The study described in the previous exercise also measured time to exhaustion for the 11 triathletes on a day when they listened to music that the runners had classified as neutral as compared to motivational. 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 27 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 was s_d = 80. 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 ? = 0.05.

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