Does 10K running time increase 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 48 45 49 45 47 43 46 44 46 Without Music 45 44 44 52 50 41 51 35 37 Assume a Normal distribution. What can be concluded at the the αα = 0.10 level of significance? For this study, we should use Select an answer z-test for the difference between two population proportions t-test for the difference between two independent population means z-test for a population proportion t-test for the difference between two dependent population means t-test for a population mean The null and alternative hypotheses would be: H0:H0: Select an answer p1 μ1 μd Select an answer ≠ > = < Select an answer p2 μ2 0 (please enter a decimal) H1:H1: Select an answer μ1 p1 μd Select an answer = > < ≠ Select an answer 0 p2 μ2 (Please enter a decimal) The test statistic ? t z = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is ? > ≤ αα Based on this, we should Select an answer accept fail to reject reject the null hypothesis. Thus, the final conclusion is that ... The results are statistically insignificant at αα = 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. The results are statistically insignificant at αα = 0.10, so there is insufficient evidence to conclude that the population mean running time with music is greater than the population mean running time without music. The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the population mean running time with music is greater than the population mean running time without music. The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the nine runners finished in more time on average with music compared to running without music.

Does 10K running time increase 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 48 45 49 45 47 43 46 44 46 Without Music 45 44 44 52 50 41 51 35 37 Assume a Normal distribution. What can be concluded at the the αα = 0.10 level of significance? For this study, we should use Select an answer z-test for the difference between two population proportions t-test for the difference between two independent population means z-test for a population proportion t-test for the difference between two dependent population means t-test for a population mean The null and alternative hypotheses would be: H0:H0: Select an answer p1 μ1 μd Select an answer ≠ > = < Select an answer p2 μ2 0 (please enter a decimal) H1:H1: Select an answer μ1 p1 μd Select an answer = > < ≠ Select an answer 0 p2 μ2 (Please enter a decimal) The test statistic ? t z = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is ? > ≤ αα Based on this, we should Select an answer accept fail to reject reject the null hypothesis. Thus, the final conclusion is that ... The results are statistically insignificant at αα = 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. The results are statistically insignificant at αα = 0.10, so there is insufficient evidence to conclude that the population mean running time with music is greater than the population mean running time without music. The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the population mean running time with music is greater than the population mean running time without music. The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the nine runners finished in more time on average with music compared to running without 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

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Does 10K running time increase 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	48	45	49	45	47	43	46	44	46
Without Music	45	44	44	52	50	41	51	35	37

Assume a Normal distribution. What can be concluded at the the αα = 0.10 level of significance?

For this study, we should use Select an answer z-test for the difference between two population proportions t-test for the difference between two independent population means z-test for a population proportion t-test for the difference between two dependent population means t-test for a population mean

The null and alternative hypotheses would be:

H0:H0: Select an answer p1 μ1 μd Select an answer ≠ > = < Select an answer p2 μ2 0 (please enter a decimal)

H1:H1: Select an answer μ1 p1 μd Select an answer = > < ≠ Select an answer 0 p2 μ2 (Please enter a decimal)

The test statistic ? t z = (please show your answer to 3 decimal places.)
The p-value = (Please show your answer to 4 decimal places.)
The p-value is ? > ≤ αα
Based on this, we should Select an answer accept fail to reject reject the null hypothesis.
Thus, the final conclusion is that ...
- The results are statistically insignificant at αα = 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.
- The results are statistically insignificant at αα = 0.10, so there is insufficient evidence to conclude that the population mean running time with music is greater than the population mean running time without music.
- The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the population mean running time with music is greater than the population mean running time without music.
- The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the nine runners finished in more time on average with music compared to running without music.
Interpret the p-value in the context of the study.
- If 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 21.93% chance of concluding that the mean running time with music for the 9 runners is at least 1.6 minutes more than the mean running time for these 9 runners without music.
- 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 21.93% chance that the mean running time for the 9 runners would be at least 1.6 minutes more with music compared to them running without music.
- There is a 21.93% chance that the mean running time for the 9 runners with music is at least 1.6 minutes more than the mean time for these 9 runners without music.
- There is a 21.93% chance of a Type I error.
Interpret the level of significance in the context of the study.
- 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 greater than the population mean running time without music
- There is a 10% chance that the population mean running time is the same with and without music.
- There is a 10% chance that the runners aren't in good enough shape to run a 10K, so music is irrelevant.
- 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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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