deletions | additions       diff --git a/After_letting_our_data_run__.tex b/After_letting_our_data_run__.tex  index 07a9cf6..21e73b6 100644  --- a/After_letting_our_data_run__.tex  +++ b/After_letting_our_data_run__.tex 
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where $N$ is the number of points. Only 23 points were included in Figure ~\ref{fig:Muon} because some of the data at high time measurements had an extremely large uncertainty, and was thus removed. Therefore in order to find $N$ for Equation 4, we subtracted the number of data points, 23,from the number of fit parameters, 3, which gives us $N=20$.   The amount of data points we chose produced a good fit because $\tilde\chi^2$ is close to 1, more precisely it is $0.6211$. Since the value of $\tilde\chi^2$ is not $\ll 1$ nor is it $\tilde\chi^2>2$, we do not have to reject the null hypothesis, and thus can assume our fit is reasonable. 6 different histograms with different bin sizes were plotted before we decided on the parameters used in Figure ~\ref{fig:muon}, ~\ref{fig:Muon},  which had a $\tilde\chi^2$ value closest to 1. \par The final value was found to be $2.04\pm0.04 \mu\textrm{seconds}$, which is within the expected value for the lifetime of a muon, $2\mu\textrm{seconds}$, but not within the value for the lifetime of an antimuon, $2.197\mu\textrm{seconds}$. However, it is not particularly important that the calculated value does not match the lifetime for an antimuon, since we are most concerned with the lifetime of a muon. The discrepancy could also be explained by arguing that there were significantly more muon decays detected than antimuon decays detected, thus weighting the average. In addition, some experimental uncertainty is expected, since energy parameters were set for muon detection. Though this was done in order to eliminate events that were not assumed to be associated with muon decay, it is entirely possible that some muons escaped detection due to the applied parameters.