1 triathletes while running on a treadmill at a speed 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 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 (in seconds) Motivational music Runner 1 2 3 4 5 6 7 no 8 9 10 11 535 533 527 521 432 499 555 398 536 544 523 USE SALT No music 467 448 484 573 564 594 473 498 554 500 521
1 triathletes while running on a treadmill at a speed 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 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 (in seconds) Motivational music Runner 1 2 3 4 5 6 7 no 8 9 10 11 535 533 527 521 432 499 555 398 536 544 523 USE SALT No music 467 448 484 573 564 594 473 498 554 500 521
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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Question
Transcribed Image Text: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 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)
Motivational
music
Runner
1
2
онот на ко
Ha: d>
3
4
5
H₁: d=0
H₂H #0
6
7
8
9
10
11
Ho: d=0
Ha: Hd <0
535
Ho Hd O
H₂:μ <0
533
527
521
432
499
555
398
536
544
523
USE SALT
No music
467
448
484
573
564
594
473
498
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 μmusic - no music.)
State the appropriate null and alternative hypotheses.
ⒸH₁: Hd = 0
Ha: Md > 0
554
500
521
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 Ho. The data provide convincing evidence that the mean time to exhaustion for experienced triathletes is greater when they run while listening to motivational music.
O We fail to reject Ho. 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 Ho. 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 Ho. The data provide convincing evidence that the mean time to exhaustion for experienced triathletes is greater when they run while listening to motivational music.
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