Sgt. Samuel H. Buckstein edited Results and Discussion.tex  about 10 years ago

Commit id: 3544a3210c4fbf924464fed76343a47f44906e72

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The null hypothesis claiming an even distribution in shooting time was therefore confirmed.   \subsubsection{10m to 20m}  An F-test was conducted and it was found that the P-value was greater than the alpha-significance level of 0.05, correlating with equal variances.  A paired t-test was conducted because the same of people participated at 10 and 20m, and the P-value was found to be greater than the significance level. The means are therefore unequal, shooting time was faster at 20m. The alternate hypothesis was therefore accepted over the null hypothesis.   \subsubsection{20m to 30m}  Using an F-test it was found that the P-value was greater than the significance level, therfore the variances within the two data sets were found to be the same.  Participants did not all fire at 20m and 30m, therefore a two-sample t-test was used instead of a paired t-test.  It was found that the P-value was greater than the significance level, therefore fail to reject the null hypothesis.  \subsubsection{10m to 30m}  An F-test was conducted and it was found that the P-value was greater than the alpha-significance level of 0.05, correlating with equal variances.  Participants did not all fire at 10m and 30m, so a two-sample t-test was used instead of a paired t-test.  It was found that the P-value was lower than the significance level. The mean at 10m was less than the mean at 30m, meaning that shooting time was faster at 10m. Therefore the null hypothesis was rejected in favor of the alternate hypothesis.   \subsection{Summary}  Two of the three comparisons made of shooting times at different distances resulted in a P-value less than the significance level, with the mean of the data from the closer range being less than the mean of the data at the further range.  The null hypothesis was therefore rejected, that shooting time does not change with distance, in favor of the alternate hypothesis, that shooting time is fastest the closer the shooter is to the target.