Question

An exercise physiologist records the mile times in seconds for 10 college distance runners before and after a twelve-week training cycle. Is there evidence at the .05 level that the runners' mile times improved (were lower...) following the twelve weeks' training?

Before	After
249.9	250.2
278.8	266.2
254.2	244.7
261.8	252.7
238.8	237.6
267.2	269.7
267.8	256.8
259.8	263.1
254.5	252.1
255.4	243.5

1What's the value of the test statistic (based on the After-Before differences)?

2What's the p-value?

3Which of the following is(are) the correct critical value(s)?

4What is the correct decision?

Answer 1

Define , X : Times in seconds for 10 college distance runners after a twelve-week training cycle

Y : Times in seconds for 10 college distance runners before a twelve-week training cycle

Let , d = X-Y

To test :

Test statistic :

Degrees of freedom = 9

Now ,

The value of the test statistic :  

b )  

c ) Critical value :

d ) We reject H₀ if the

Now ,

Hence we reject the null hypothesis or H₀ .

Thus we have sufficient evidence to support the claim that the runners' mile times improved (were lower) following the twelve weeks' training .