

\documentclass{article}
\usepackage{amsmath}
\begin{document}
%% look 1: \tfrac and \big parentheses
\begin{alignat*}{2}
\hat{\beta}_1 &\sim N\bigl(\beta_1,\tfrac{\sigma^2_{\!\epsilon}}{S_{xx}}\bigr) \sim N(\beta_1,\sigma^2_{\!\beta_1})
&&\Rightarrow \tfrac{\hat{\beta}_1-\beta_1}{\sigma^{}_{\!\beta_1}}
=\tfrac{\hat{\beta}_1-\beta_1}{\sigma^{}_{\!\epsilon}/\sqrt{S_{xx}}} \sim N(0,1)\\
\hat{\beta}_0 &\sim N\bigl(\beta_0,\sigma^2_{\!\epsilon} \bigl[\tfrac{1}{n}+\tfrac{\bar{X}^2}{S_{xx}}\bigr]\bigr)
\sim N(\beta_1,\sigma^2_{\!\beta_0})
&&\Rightarrow \tfrac{\hat{\beta}_0-\beta_0}{\sigma^{}_{\!\beta_1}}
=\tfrac{\hat{\beta}_0-\beta_0}{\sigma^{}_{\!\epsilon}
\sqrt{\frac{1}{n}+\frac{\bar{X}^2}{S_{xx}}}}
\sim N(0,1)
\end{alignat*}
%% look 2: \frac and \bigg parentheses
\begin{alignat*}{2}
\hat{\beta}_1 &\sim N\biggl(\beta_1,\frac{\sigma^2_{\!\epsilon}}{S_{xx}}\biggr) \sim N(\beta_1,\sigma^2_{\!\beta_1})
&&\Rightarrow \frac{\hat{\beta}_1-\beta_1}{\sigma^{}_{\!\beta_1}}
=\frac{\hat{\beta}_1-\beta_1}{\sigma^{}_{\!\epsilon}/\sqrt{S_{xx}}} \sim N(0,1)\\
\hat{\beta}_0 &\sim N\biggl(\beta_0,\sigma^2_{\!\epsilon} \biggl[\frac{1}{n}+\frac{\bar{X}^2}{S_{xx}}\biggr]\biggr)
\sim N(\beta_1,\sigma^2_{\!\beta_0})
&&\Rightarrow \frac{\hat{\beta}_0-\beta_0}{\sigma^{}_{\!\beta_1}}
=\frac{\hat{\beta}_0-\beta_0}{\sigma^{}_{\!\epsilon}
\sqrt{\frac{1}{n}+\frac{\bar{X}^2}{S_{xx}}}}
\sim N(0,1)
\end{alignat*}
\end{document}
\sigma^{}_{\beta_1}
for the third case and the similar ones.\hat{beta}_0
should be distributed normally about\beta_0
and not about\beta_1
, right?