Question

A coach times 6 randomly selected runners to measure their times early in the week and...

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 µD.

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

Homework Answers

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

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