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 520 518 512 509 416 483 540 381 524 527 508 No Music 452 431 467 558 547 577 458 481 537 485 509 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 Interpret the interval. We are 95% confident that the difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music is not in the interval. Because zero is not included in the interval we conclude there is likely a difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music.We are 95% confident that the difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music is in the interval. Because zero is included in the interval there may be no difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music. We are 95% confident that the difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music is not in the interval. Because zero is not included in the interval there may be no difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music.We are 95% confident that the difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music is in the interval. Because zero is not included in the interval we conclude there is likely a difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music.We are 95% confident that the difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music is in not the interval. Because zero is included in the interval we conclude there is likely a difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music.

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 520 518 512 509 416 483 540 381 524 527 508 No Music 452 431 467 558 547 577 458 481 537 485 509 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 Interpret the interval. We are 95% confident that the difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music is not in the interval. Because zero is not included in the interval we conclude there is likely a difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music.We are 95% confident that the difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music is in the interval. Because zero is included in the interval there may be no difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music. We are 95% confident that the difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music is not in the interval. Because zero is not included in the interval there may be no difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music.We are 95% confident that the difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music is in the interval. Because zero is not included in the interval we conclude there is likely a difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music.We are 95% confident that the difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music is in not the interval. Because zero is included in the interval we conclude there is likely a difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

DETAILS

MY NOTES

ASK YOUR TEACHER

PRACTICE ANOTHER

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	520	518	512	509	416	483	540	381	524	527	508
No Music	452	431	467	558	547	577	458	481	537	485	509

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

Interpret the interval.

We are 95% confident that the difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music is not in the interval. Because zero is not included in the interval we conclude there is likely a difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music.We are 95% confident that the difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music is in the interval. Because zero is included in the interval there may be no difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music. We are 95% confident that the difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music is not in the interval. Because zero is not included in the interval there may be no difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music.We are 95% confident that the difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music is in the interval. Because zero is not included in the interval we conclude there is likely a difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music.We are 95% confident that the difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music is in not the interval. Because zero is included in the interval we conclude there is likely a difference in the mean time to exhaustion for experienced triathletes when running to motivational music and the mean time when running with no music.

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 + ...

Expert Solution

Step by step

Solved in 3 steps with 1 images

SEE SOLUTION Check out a sample Q&A here