Question

A coach times 6 randomly selected runners to measure their times early in the week and at the end of the week (in minutes). Using the parts below, help the coach run a paired t-test to determine if the runners were faster (had lower times) at the end of the week. Use α = 0.05.

Runner	Monday time	Fridays time
1	26.2	25.6
2	25.1	24.6
3	24.8	24.6
4	24.1	24.6
5	25.9	25.2
6	26	25.5

A. State the null and alternative hypotheses in terms of µ_D.

B. Find the critical value, test statistic, p-value.

C. What is the decision. Reject / fail to Reject

D. Based on the results, would you tell the coach that the runners were faster at the end of the week? yes/no

Answer 1

Ans:

Let d=Monday's time-Friday's time

a)

Runner	Monday time	Fridays time	d
1	26.2	25.6	0.6
2	25.1	24.6	0.5
3	24.8	24.6	0.2
4	24.1	24.6	-0.5
5	25.9	25.2	0.7
6	26	25.5	0.5
		d-bar	0.333
		sd	0.441

b)

df=6-1=5

critical t value=2.015

Test statistic:

t=(0.333-0)/(0.441/sqrt(6))

t=1.850

p-value=tdist(1.850,5,1)=0.0618

c)

As,test statistic is less than the critical value of 2.015,so fail to reject H₀.

d)

There is not sufficient evidence to suggest that he runners were faster at the end of the week.

No