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 TimeWith Music453441384640315646Without Music443348375342305145Assume a Normal distribution. What can be concluded at the the αα = 0.05 level of significance?For this study, we should use Select an answer z-test for a population proportion z-test for the difference between two population proportions t-test for the difference between two dependent population means t-test for a population mean t-test for the difference between two independent population means The null and alternative hypotheses would be: H0:H0: Select an answer p1 μ1 μd Select an answer ≠ > = < Select an answer 0 μ2 p2 (please enter a decimal) H1:H1: Select an answer μ1 μd p1 Select an answer > < ≠ = Select an answer μ2 0 p2 (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 ? ≤ > ααBased on this, we should Select an answer reject fail to reject accept the null hypothesis.Thus, the final conclusion is that ...The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the nine runners finished in less time on average with music compared to running without music.The results are statistically insignificant at αα = 0.05, 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 significant at αα = 0.05, 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.The results are statistically insignificant at αα = 0.05, 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.Interpret the p-value in the context of the study.There is a 31.53% chance that the mean running time for the 9 runners with music is at least 0.7 minutes less than the mean 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 31.53% chance that the mean running time for the 9 runners would be at least 0.7 minutes less with music compared to them running without music.There is a 31.53% chance of a Type I error.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 31.53% chance of concluding that the mean running time with music for the 9 runners is at least 0.7 minutes less than the mean running time for these 9 runners without music.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 in the 10K with and without music, then there would be a 5% 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.There is a 5% chance that the population mean running time is the same with and without music.There is a 5% 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 with and without music then there would be a 5% 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

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Description: 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 TimeWith Music453441384640315646Without Music44334837

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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	34	41	38	46	40	31	56	46
Without Music	44	33	48	37	53	42	30	51	45

Assume a Normal distribution. What can be concluded at the the αα = 0.05 level of significance?

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

The null and alternative hypotheses would be:

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

H1:H1: Select an answer μ1 μd p1 Select an answer > < ≠ = Select an answer μ2 0 p2 (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 reject fail to reject accept the null hypothesis.
Thus, the final conclusion is that ...
- The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the nine runners finished in less time on average with music compared to running without music.
- The results are statistically insignificant at αα = 0.05, 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 significant at αα = 0.05, 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.
- The results are statistically insignificant at αα = 0.05, 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.
Interpret the p-value in the context of the study.
- There is a 31.53% chance that the mean running time for the 9 runners with music is at least 0.7 minutes less than the mean 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 31.53% chance that the mean running time for the 9 runners would be at least 0.7 minutes less with music compared to them running without music.
- There is a 31.53% chance of a Type I error.
- 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 31.53% chance of concluding that the mean running time with music for the 9 runners is at least 0.7 minutes less than the mean running time for these 9 runners without music.
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 in the 10K with and without music, then there would be a 5% 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.
- There is a 5% chance that the population mean running time is the same with and without music.
- There is a 5% 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 with and without music then there would be a 5% 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

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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