deletions | additions       diff --git a/We_expect_the_transmission_data__.tex b/We_expect_the_transmission_data__.tex  index c2b0263..a0895c4 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.  \par 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\ll $\tilde{\chi}_\nu^2 \ll  1$ due to an error in the uncertainty calculations. Thus we believe that our error bars on the plot of $\frac{\delta t}{\delta \omega}$ versus ratio number should be much larger. Therefore it is likely that given larger error bars, the plots of $\frac{\delta t}{\delta \omega}$ should either fit a line with a slope equal to zero or some non zero slope, which would indicate that our frequency scan is non-linear.}