The Effects of Travel Time on Performance
Throughout the winter and spring months, Cross Country coaches spend a majority of their time selecting meets for their athletes to compete in. There are many factors that contribute to choosing the perfect meet. A few of these factors include the terrain of the course and competitiveness of the competition, which includes both the caliber of the athletes and the number of participants. One unknown factor is if the distance traveled to a meet could affect the times that the athletes run. To further understand if there is any correlation between the distances traveled and times ran, two concepts were explored. First, if the team travels farther to a meet, then will the athletes perform better. Second, …show more content…
The sample data from the athletes in the MIAA showed a correlation of -0.026, meaning there is no correlation between the two variables. The statistical tests used were both a bootstrap test and a randomization hypothesis test for a correlation.
Figure 1. Scatter plot and summary statistics from the sample data. This display has the time in seconds on the X-axis and the distance in miles on the Y-axis.
Then, to examine if the distance traveled has any impact on the speed of the athlete, a randomization hypothesis test was completed. The hypothesis states if a team travels farther to a meet, they will run faster. Allowing, ρ to be the population correlation between distance traveled and times ran, the hypotheses are, Ho :ρ =0 verses Ha:ρ > 0 . The p-value, the probability of observing the same results or more extreme results, was then computed. The p-value for this data was p= 0.614 compared to the standard significance level of 0.05showing we cannot reject the null hypothesis (Figure 3). In other words, if we were to see this population again, if the two samples were the same is 61.4%. This suggests that there is no significant evidence showing that a longer drive will lead to a better …show more content…
Randomization hypothesis test comparing the distance traveled to a meet and the times ran by the athletes.
A bootstrap confidence interval was constructed to find the 95% confidence level between distances traveled and times ran (Figure 3). With the information gathered from the bootstrap sample, we are 95% confident that the true correlation will fall between -0.170 and 0.127. Given these conditions, the correlation of zero could fall within the confidence interval. This means there could be little to no correlation between distanced traveled to a meet and the times ran.
Figure 3. A bootstrap dot plot of the correlation coefficients between distances traveled to a meet and times
Throughout the winter and spring months, Cross Country coaches spend a majority of their time selecting meets for their athletes to compete in. There are many factors that contribute to choosing the perfect meet. A few of these factors include the terrain of the course and competitiveness of the competition, which includes both the caliber of the athletes and the number of participants. One unknown factor is if the distance traveled to a meet could affect the times that the athletes run. To further understand if there is any correlation between the distances traveled and times ran, two concepts were explored. First, if the team travels farther to a meet, then will the athletes perform better. Second, …show more content…
The sample data from the athletes in the MIAA showed a correlation of -0.026, meaning there is no correlation between the two variables. The statistical tests used were both a bootstrap test and a randomization hypothesis test for a correlation.
Figure 1. Scatter plot and summary statistics from the sample data. This display has the time in seconds on the X-axis and the distance in miles on the Y-axis.
Then, to examine if the distance traveled has any impact on the speed of the athlete, a randomization hypothesis test was completed. The hypothesis states if a team travels farther to a meet, they will run faster. Allowing, ρ to be the population correlation between distance traveled and times ran, the hypotheses are, Ho :ρ =0 verses Ha:ρ > 0 . The p-value, the probability of observing the same results or more extreme results, was then computed. The p-value for this data was p= 0.614 compared to the standard significance level of 0.05showing we cannot reject the null hypothesis (Figure 3). In other words, if we were to see this population again, if the two samples were the same is 61.4%. This suggests that there is no significant evidence showing that a longer drive will lead to a better …show more content…
Randomization hypothesis test comparing the distance traveled to a meet and the times ran by the athletes.
A bootstrap confidence interval was constructed to find the 95% confidence level between distances traveled and times ran (Figure 3). With the information gathered from the bootstrap sample, we are 95% confident that the true correlation will fall between -0.170 and 0.127. Given these conditions, the correlation of zero could fall within the confidence interval. This means there could be little to no correlation between distanced traveled to a meet and the times ran.
Figure 3. A bootstrap dot plot of the correlation coefficients between distances traveled to a meet and times