Does 10K running time decrease when the runner listens to music? Nine runners were timed as they ran a 10K with and without listening to music. The running times in minutes are shown below. Running Time 45 36 42 37 52 47 40 53 50 With Music Without 46 37 47 38 54 44 43 51 53 Music Assume a Normal distribution. What can be concluded at the the a = 0.10 level of significance?
Does 10K running time decrease when the runner listens to music? Nine runners were timed as they ran a 10K with and without listening to music. The running times in minutes are shown below. Running Time 45 36 42 37 52 47 40 53 50 With Music Without 46 37 47 38 54 44 43 51 53 Music Assume a Normal distribution. What can be concluded at the the a = 0.10 level of significance?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![Does 10K running time decrease when the runner listens to music? Nine runners were timed as they ran a
10K with and without listening to music. The running times in minutes are shown below.
Running Time
With
Music 45 36 42 37 52 47 40 53 50
Without
46 37 47 38 54 44 43 51 53
Music
Assume a Normal distribution. What can be concluded at the the a = 0.10 level of significance?
For this study, we should use Select an answer
a. The null and alternative hypotheses would be:
Ho: Select an answer vSelect an answer vSelect an answer v (please enter a decimal)
H: Select an answer v
Select an answer vSelect an answer v
| (Please enter a decimal)
b. The test statistic ?v =
|(please show your answer to 3 decimal places.)
c. The p-value =
(Please show your answer to 4 decimal places.)
d. The p-value is ? va
e. Based on this, we should Select an answer
f. Thus, the final conclusion is that...
v the null hypothesis.
O The results are statistically significant at a = 0.10, so there is sufficient evidence to conclude
that the nine runners finished in less time on average with music compared to running without
music.
O The results are statistically insignificant at a = 0.10, so there is statistically significant
evidence to conclude that the population mean running time with music is equal to the
population mean running time without music.
O The results are statistically insignificant at a = 0.10, so there is insufficient evidence to
conclude that the population mean running time with music is less than the population mean
running time without music.
O The results are statistically significant at a = 0.10, so there is sufficient evidence to conclude
that the population mean running time with music is less than the population mean running
time without music.
g. Interpret the p-value in the context of the study.
O If the population mean running time with music is the same as the population mean running
time without music and if another 9 runners compete with and without music then there would
be a 8.95% chance that the mean running time for the 9 runners would be at least 1.2 minutes
less with music compared to them running without music.
O There is a 8.95% chance that the mean running time for the 9 runners with music is at least 1.2
minutes less than the mean time for these 9 runners without music.
O There is a 8.95% chance of a Type I error.
Olf the sample mean running time with music for the 9 runners is the same as the sample mean
running time without music for these 9 runners and if another 9 runners are observed running
the 10K with and without music then there would be a 8.95% chance of concluding that the
mean running time with music for the 9 runners is at least 1.2 minutes less than the mean
running time for these 9 runners without music.
h. Interpret the level of significance in the context of the study.
O If the population mean running time with music is the same as the population mean running
time without music and if another 9 runners compete with and without music then there would
be a 10% chance that we would end up falsely concluding that the population mean running
time with music is less than the population mean running time without music
O There is a 10% chance that the population mean running time is the same with and without
music.
O If the population mean running time with music is the same as the population mean running
time without music and if another 9 runners compete in the 10K with and without music, then
there would be a 10% chance that we would end up falsely concluding that the sample mean
running times with music and without music for these 9 runners differ from each other.
O There is a 10% chance that the runners aren't in good enough shape to run a 10K, so music is
irrelevant.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc982bc3f-99f0-4b2c-9f40-dc92d0e6c3f8%2F8e53e35c-b29d-48a2-aafa-0556dd12644f%2F2d2iacs_processed.png&w=3840&q=75)
Transcribed Image Text:Does 10K running time decrease when the runner listens to music? Nine runners were timed as they ran a
10K with and without listening to music. The running times in minutes are shown below.
Running Time
With
Music 45 36 42 37 52 47 40 53 50
Without
46 37 47 38 54 44 43 51 53
Music
Assume a Normal distribution. What can be concluded at the the a = 0.10 level of significance?
For this study, we should use Select an answer
a. The null and alternative hypotheses would be:
Ho: Select an answer vSelect an answer vSelect an answer v (please enter a decimal)
H: Select an answer v
Select an answer vSelect an answer v
| (Please enter a decimal)
b. The test statistic ?v =
|(please show your answer to 3 decimal places.)
c. The p-value =
(Please show your answer to 4 decimal places.)
d. The p-value is ? va
e. Based on this, we should Select an answer
f. Thus, the final conclusion is that...
v the null hypothesis.
O The results are statistically significant at a = 0.10, so there is sufficient evidence to conclude
that the nine runners finished in less time on average with music compared to running without
music.
O The results are statistically insignificant at a = 0.10, so there is statistically significant
evidence to conclude that the population mean running time with music is equal to the
population mean running time without music.
O The results are statistically insignificant at a = 0.10, so there is insufficient evidence to
conclude that the population mean running time with music is less than the population mean
running time without music.
O The results are statistically significant at a = 0.10, so there is sufficient evidence to conclude
that the population mean running time with music is less than the population mean running
time without music.
g. Interpret the p-value in the context of the study.
O If the population mean running time with music is the same as the population mean running
time without music and if another 9 runners compete with and without music then there would
be a 8.95% chance that the mean running time for the 9 runners would be at least 1.2 minutes
less with music compared to them running without music.
O There is a 8.95% chance that the mean running time for the 9 runners with music is at least 1.2
minutes less than the mean time for these 9 runners without music.
O There is a 8.95% chance of a Type I error.
Olf the sample mean running time with music for the 9 runners is the same as the sample mean
running time without music for these 9 runners and if another 9 runners are observed running
the 10K with and without music then there would be a 8.95% chance of concluding that the
mean running time with music for the 9 runners is at least 1.2 minutes less than the mean
running time for these 9 runners without music.
h. Interpret the level of significance in the context of the study.
O If the population mean running time with music is the same as the population mean running
time without music and if another 9 runners compete with and without music then there would
be a 10% chance that we would end up falsely concluding that the population mean running
time with music is less than the population mean running time without music
O There is a 10% chance that the population mean running time is the same with and without
music.
O If the population mean running time with music is the same as the population mean running
time without music and if another 9 runners compete in the 10K with and without music, then
there would be a 10% chance that we would end up falsely concluding that the sample mean
running times with music and without music for these 9 runners differ from each other.
O There is a 10% chance that the runners aren't in good enough shape to run a 10K, so music is
irrelevant.
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