Question 3 5 pts 9 1 99 0 Details 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 46 55 53 44 48 46 51 49 43 Without Music 48 70 55 51 58 47 51 43 40 Assume a Normal distribution. What can be concluded at the the or = 0.01 level of significance? For this study, we should use Select an answer a. The null and alternative hypotheses would be: Ho: Select an answer Select an answer Select an answer (please enter a decimal) H1: Select an answer Select an answer Select an answer (Please enter a decimal) b. The test statistic ? (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 ? a e. Based on this, we should [ Select an answer ] the null hypothesis. f. Thus, the final conclusion is that ... 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. 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 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 statistically significant evidence to conclude that the population mean running time with music is equal to the population mean running time 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 9.53% chance that the mean running time for the 9 runners would be at least 3.1 minutes less with music compared to them running 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 9.53% chance of concluding that the mean running time with music for the 9 runners is at least 3.1 minutes less than the mean running time for these 9 runners without music. There is a 9.53% chance of a Type k error. There is a 9.53% chance that the mean running time for the 9 runners with music is at least 3.1 minutes less than the mean time for these 9 runners without music. h. Interpret the level of significance in the context of the study. There is a 1% chance that the runners aren't in good enough shape to run a 10K, so music is irrelevant. There is a 1% chance that the population mean running time is the same with and without music. Off 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 1% 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 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 1% 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. Hint: Helpful Video ) [+]
