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Madeline Horn edited subsection_Analysis_After_letting_our__.tex
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\subsection{Analysis}
After letting our data run for about 14 (as seen from Table \ref{table:Final_values}) days, we needed to analyze all of the data points. Figue \ref{fig:Muon} shows a histogram of the real
time. The real time
(the is the actual time the data was being collected because there was a small amount of time needed to process the
data). data, whereas the actually time is how much time has passed since starting the experiment. As you can see, the histogram is similar to an
exponential, and that is the fit exponential curve, so we
chose. chose to fit an exponential. Our bin size was
30. 30 for the histogram was 30, so there are 30 points on Figure \ref{fig:Muon}. I chose 30 bins because I wanted to get the lowest $\chi$ squared and 30 bins seemed to create a very good histogram and fit. In order to fit the data, we had to chose the best
data. data from the experiment and eliminate the data points that seem false. We needed to remove data that was incorrect because
he the scintillator occasionally detects a "false" muon decay (as stated above in the Introduction). Sometimes the scintillator is set off by other cosmic particles, so we sift the data to delete what appears as false data. After fitting an exponential, we needed to find the Rediuced $\chi$ squared. To do this, we needed to use the following formula,
\begin{equation}\label{eq:reducedchi}
\textrm{Reduced } \chi \textrm{ Squared} = \chi / N
\end{equation}
where $N$ is the number of points. There are 23 points on the
follow graph, following graph (we removed 7 points because they were false data), but
in order to find N for Equation you need to take into account that there are two fit parameters that need to be subtracted and one number that needs to be removed because of the exponential fit. Therefore, the $N$ used was $23 - 3 = 20$.
The amount of data points we chose produced a good fit because our $\chi$ squared is close to 1, it is $0.6211$. Error would result from the fact that some of the data points are not perfectly on the fit line.