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	25.8
2	25.2	24.9
3	24.8	24.9
4	24.1	24.6
5	25.9	25.2
6	25.1	24.5

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

(A)

H0: Null Hypothesis:    ( The runners were not faster (had lower times) at the end of the week)

HA: Alternative Hypothesis:    ( The runners were faster (had lower times) at the end of the week) (claim)

(B)

(i)

= 0.05

ndf = n - 1 = 6 - 1 = 5

One Tail - Right Side Test

From Table, critical value of t = 2.0150

(ii)

From the given data, the following Table is calculated:

Runner	Monday time	Fridays time	d = Monday time - Fridays time
1	26.2	25.8	0.4
2	25.2	24.9	0.3
3	24.8	24.9	- 0.1
4	24.1	24.6	- 0.5
5	25.9	25.2	0.7
6	25.1	24.5	0.6

From d values, the following Table is calculated:

n = 6

d	(d - )	(d - )2
0.4	0.1667	0.0278
0.3	0.0667	0.0044
-0.1	-0.3333	0.1111
-0.5	0.7333	0.5378
0.7	0.4667	0.2178
0.6	0.3667	0.1374
Total =		1.0333

SE=s_d/

= 0.4546/

= 0.1856

Test Statistic is given by:

t = 0.2333/0.1856

= 1.2572

So,

test statistic = 1.2572

(iii) By Technology, p - value = 0.1321

So,

p-value = 0.1321

(C)

Since p - value = 0.1321 is greater than = 0.05:

the decision. Fail to Reject

(D)

Correct option:

No