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	468
2	534	446
3	528	483
4	522	574
5	431	563
6	499	593
7	555	474
8	396	496
9	537	553
10	543	500
11	524	522

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 μ_d = μ_music − μ_{no music}.)

State the appropriate null and alternative hypotheses.

H₀: μ_d > 0

H_a: μ_d < 0

H₀: μ_d = 0

H_a: μ_d > 0

    

H₀: μ_d < 0

H_a: μ_d > 0

H₀: μ_d = 0

H_a: μ_d ≠ 0

H₀: μ_d = 0

H_a: μ_d < 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 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.

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 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 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

The statistical software output for this problem is:

Hence,

H₀: μ_d = 0

H_a: μ_d > 0

t = -0.3

P-value = 0.601

Conclusion: 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.

Option A is correct.