Question

A statisitcs instructor participates in triathalons. the table lists the times in minutes and seconds, he recorded while riding five laps through each mile of a 3-mile loop. Use a .05 significance level to test the claim that is takes the same time to ride each of the miles.

Mile 1	3:15	3:25	3:23	3:22	3:22
Mile 2	3:19	3:23	3:20	3:17	3:19
Mile 3	3:34	3:30	3:29	3:30	3:29

Determine the null and alternate hypotheses.

Find the F statistic

P VALUE

What is the conlusion for this hypothesis test?

(fail to reject, reject) There is (sufficient, insufficient) evidence to warrant the rejection of the claime that the three different miles have the same mean ridetime.

Does one of the miles appear to have a hill?

Answer 1

Here we are given time in minutes and seconds. First we convert time in secconds.

e.g : 3:15 = 3 minutes and 15 seconds.

60 seconds = 1 minute

so 3 minutes = 180 seconds.

Hence 3:15 = 180+15 = 195 seconds.

So we have table as :

Mile1	Mile2	Mile3
195	199	214
205	203	210
203	200	209
202	197	210
202	199	209

We run one way ANOVA in excel :

Data tab > data analysis > ANOVA:Single factor

We get output as :

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Mile1	5	1007	201.4	14.3
Mile2	5	998	199.6	4.8
Mile3	5	1052	210.4	4.3
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	334.8	2	167.4	21.46154	0.000109	3.885294
Within Groups	93.6	12	7.8
Total	428.4	14

The hypothesis are :

H0: The three different miles have the same mean ridetime.

H1: The three different miles have different mean ridetime.

The test statistic is

F = 21.462

P value : 0.0001

Here p value <

Hence we reject null hypothesis.

There is sufficient evidence to warrant the rejection of the claim that the three different miles have the same mean ridetime.

This means one of the miles appear to have a hill.