deletions | additions       diff --git a/After_letting_our_data_run__.tex b/After_letting_our_data_run__.tex  index f5def88..7a8b79c 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. Error would result from the fact that some of the data points are not perfectly on the fit line. Also, we had to chose which points we removed that seemed false, we easily could have chosen wrong there. We ended up trying about 6 different histograms with different bin sizes and amount of points removed because they were incorrect, but Figure \ref{fig:Muon} shows the best histogram spread and a reduced $\chi$ squared closest to one. \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.