### Analyzing the Effect of Music on 10K Running TimesThis study aims to determine whether listening to music affects 10K running times. Nine runners were timed running a 10K with and without music. Their times in minutes are as follows:| Running Time | | | | | | | | | ||--------------|----|----|----|----|----|----|----|----|----|| **With Music** | 46 | 44 | 58 | 44 | 57 | 37 | 41 | 47 | 48 || **Without Music** | 43 | 47 | 61 | 43 | 49 | 64 | 39 | 42 | 54 |Assuming a normal distribution, the study uses a significance level of \( \alpha = 0.10 \).#### Hypothesis Testing Instructionsa. **The Null and Alternative Hypotheses** would be defined based on mean running times:- \( H_0: \mu_{\text{with music}} = \mu_{\text{without music}} \)- \( H_1: \mu_{\text{with music}} < \mu_{\text{without music}} \)b. **Calculate the Test Statistic**: - Enter the computed value showing 3 decimal places.c. **Determine the p-value**: - Show the calculated result to 4 decimal places.d. **Compare the p-value to \( \alpha \)**: - Determine whether the p-value is less than or equal to \( \alpha \).e. **Decision Rule**: - Decide to reject or fail to reject the null hypothesis based on the p-value comparison.f. **Conclusion**: - Choose the final conclusion based on the statistical analysis: - If results are statistically significant: Conclude the effect of music on reducing running time. - If not statistically significant: Conclude that there is insufficient evidence to show music reduces running time.By following these steps and completing the calculations, conclusions about the effect of music on running time can be drawn.

Suppose μd is the population mean differences of running time with music and without music.

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 46 44 58 44 44 57 37 41 48 With Music Ho: Select an answer ✓ H₁: Select an answer Without 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: 43 47 61 43 49 64 39 42 54 Select an answer V Select an answer V = Select an answer Select an answer (please enter a decimal) (Please enter a decimal) b. The test statistic ? c. The p-value = 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 ... (please show your answer to 3 decimal places.) (Please show your answer to 4 decimal places.) 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. 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 insufficient evidence to conclude that the population mean running time with music is less than the population mean running time without music.

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...