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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\% $5.8\%$  . Both sets of data we obtained (with a $1\textrm{k}\Omega$ resister resistor  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 resistor  is, may be higher. As we can see in equation \ref{eq:Equatoin}, with a higher $T$, we would have a lower $k_b$ value which is opposite to what our value is, so this is unlikely what is causing the error. The measured 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.