Many runners believe that listening to music while running enhances their performance. The authors of a paper wondered if this was 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 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 (seconds) Runner 1 2 3 4 5 6 7 8 9 10 11 Motivational Music 530 528 522 519 426 493 550 391 534 537 518 No Music 462 441 477 568 557 587 468 491 547 495 519 In an earlier exercise, a hypothesis test leads to the conclusion that there is not convincing evidence that the mean time to exhaustion for experienced triathletes is greater when they run while listening to motivational music. Use the given information to construct a 95% confidence interval for the difference in mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music. (Use ?motivational music − ?no music. Round your answers to three decimal places.) ( _to __ )seconds

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Many runners believe that listening to music while running enhances their performance. The authors of a paper wondered if this was 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 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 (seconds)
Runner	1	2	3	4	5	6	7	8	9	10	11
Motivational Music	530	528	522	519	426	493	550	391	534	537	518
No Music	462	441	477	568	557	587	468	491	547	495	519

In an earlier exercise, a hypothesis test leads to the conclusion that there is not convincing evidence that the mean time to exhaustion for experienced triathletes is greater when they run while listening to motivational music.

Use the given information to construct a 95% confidence interval for the difference in mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music. (Use ?_{motivational music} − ?_{no music}. Round your answers to three decimal places.)

( _______to ________ )seconds

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