Error analysis
The discrepancy between our result (\(1.46 \cdot 10^{-23} \textrm{ m}^2 \textrm{ kg} \textrm{ s}^{-2} \textrm{ K}^{-1}\)) and the accepted Boltzmann constant (\(1.38 \cdot 10^{-23} \textrm{ m}^2 \textrm{ kg} \textrm{ s}^{-2} \textrm{ K}^{-1}\))is approximately 5.8% . Both sets of data we obtained (with a \(1\textrm{k}\Omega\) resister and a \(10\textrm{k}\Omega\)) gave a consistent value for the Boltzmann constant which is a matter of accuracy rather than precision, so this error is most likely a systematic error.
Assuming that our thermometer is accurate (for room temperature), the temperature within the instrument, where the resister is, may be higher. As we can see in Eq. \ref{eq:boltzmann}, with a higher \(\textrm{T(K)}\), we would have a lower \(\textrm{K}_\textrm{B}\) value which is opposite to what our value is, so this is unlikely what is causing the error.
The measured values(Table 6 in appendix) for Rin is about \(0.3\%\) different from the claimed value. Rin is also not the main source of error.
\(\Delta{f}\)? \(V^2\)?