**Hypothesis Testing of Triathlon Riding Times****Objective:**To determine if all three miles in a triathlon loop have the same mean riding time, using a 0.05 significance level, indicating if any of the miles might have a hill affecting the riding time.**Riding Time Data:**For each mile, the times for five laps are recorded in minutes and seconds.- **Mile 1:** 3:16, 3:23, 3:21, 3:23, 3:21- **Mile 2:** 3:19, 3:22, 3:22, 3:16, 3:20- **Mile 3:** 3:33, 3:31, 3:28, 3:30, 3:28(Note: When using this data, convert each time into total seconds for analysis.)**Hypothesis Setup:**- **Null Hypothesis (H₀):** All three miles have the same mean riding time.- **Alternative Hypothesis (H₁):** At least one mile has a different mean riding time.**Analysis Method:**- Compute the F test statistic. (Formula and computation required)- Find the P-value associated with the F test statistic.**Conclusion Criteria:**- **Fail to Reject H₀:** Insufficient evidence to claim a difference in mean times.- **Reject H₀:** Sufficient evidence that mean times differ among the miles.**Conclusion Options:**- **A. Fail to reject H₀** – The three different miles have the same mean ride time.- **B. Reject H₀** – The three different miles do not have the same mean ride time.**Hill Analysis:**Determine if any mile appears to take longer, potentially due to a hill:- **A. Mile 1 appears longer - possible hill**- **B. Mile 2 appears longer - possible hill**- **C. Mile 3 appears longer - possible hill**- **D. No mile appears longer**- **E. Both Mile 1 and Mile 3 appear longer - possible hills**Use this analysis framework to evaluate the provided data and draw conclusions regarding the riding times and the potential presence of hills along the course.

Denote μ1, μ2, and μ3 as the true mean times to ride the bicycle for five laps through Mile 1, Mile…

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. Determine the null and alternative hypotheses. H₂ Find the F test statistic F=(Round to four decimal places as needed.) Find the P-value using the F test statistic. P-value = What is the conclusion for this hypothesis test? (Round to four decimal places as needed.) OA. 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. OB. Reject H₂. There is sufficient evidence to warrant rejection of the claim that the three different miles have the same mean ride time. OC. 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. OD. Reject H₂. 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? OA. Yes, these data suggest that the first mile appears to take longer, and a reasonable explanation is that it has a hill. OB. Yes, these data suggest that the second mile appears to take longer, and a reasonable explanation is that it has a hill. OC. Yes, these data suggest that the third mile appears to take longer, and a reasonable explanation is that it has a hill. OD. No, these data do not suggest that any of the miles have a hill OE. Yes, these data suggest that the third and first miles appear to take longer, and a reasonable explanation is that they both have hills. Riding Times (minutes and seconds) 0 Mile 1 3:16 3:23 3:22 3:21 3:21 Mile 2 3:19 3:22 3:22 3:16 3:20 Mile 3 3:33 3:31 3:28 3:30 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.) Print Done X