A certain statistics instructor participates in triathlons. The accompanying tab
ID: 3218129 • Letter: A
Question
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 3mile 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 altermative hypotheses. Ho: Find H1 H2 H3 Find Exactly two of the population means are different from each other. P-va Wha At least one of the three population means is different from the others. O A. 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. that the different miles have the same O B. Reject Ho. There is sufficient evidence to warrant rejection of the claim three mean ride time. the claim that the three different miles have the O C. Reject Ho. There is insufficient evidence to warrant rejection of same mean ride time, Click to select your answer(s)Explanation / Answer
H0: µ1 = µ2 = µ3, for null hypothesis we believe, the time taken for each of the mile is equal.
H1: At least one of the three population means is different from the others
Mile 1- 3:14 3:23 3:22 3:22 3:21 Mile 2- 3:18 3:21 3:21 3:16 3:20 Mole 3- 3:35 3:32 3:28 3:32 3:30
Corrected mean, CM = (Sum of all observations)2/N = (194+203+202+202+201+198+201+201+196+200+215+212+208+212+210)2/15 = 622201.6667
SStotal = sum of squares of all observations - CM = 551.3333
The treatment sum of squares, SST = SUM[(Sum of each times in each mile)2/n] - CM
(194+203+202+202+201)2/5+(198+201+201+196+200)2/5+(215+212+208+212+210)2/5 - 622201.6667= 452.1333
Error sum of square, SSE = SStotal - SST = 99.2
MST = SST/(k-1) where k is the number of treatments = 452.1333/2 = 226.0667
MSE = SSE/(N-k) = 99.2/(15-3) = 8.2667
F = MST/MSE = 27.35
P = 0
Reject H0: There is sufficient evidence to warrant rejection of the claim that the 3 different miles have the same mean ride time
Yes, these data suggest that the 3rd mile appears to take longer, and a reasonable explanation is that it has a hill
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