Question

A high-school track-and-field coach decided to check whether her athletes run 200m faster in the morning or in the evening. She selected 7 students and obtained the following results.

Student #	1	2	3	4	5	6	7
Morning time, s	24.7	27.6	29.3	28.1	24.6	26.1	25.7
Evening time, s	24.4	27	28.3	28.1	24.9	26.2	25.3

Do these result show a significant difference at a = 0.05 level. (10 points)

a. State the hypotheses and identify the claim. (2 points)

b. Compute the test value. (3 points)

c. Find the p-value. (2 points)

d. Make the decision to reject or not reject the null hypothesis. Justify. (1 point)

e. Summarize the results. (2 points)

Answer 1

using excel>Addin>phstat>two sample test

we have

Paired t Test
Data
Hypothesized Mean Difference	0
Level of significance	0.05
Intermediate Calculations
Sample Size	7
DBar	0.2714
Degrees of Freedom	6
SD	0.4461
Standard Error	0.1686
t Test Statistic	1.6096
Two-Tail Test
Lower Critical Value	-2.4469
Upper Critical Value	2.4469
p-Value	0.1586
Do not reject the null hypothesis

a.the hypotheses are

Ho:ud = 0

Ha:ud 0a

the claim. is there is significant difference between time taken in morning and evening

b. the value of test stat t =1.6096

c. the p vaue is 0.1586

d. not reject the null hypothesis becaude p value is greater than 0.05

e. we do nohave sufficient evidence to avcept the claim that there is significant difference