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Add comment on reduced chi square and choice of model
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danielunderwood committed Feb 8, 2016
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Expand Up @@ -62,7 +62,7 @@ \section{Discussion}

In future experiments, careful considerations of the differences between $\mu^{+}$ and $\mu^{-}$ should be made. The ratio of their lifetimes is given in \cite{PDG}, which is nearly unity. However, there are differences in the possible sources of error coming from the negative muon and positive muon, such as the capture mechanism mentioned previously only occurring with the negative variety \cite{Coan2005}.

Additional improvements may be made in future experiments by using a longer measurement interval and carefully examining the uncertainties contributed by the timing mechanism and subsequently using a fitting method that takes into account the errors on the independent variable in the fit. In this scenario, the bins can be made the width of the uncertainties in order for the bins to be able to both accurately bin the data and not contribute to further errors.
Additional improvements may be made in future experiments by using a longer measurement interval and carefully examining the uncertainties contributed by the timing mechanism and subsequently using a fitting method that takes into account the errors on the independent variable in the fit. In this scenario, the bins can be made the width of the uncertainties in order for the bins to be able to both accurately bin the data and not contribute to further errors. The fit model could also be considered, although the $\chi^2 / \nu$ value of $0.941$ seems to indicate a good fit by the model given in \cref{eqn: fit-model}.


\bibliography{muon-lifetime}
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