A Student’s t-test with a 0.05 significance level was also conducted on the accuracy data at the three distances and established a difference in the mean of the distributions between the 10 m, 20 m and 30 m mark. The distribution mean was lowest for accuracy at 10 m.
The null hypothesis is therefore rejected in favor of the alternate hypothesis that shooting accuracy is best closest to the target.
By examining the results of the F-test and the paired t-test (as the same individuals shot in both trials), we can make several conclusions about the relationship between the variances and means for shooting accuracy at 10 m and 20 m. Using the F-test distribution, it was determined that the variances of the two samples are unequal, as p < 0.05 for this test. Furthermore, it was determined using the paired t-test that the mean accuracy of the two samples was not the same, as p < 0.05. The mean value of accuracy at 10 m and the mean value of accuracy at 20 m differed by 35.68 cm. From this information, we can initially reject the null hypothesis, as it is clear that accuracy decreases with distance.