Many runners believe that that listening to m o 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 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 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. Time to exhaustion (in seconds) Runner 1 2 3 4 5 6 7 a 9 10 11 OH₂H₂O H₂H<0 OHO H₂Hg Motivational music 535 533 528 521 432 497 555 399 536 544 523 No music 468 449 484 573 564 504 472 499 554 500 LAUSE SALT 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. (Use #music #music) State the appropriate null and alternative hypotheses OH₂H₂O Mg: HO 521 OM₂H₂ = 0 H₂H₂O ⒸM₂ M₂ <0 H₂H0 find the test statistic, (Round your answer to two decimal places.) t= Use technology to find the P-value. (Round your answer to four decimal places.) P-value= State the conclusion in the problem context. O We fail to reject M. The data do not provide convincing evidence that the mean time to exhaustion for experienced triathletes is greater when they run while listening to motivational music. O We reject H. The data do not provide convincing evidence that the mean time to exhaustion for experienced triathletes is greater when they run while listening to motivational music. O We reject H The data provide convincing evidence that the mean time to exhaustion for experienced triathletes is greater when they run while listening to motivational music. Owe fail to reject H. The data provide convincing evidence that the mean time to exhaustion for experienced triathletes is greater when they run while listening to motivational music.