Question

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. Runner Time to exhaustion (in seconds) Motivational music No music 1 535 466 2 531 448 3 526 483 4 524 571 5 432 563 6 497 593 7 555 471 8 398 498 9 539 553 10 543 500 11 521 524 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 α = 0.05. (Use μd = μmusic − μno music.) State the appropriate null and alternative hypotheses. H0: μd = 0 Ha: μd > 0 H0: μd < 0 Ha: μd > 0 H0: μd > 0 Ha: μd < 0 H0: μd = 0 Ha: μd ≠ 0 H0: μd = 0 Ha: μd < 0 Find the test statistic and P-value. (Use a table or technology. Round your test statistic to one decimal place and your P-value to three decimal places.) t = P-value = State the conclusion in the problem context. We reject H0. 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. We fail to reject H0. The data provide convincing evidence that the mean time to exhaustion for experienced triathletes is greater when they run while listening to motivational music. We reject H0. The data provide convincing evidence that the mean time to exhaustion for experienced triathletes is greater when they run while listening to motivational music. We fail to reject H0. 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.

Answer 1