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\subsection{Analysis}  Error analysis for Johnson Noise  The discrepancy between our result ($1.46 \pm0.0054 \cdot 10^{-23}\textrm{ m}^2 \textrm{ kg} \textrm{ s}^{-2} \textrm{ K}^{-1}$ and $1.46 \pm0.0052 \cdot 10^{-23} \textrm{ m}^2 \textrm{ kg} \textrm{ s}^{-2} \textrm{ K}^{-1}$) 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}, equation \ref{eq:Equatoin},  with a higher $\textrm{T(K)}$, $T$,  we would have a lower $\textrm{K}_\textrm{B}$ $k_b$  value which is opposite to what our value is, so this is unlikely what is causing the error. The measured values(\textbf{Table 6 in appendix}) values(Table \ref{table:True_Resistance})  for Rin is about $0.3\%$ different from the claimed value. Rin is also not the main source of error. $\Delta{f}$? $V^2$? Unfortunately, we only took one error value for all of the Johnson data. We found that the average error for the $1 \Omega$ resistor was $0.003 \textrm{Volts}^2$. Because we did not take any other error data, it is impossible to find the total error in our measurements.