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 takes the 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. X Riding Times (minutes and seconds) Determine the null and alternative hypotheses. D 3:16 3:23 3:24 3:21 3:22 Ho Mile 1 Mile 2 Mile 3 H₁ 3:18 3:21 3:20 3:20 3:16 3:33 3:30 3:28 3:31 3:28 Find the F test statistic. 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? Print Done ▼
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 takes the 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. X Riding Times (minutes and seconds) Determine the null and alternative hypotheses. D 3:16 3:23 3:24 3:21 3:22 Ho Mile 1 Mile 2 Mile 3 H₁ 3:18 3:21 3:20 3:20 3:16 3:33 3:30 3:28 3:31 3:28 Find the F test statistic. 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? Print Done ▼
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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![### Hypothesis Testing for Bicycle Riding Times in a Triathlon
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 takes the same time to ride each of the miles. Does one of the miles appear to have a hill?
#### Riding Times (minutes and seconds)
| Mile | Lap 1 | Lap 2 | Lap 3 | Lap 4 | Lap 5 |
|------|-------|-------|-------|-------|-------|
| **Mile 1** | 3:16 | 3:23 | 3:24 | 3:21 | 3:22 |
| **Mile 2** | 3:18 | 3:21 | 3:20 | 3:16 | 3:20 |
| **Mile 3** | 3:33 | 3:30 | 3:28 | 3:31 | 3:28 |
(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.)
#### Hypothesis
Determine the null and alternative hypotheses.
- **Null Hypothesis (H₀)**:
- There is no significant difference in the riding times for the three miles.
- **Alternative Hypothesis (H₁)**:
- There is a significant difference in the riding times for the three miles.
#### Analysis Steps
1. **Find the F test statistic**:
- Compute the F-value after converting the times into a single unit (seconds).
- Round to four decimal places as needed.
2. **Find the P-value using the F test statistic**:
- Determine the significance of the computed F-value.
- Round to four decimal places as needed.
#### Conclusion
State the conclusion for this hypothesis test. Determine whether to reject the null hypothesis based on the comparison between the P-value and the significance level (0.05).
Click on the icon below to view the data table of the riding times:
[Data Table Icon]
#### Tools and Interpretation
- It is important to convert the times from](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fadafbebc-0641-4102-b64a-091c0f61c4bb%2F514ff98f-f0ff-49d6-bca8-6582cd33f9d8%2Fv654bi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing for Bicycle Riding Times in a Triathlon
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 takes the same time to ride each of the miles. Does one of the miles appear to have a hill?
#### Riding Times (minutes and seconds)
| Mile | Lap 1 | Lap 2 | Lap 3 | Lap 4 | Lap 5 |
|------|-------|-------|-------|-------|-------|
| **Mile 1** | 3:16 | 3:23 | 3:24 | 3:21 | 3:22 |
| **Mile 2** | 3:18 | 3:21 | 3:20 | 3:16 | 3:20 |
| **Mile 3** | 3:33 | 3:30 | 3:28 | 3:31 | 3:28 |
(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.)
#### Hypothesis
Determine the null and alternative hypotheses.
- **Null Hypothesis (H₀)**:
- There is no significant difference in the riding times for the three miles.
- **Alternative Hypothesis (H₁)**:
- There is a significant difference in the riding times for the three miles.
#### Analysis Steps
1. **Find the F test statistic**:
- Compute the F-value after converting the times into a single unit (seconds).
- Round to four decimal places as needed.
2. **Find the P-value using the F test statistic**:
- Determine the significance of the computed F-value.
- Round to four decimal places as needed.
#### Conclusion
State the conclusion for this hypothesis test. Determine whether to reject the null hypothesis based on the comparison between the P-value and the significance level (0.05).
Click on the icon below to view the data table of the riding times:
[Data Table Icon]
#### Tools and Interpretation
- It is important to convert the times from
Transcribed Image Text:### Hypothesis Testing in Triathlons Study
**Context:**
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 takes the same time to ride each of the miles. Does one of the miles appear to have a hill?
**Data Access:**
Click the icon to view the data table of the riding times.
---
**Hypothesis Test Conclusion:**
What is the conclusion for this hypothesis test?
- **A.** Reject H₀. There is sufficient evidence to warrant rejection of the claim that the three different miles have the same mean ride time.
- **B.** Fail to reject H₀. There is insufficient evidence to warrant rejection of the claim that the three different miles have the same mean ride time.
- **C.** Fail to reject H₀. There is sufficient evidence to warrant rejection of the claim that the three different miles have the same mean ride time.
- **D.** Reject H₀. There is insufficient evidence to warrant rejection of the claim that the three different miles have the same mean ride time.
**Further Analysis:**
Does one of the miles appear to have a hill?
- **A.** Yes, these data suggest that the second mile appears to take longer, and a reasonable explanation is that it has a hill.
- **B.** No, these data do not suggest that any of the miles have a hill.
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