Therefore
\begin{equation*}
E_1 = \frac{8 \cdot 479.5}{456.24} \approx 419.3
\end{equation*}
and
\begin{equation*}
E_2 = \frac{8 \cdot 479.5}{345.55} \approx 553.7.
\end{equation*}
Hence, you are 95% certain that
\begin{equation*}
419.24 \lt \sigma^2 \lt 553.7.
\end{equation*}
By taking square roots you get
\begin{equation*}
20.48 \lt \sigma \lt 23.53
\end{equation*}
which is a relatively tight confidence interval. Notice, these are also completely contained in the confidence intervals from the previous small n example.