Question

A track coach claims that their new month long training program will reduce your mile time by 1 minute.You want to statistically test if the training program reduces your mile time by something other than 1minute. You decide to randomly select 8 people and record their mile times. You then have them follow thecoach’s training program for a month and record their mile times post training program. The times of thesubjects are listed below. Subject#1-8 Mile Time Before Training - Mile Time After Training 1: 9.5 - 9 2: 7 - 7.1 3: 6.7 - 5.2 4: 8.45-6.8 5: 6.2 - 6.2 6: 6.3 - 8 7: 7 - 5.5 8: 9 - 7.3 (a) What type of test is appropriate for this experiment set up? (b) State the appropriate hypotheses.(c) How many degrees of freedom are involved in this test? (d) Perform a test of the hypotheses from (a) using a significance level of 5%. Make sure to compute thetest statistic and P-value, and make a conclusion in context.

Answer 1

a)

t-test for two paired samples. This test applies when we have two samples that are dependent (paired or matched)

b)

null hypothesis:

new month long training program will reduce your mile time by 1 minute

Ho: μD​ = 1

alternative hypothsis:the training program reduces your mile time by something other than 1minute

Ha:μD1

This corresponds to a two-tailed test, for which a t-test for two paired samples be used.

c)

df=n-1=7

d)

	Sample 1	Sample 2	Difference = Sample 1 - Sample 2
	9.5	9	0.5
	7	7.1	-0.1
	6.7	5.2	1.5
	8.45	6.8	1.65
	6.2	6.2	0
	6.3	8	-1.7
	7	5.5	1.5
	9	7.3	1.7
Average	7.519	6.888	0.631
St. Dev.	1.277	1.263	1.2
n	8	8	8

p=0.1803, and since p=0.1803≥0.05, it is concluded that the null hypothesis is not rejected.

so, there is not suffficient evidence to conclude that the training program reduces your mile time by something other than 1minute