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 515 513 507 504 411 478 535 376 519 522 503 No Music 482 461 497 588 577 607 488 511 567 515 539 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	515	513	507	504	411	478	535	376	519	522	503
No Music	482	461	497	588	577	607	488	511	567	515	539

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

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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