deletions | additions       diff --git a/We_expect_the_transmission_data__.tex b/We_expect_the_transmission_data__.tex  index 41ea8ba..b51a719 100644  --- a/We_expect_the_transmission_data__.tex  +++ b/We_expect_the_transmission_data__.tex 
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\end{equation}  where the offset is a polynomial fit in time up to order 2 and $\omega_{1},\cdots,\omega_{6}$ are the resonant frequency of the hyperfine peaks in the scan ordered by time.  Thus the transition frequency of the different peaks should theoretically be given by, $\omega_{1},\cdots,\omega_{6}$. The offset accounts for the background Gaussian distribution, which the Lorentzian functions are superimposed onto.  We used a $\tilde{\chi}_\nu^2$ test to determine if the proposed fit model (Equation~\ref{eq2}), is in good agreement with the data. From the four plots of transmission data and their corresponding fits shown in Figure~\ref{fig:HyperfineFits}, the values of $\tilde{\chi}_\nu^2$ ranged from $0.08$ to $0.17$. Since we expect that for a reasonable fit, $\tilde{\chi}_\nu^2\approx 1$ we reject the null hypothesis. In this specific case we do not believe that this indicates a disagreement between our proposed model and the data, since it qualitatively appears to be a good fit. Instead we believe $\tilde{\chi}_\nu^2\approx 1$ due to an error in the uncertainty calculations.  %The equation is given by,   %\begin{equation}\label{eq3}  %T(\omega)=\left( \frac{\Gamma}{2}\right )^{2}*\left( \frac{A_{1}}{(\omega-\omega_{1})^{2}+\frac{\Gamma}{2}^{2}} +\cdots+ \frac{A_{6}}{(\omega-\omega_{6})^{2}+\frac{\Gamma}{2}^{2}} \right)+\text{offset}