A certain statistics instructor participates in triathlons. The accompanying table lists times (in minutes and seconds) he recorded while riding a bicycle for five laps through each mile of a 3-mile loop. Use a 0.05 significance level to test the claim that it tak same time to ride each of the miles. Does one of the miles appear to have a hill? Click the icon to view the data table of the riding times. Riding times (minutes and seconds) Determine the null and alternative hypotheses. Ho Mile 1 3:14 3:24 3:23 3:22 3:20 Find the F test statistic. Mile 2 3:18 3:22 3:20 3:16 3:20 Mile 3 3:34 3:31 3:28 3:31 3:30 F= (Round to four decimal places as needed.) (Note: when pasting the data into your technology, each mile row will have separate columns for each minute and second entry. You will need to convert each minute/second entry into seconds only.) Find the P-value using the F test statistic. P-value = (Round to four decimal places as needed.) What is the conclusion for this hypothesis test? O A. Fail to reject Ho. There is insufficient evidence to warrant rejection of the claim that the three different miles have the same mean ride time. O B. Fail to reject Ho. There is sufficient evidence to warrant rejection of the claim that the three different miles have the same mean ride time. OC. Reject Ho. There is insufficient evidence to warrant rejection of the claim that the three different miles have the same mean ride time. Print Done . D. Reject Ho. There is sufficient evidence to warrant rejection of the claim that the three different miles have the same mean ride time. Does one of the miles appear to have a hill? O A. Yes, these data suggest that the first mile appears to take longer, and a reasonable explanation is that it has a hil.
A certain statistics instructor participates in triathlons. The accompanying table lists times (in minutes and seconds) he recorded while riding a bicycle for five laps through each mile of a 3-mile loop. Use a 0.05 significance level to test the claim that it tak same time to ride each of the miles. Does one of the miles appear to have a hill? Click the icon to view the data table of the riding times. Riding times (minutes and seconds) Determine the null and alternative hypotheses. Ho Mile 1 3:14 3:24 3:23 3:22 3:20 Find the F test statistic. Mile 2 3:18 3:22 3:20 3:16 3:20 Mile 3 3:34 3:31 3:28 3:31 3:30 F= (Round to four decimal places as needed.) (Note: when pasting the data into your technology, each mile row will have separate columns for each minute and second entry. You will need to convert each minute/second entry into seconds only.) Find the P-value using the F test statistic. P-value = (Round to four decimal places as needed.) What is the conclusion for this hypothesis test? O A. Fail to reject Ho. There is insufficient evidence to warrant rejection of the claim that the three different miles have the same mean ride time. O B. Fail to reject Ho. There is sufficient evidence to warrant rejection of the claim that the three different miles have the same mean ride time. OC. Reject Ho. There is insufficient evidence to warrant rejection of the claim that the three different miles have the same mean ride time. Print Done . D. Reject Ho. There is sufficient evidence to warrant rejection of the claim that the three different miles have the same mean ride time. Does one of the miles appear to have a hill? O A. Yes, these data suggest that the first mile appears to take longer, and a reasonable explanation is that it has a hil.
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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Transcribed Image Text:### Analyzing Riding Times in a Triathlon: A Statistical Approach
**Scenario:**
A statistics instructor participates in triathlons and records the riding times for five laps through each mile of a 3-mile loop. The instructor is interested in determining whether one of the miles has a hill, affecting the riding times. Using a 0.05 significance level, the goal is to test the claim that it takes the same time to ride each of the miles.
**Steps for Analysis:**
1. **Determine the Null and Alternative Hypotheses:**
- \( H_0 \): All three miles have the same mean ride time.
- \( H_1 \): At least one mile has a different mean ride time.
2. **Calculate the F test statistic:**
- Use the given data and statistical tools to calculate the F statistic, rounding to four decimal places as needed.
3. **Determine the P-value:**
- Find the P-value from the F-statistic, rounding to four decimal places. This helps assess whether the differences in means are statistically significant.
4. **Conclusion of the Hypothesis Test:**
- Different options explain the possible outcomes:
- **A.** Fail to reject \( H_0 \): No sufficient evidence to claim a difference in means.
- **B.** Reject \( H_0 \): Sufficient evidence to claim a difference in means.
- **C.** Reject \( H_0 \): Insufficient evidence, despite rejecting.
- **D.** Fail to reject \( H_0 \): Sufficient evidence to affirm equal means.
5. **Analysis of Potential Hill:**
- Does one mile have a hill? Choose:
- **A.** Yes, data suggests the first mile takes longer, possibly due to a hill.
**Graph/Diagram Explanation:**
The accompanying box provides the recorded riding times in minutes and seconds for each mile:
- **Mile 1:** 3:14, 3:24, 3:23, 3:23, 3:20
- **Mile 2:** 3:18, 3:22, 3:20, 3:16, 3:20
- **Mile 3:** 3:34, 3:31, 3:28, 3:31, 3:30
(Note: Convert each time
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