Some runners believe that listening to music while running enhances their performance. Some say mus hinders their performance. The authors of a paper wondered if this is true for experienced runners. The recorded time to exhaustion for these triathletes whi

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Scenario 3
Some runners believe that listening to music while
running enhances their performance. Some say music
hinders their performance. The authors of a paper
wondered if this is true for experienced runners. They
recorded time to exhaustion for these 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 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.
Transcribed Image Text:Scenario 3 Some runners believe that listening to music while running enhances their performance. Some say music hinders their performance. The authors of a paper wondered if this is true for experienced runners. They recorded time to exhaustion for these 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 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.
Scenario 3
Runner Music No Music
1
535
468
2
531
449
528
482
4
524
571
433
562
496
592
7
555
471
8
399
499
537
552
10
542
500
11
521
524
12
534
555
Do the data provide convincing evidence that the mean
time to exhaustion for experienced triathletes is
different when they run while listening to motivational
music? Test the relevant hypotheses using a
significance level of 0.1.
Suggestion: write out every step in the hypothesis
test.
3.
6.
Transcribed Image Text:Scenario 3 Runner Music No Music 1 535 468 2 531 449 528 482 4 524 571 433 562 496 592 7 555 471 8 399 499 537 552 10 542 500 11 521 524 12 534 555 Do the data provide convincing evidence that the mean time to exhaustion for experienced triathletes is different when they run while listening to motivational music? Test the relevant hypotheses using a significance level of 0.1. Suggestion: write out every step in the hypothesis test. 3. 6.
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