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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 K}^{-1}$) is  approximately $5.8\%$ . Both sets of data we obtained (with a $1\textrm{k}\Omega$ 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 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.