Many runners believe that listening to music while running enhances their performance. The authors of a paper wondered if this was 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 wile listening to music that the runners had classified as neutral as compared to motivational. You can assume that it is reasonable to regard these 11 triathletes as representative of the population of experienced triathletes. The researchers calculated the difference between the time to exhaustion while running to motivational music and while running to neutral music. The mean difference in (motivational – neutral) was -8 seconds (the sample mean time to exhaustion was actually lower when listening to music the runner viewed as motivational than when listening to music the runner viewed as neutral). Suppose that the standard deviation of the differences wass, = 75. You can assume that it is reasonable to regard these 11 triathletes as representative of the population of experienced triathletes and that the population difference distribution is approximately normal. Is there convincing evidence that the mean time to exhaustion for experienced triathletes running to motivational music differs from the mean time to exhaustion when running to neutral music? Carry out a hypothesis test using a = 0.05. (Use umotivational - Hneutral:) n USE SALT Find the test statistic. (Round your answer to two decimal places.) t = Find the df. df = Use technology to find the P-value. (Round your answer to four decimal places.) P-value = State your conclusion. O Fail to reject Ho. We have convincing evidence that the mean time to exhaustion for experienced triathletes running to motivational music differs from the mean time to exhaustion when running to neutral music. O Fail to reject H. We do not have convincing evidence that the mean time to exhaustion for experienced triathletes running to motivational music differs from the mean time to exhaustion when running to neutral music.