Question

5. A new exercise program is proposed to increase the V02 max (a measure of fitness in mL/kg/min) of men with sedentary lifestyles. The researchers randomly recruited 25 such men from their local health care centre. They measured the V02 max of each individual at the start of the study (pre) and then again after 6 months of participating in the exercise program (post). The data are available in the file VO2max.csv.

pre	post
28.3	28.9
29.3	36.5
34.7	34.5
30.2	30.6
30.4	37.8
35.1	35.3
31.4	33.1
26.2	36.7
27.9	36.6
28.7	36.5
33.7	36.1
31.1	35.7
31.2	33.8
30.3	33.1
28.3	32.9
35.4	31.9
31.5	33.4
24.1	30.2
32.1	40.5
28.6	37.6
26.8	30.6
29.3	32.8
26.9	32.6
27.8	36.3
28.1	33.7

a. What are the null and alternative hypotheses?
b. (1 mark) What is the value of the test statistic?
c. (1 mark) What is the distribution of the test statistic if the null hypothesis is true?
d. What is the p-value?
e. Using a significance level of 5%, state your conclusions about this test in the language of the problem.
f. Name the two key unstated assumptions required for the validity of your hypothesis test and explain why they are reasonable in this context.

Answer 1

(2 marks) What are the null and alternative hypotheses?

Difference d = pre-post

Lower tail test

b. (1 mark) What is the value of the test statistic?

paired t test used

t = -2.0732

c. (1 mark) What is the distribution of the test statistic if the null hypothesis is true?

t distribution

d. (1 marks) What is the p-value?

P=0.0245

e. (2 marks) Using a significance level of 5%, state your conclusions about this test in the language of the problem.

calculated P= 0.0245 which is < 0.05 level of significance. Ho is rejected. we conclude that new exercise program increased the V02 max of men with sedentary lifestyles.

f. (4 marks) Name the two key unstated assumptions required for the validity of your hypothesis test and explain why they are reasonable in this context.

The assumptions are the sample are random and from normal population. The assumptions are reasonably valid since the data are selected at random and the sample size(25) is reasonable large( about 30).

Paired t Test
Data
Hypothesized Mean Difference	0
Level of significance	0.05
Intermediate Calculations
Sample Size	25
DBar	-3.0640
Degrees of Freedom	24
SD	7.3895
Standard Error	1.4779
t Test Statistic	-2.0732
Lower-Tail Test
Lower Critical Value	-1.7109
p-Value	0.0245
Reject the null hypothesis