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. You can assume that it is reasonable to regard these 11 tri athletes 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. Do the data provide convincing evidence that the mean time to exhaustion for experienced triathletes is greater when they run while listening to motivational music? Test the relevant hypotheses using a significance level of 0.05.

Time to exhaustion (in seconds) Motivational
Runner 1 2 3 4 5 6 7 8 9 10 11
Motivaltional Music 535 533 527 524 431 498 555 396 539 542 523
No Music 467 446 482 573 562 592 473 496 552 500 524