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 46 33 45 64 49 54 59 49 44 Music Without 50 32 45 65 55 54 60 55 43 Music Assume a Normal distribution. What can be concluded at the the a = 0.01 level of significance? For this study, we should use Select an answer (if you chose to use the test for the difference between means, define µa to be the average time with music minus the average time without music.) a. The null and alternative hypotheses would be: Ho: Select an answer Select an answer Select an answer H : Select an answer Select an answer Select an answer b. The test statistic ? (please show your answer to 2 decimal places.) c. The p-value = (Please show your answer to 4 decimal places.) d. The p-value is ? e. Based on this, we should O the null hypothesis. Select an answer f. Thus, the final conclusion is that The results are statistically insignificant at a = 0.01, 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 a = 0.01, 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 a = 0.01, 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. The results are statistically significant at a = 0.01, so there is sufficient evidence to conclude that the nine runners finished in less time on average with music compared to running without music g. Interpret the p-value 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 4.76% chance that the mean running time for the 9 runners would be at least 1.8 minutes less with music compared to them running without music. There is a 4.76% chance of a Type I error. There is a 4.76% chance that the mean running time for the 9 runners with music is at least 1.8 minutes less than the mean time for these 9 runners without music. 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 4.76% chance of concluding that the mean running time with music for the 9 runners is at least 1.8 minutes less than the mean runhing time for thoro 0