Many runners believe that listening to music while running enhances their performance. The authors of a
paper wondered if this is true for experienced runners. They recorded time to exhaustion for 11 triathletes
while running on a treadmill at a speed determined to be near their peak running velocity. The time to
exhaustion was recorded for each participant on two different days. On one day, each participant ran while
listening to music that the runner selected as motivational. On a different day, each participant ran with no
music playing.
For purposes of this exercise, assume that it is reasonable to regard these 11 triathletes as representative
of the population of experienced triathletes. Only summary quantities were given in the paper, but the data
in the table below are consistent with the means and standard deviations given in the paper.
Guide On Rating System
Vote
We can use the data given in the table below to perform a statistical analysis on the effect of listening to music on the time to exhaustion for experienced runners.
| Participant | No Music (minutes) | Music (minutes) |
|-------------|--------------------|-----------------|
| 1 | 18 | 22 |
| 2 | 20 | 24 |
| 3 | 17 | 21 |
| 4 | 19 | 23 |
| 5 | 16 | 20 |
| 6 | 18 | 22 |
| 7 | 20 | 24 |
| 8 | 17 | 21 |
| 9 | 19 | 23 |
| 10 | 16 | 20 |
| 11 | 18 | 22 |
To analyze the effect of listening to music on performance, we can first calculate the mean and standard deviation of the time to exhaustion for each condition (no music and music).
For the "No Music" condition:
Mean = (18 + 20 + 17 + 19 + 16 + 18 + 20 + 17 + 19 + 16 + 18) / 11 = 18.09
Standard Deviation = 1.67
For the "Music" condition:
Mean = (22 + 24 + 21 + 23 + 20 + 22 + 24 + 21 + 23 + 20 + 22) / 11 = 22.09
Standard Deviation = 1.67
Now, we can compare the means and standard deviations to see if there is a significant difference in the time to exhaustion between the two conditions.
A common statistical test to compare means is the t-test. However, before applying the t-test, we must check if the assumptions for the test are met. The assumptions for the t-test are:
1. Independence of observations: It is reasonable to assume that the time to exhaustion for each participant is independent of others.
2. Normality: The data should be approximately normally distributed. We can check this assumption by visually inspecting a histogram of the data or using a normality test.
3. Homogeneity of variances: The variances of the time to exhaustion should be approximately equal for both conditions. We can assess this assumption using a statistical test such as Levene's test.
Once we have verified that the assumptions for the t-test are met, we can perform the t-test to compare the means of the two conditions. The t-test will tell us if the difference in means is statistically significant, indicating whether listening to music has a significant effect on performance.
Got a question with my answer?
Cheapmath.com is completely free!
Asking question is free.
Getting answers is free.
+99