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?fIND THE f STATISTIC:uSING F sTATISTC FIND THE p VALUEMile 13:143:253:243:233:20mile 23:193:213:223:163:20mile 33:333:303:283:303:28 Joes one of the miles appear to have a hill?Click the icon to view the data table of the riding times.significance level to test the claimFind 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 sufficient evidence to warrant rejection of the claim that the three different miles have thesame mean ride time.OB.OC.O D. Fail to reject Ho. There is insufficient evidence to warrant rejection of the claim that the three different miles havethe same mean ride time.Does one of the miles appear to have a hill?O A.Yes, these data suggest that the third and first miles appear to take longer, and a reasonable explanation is thatthey both have hills.Reject Ho. There is sufficient evidence to warrant rejection of the claim that the three different miles have the samemean ride time.Reject Ho. There is insufficient evidence to warrant rejection of the claim that the three different miles have thesame mean ride time.Click to select your answer(s).OB. Yes, these data suggest that the second mile appears to take longer, and a reasonable explanation is that it has ahill.

Given data: Mile 1 Mile 2 Mile 3 3:14 3:19 3:33 3:25 3:21 3:30 3:24 3:22 3:28 3:23 3:16 3:30 3:20 3:20 3:28Since the minutes part is equal to 3 for all observations, consider only the second part for the data. Sample mean for each group is computed using the formula: x¯=x1+x2+x3+...+x55 Sample standard deviation is computed using the formula: s=∑xi-x¯2n-1 Mile 1 Mile 2 Mile 3 14 19 33 25 21 30 24 22 28 23 16 30 20 20 28 x¯1=21.2 x¯2=19.6 x¯3=29.8 s1=4.4384682 s2=2.302173 s3=2.04939 Grand mean is computed as: x¯¯=21.2+19.6+29.83=23.533333 Calculation of sum of squares of Regression: SSR=521.2-23.5333332+519.6-23.5333332+529.8-23.5333332=27.22221444+77.35554244+196.3555764=300.93333333≈300.933 Calculation of sum of squares of error: SSE=[14-21.22+25-21.22+24-21.22+23-21.22+20-21.22]+19-19.62+21-19.62+22-19.62+16-19.62+20-19.62+33-29.82+30-29.82+28-29.82+30-29.82+28-29.82=78.8+21.2+16.8=116.8 Calculation of total sum of squares: SST=SSR+SSE=300.9333+116.8=417.7333 Degrees of freedom are computed as follows: dfreg=k-1=3-1=2dferror=n-k=15-3=12dftotal=n-1=15-1=14 Calculation of mean square errors: MSreg=SSRdfreg=300.933332=150.466665 MSerror=SSEdferror=116.812=9.7333333 The F-statistic is given by the formula: F=MSregMSerror=150.4666659.7333333≈15.4589 Thus, the required F-statistic is 15.4589 Use Excel function "=F.DIST.RT(15.4589,2,12)", the result is given below: Thus, the required p-value is 0.0005 Since the p-value is less than the significance level (0.05), reject the null hypothesis. Conclusion: Reject H0, There is sufficient evidence to warrant rejection of the claim that the three different miles have the same mean ride time. On comparing the sample means of each group, we observe that the average for Mile 3 is higher. This means that Mile 3 is significantly longer than Mile 1 and Mile 2. Hence, it can be concluded that: Yes, data suggest the third mile appears to take longer and a reasonable expectation is that it has a hill.