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Gradebook Data Sets eText Multimedia Library 77°F Sunny 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) 4 Determine the null and alternative hypotheses. 0₁ 3:15 3:25 3:23 3:21 Ho H₂: Mile 1 Mile 2 Mile 3 3:20 3:19 3:18 3:22 3:22 3:16 3:33 3:30 3:28 3:30 3:30 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 This course (Statistics Math 110+11 Spring 2022) is based on Triola: Elementary Statistics, Third California Edition WM - a n

Gradebook Data Sets eText Multimedia Library 77°F Sunny 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) 4 Determine the null and alternative hypotheses. 0₁ 3:15 3:25 3:23 3:21 Ho H₂: Mile 1 Mile 2 Mile 3 3:20 3:19 3:18 3:22 3:22 3:16 3:33 3:30 3:28 3:30 3:30 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 This course (Statistics Math 110+11 Spring 2022) is based on Triola: Elementary Statistics, Third California Edition WM - a n

MATLAB: An Introduction with Applications
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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### Riding Times Analysis **Description:** A statistics instructor who participates in triathlons kept track of his riding times (in minutes and seconds) for five laps through each mile of a 3-mile loop. The task involves using a significance level of 0.05 to evaluate the claim that it takes the same time to ride each of the miles. The aim is to determine if one of the miles appears to have a hill based on variations in riding times. **Instructions:** 1. **Data Viewing:** - To view the data table of the riding times, click on the provided icon. 2. **Hypothesis Testing:** - **Null Hypothesis (H₀):** - Formulate H₀ stating that the means of the riding times for each mile are equal, indicating no significant difference in riding times. - **Alternative Hypothesis (H₁):** - Formulate H₁ stating that at least one pair of means differs, indicating a significant divergence in riding times perhaps due to a hill. 3. **F-Statistic Calculation:** - Calculate the F test statistic and round to four decimal places as needed. 4. **P-Value Calculation:** - Calculate the P-value using the F test statistic and round to four decimal places as needed. 5. **Conclusion:** - Based on the calculated P-value, determine the conclusion for the hypothesis test. If the P-value is less than 0.05, reject the null hypothesis, suggesting that one of the miles takes significantly different riding time hinting at a hill. **Data Table:** **Riding Times (minutes and seconds):** | | Mile 1 | Mile 2 | Mile 3 | |------------|--------|--------|--------| | **Ride 1** | 3:15 | 3:18 | 3:33 | | **Ride 2** | 3:25 | 3:22 | 3:30 | | **Ride 3** | 3:23 | 3:22 | 3:28 | | **Ride 4** | 3:21 | 3:16 | 3:30 | | **Ride 5** | 3:20 | 3:19 | 3:30 | **Note:** When transcribing data into technological
Transcribed Image Text:### Riding Times Analysis **Description:** A statistics instructor who participates in triathlons kept track of his riding times (in minutes and seconds) for five laps through each mile of a 3-mile loop. The task involves using a significance level of 0.05 to evaluate the claim that it takes the same time to ride each of the miles. The aim is to determine if one of the miles appears to have a hill based on variations in riding times. **Instructions:** 1. **Data Viewing:** - To view the data table of the riding times, click on the provided icon. 2. **Hypothesis Testing:** - **Null Hypothesis (H₀):** - Formulate H₀ stating that the means of the riding times for each mile are equal, indicating no significant difference in riding times. - **Alternative Hypothesis (H₁):** - Formulate H₁ stating that at least one pair of means differs, indicating a significant divergence in riding times perhaps due to a hill. 3. **F-Statistic Calculation:** - Calculate the F test statistic and round to four decimal places as needed. 4. **P-Value Calculation:** - Calculate the P-value using the F test statistic and round to four decimal places as needed. 5. **Conclusion:** - Based on the calculated P-value, determine the conclusion for the hypothesis test. If the P-value is less than 0.05, reject the null hypothesis, suggesting that one of the miles takes significantly different riding time hinting at a hill. **Data Table:** **Riding Times (minutes and seconds):** | | Mile 1 | Mile 2 | Mile 3 | |------------|--------|--------|--------| | **Ride 1** | 3:15 | 3:18 | 3:33 | | **Ride 2** | 3:25 | 3:22 | 3:30 | | **Ride 3** | 3:23 | 3:22 | 3:28 | | **Ride 4** | 3:21 | 3:16 | 3:30 | | **Ride 5** | 3:20 | 3:19 | 3:30 | **Note:** When transcribing data into technological
### Hypothesis Testing in Triathlon Cycling 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.] #### Hypothesis Test Conclusion: **What is the conclusion for this hypothesis test?** - **A. 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.** - **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. 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.** **Does one of the miles appear to have a hill?** - **A. Yes, these data suggest that the third mile appears to take longer, and a reasonable explanation is that it has a hill.** - **B. Yes, these data suggest that the second mile appears to take longer, and a reasonable explanation is that it has a hill.** - **C. Yes, these data suggest that the first mile appears to take longer, and a reasonable explanation is that it has a hill.** - **D. No, these data do not suggest that one of the miles has a hill.** #### Graphs and Diagrams: (No graphs or diagrams are provided in this document for explanation. The hypothesis test results and conclusions are based on the available data table of riding times.) **Note**: To accurately interpret the results of the hypothesis test, it is crucial to have access to the data table of riding times to analyze the variance among the riding times for each mile. The significance level of 0.05 will determine the threshold for rejecting or failing to reject the null hypothesis (H₀).
Transcribed Image Text:### Hypothesis Testing in Triathlon Cycling 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.] #### Hypothesis Test Conclusion: **What is the conclusion for this hypothesis test?** - **A. 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.** - **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. 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.** **Does one of the miles appear to have a hill?** - **A. Yes, these data suggest that the third mile appears to take longer, and a reasonable explanation is that it has a hill.** - **B. Yes, these data suggest that the second mile appears to take longer, and a reasonable explanation is that it has a hill.** - **C. Yes, these data suggest that the first mile appears to take longer, and a reasonable explanation is that it has a hill.** - **D. No, these data do not suggest that one of the miles has a hill.** #### Graphs and Diagrams: (No graphs or diagrams are provided in this document for explanation. The hypothesis test results and conclusions are based on the available data table of riding times.) **Note**: To accurately interpret the results of the hypothesis test, it is crucial to have access to the data table of riding times to analyze the variance among the riding times for each mile. The significance level of 0.05 will determine the threshold for rejecting or failing to reject the null hypothesis (H₀).
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