Question

In an experiment on relaxation techniques, subjects brain signals were measured before and after the relaxation exercises with the following results:

Person 1 2 3 4 5
Before 31 38 62 52 28
After 27 36 58 49 24
Assuming the population is normally distributed, is there sufficient evidence to suggest that the relaxation exercise slowed the brain waves? (Use α=0.05)
a) Fail to reject the null hypothesis which states there is no change in brain waves.
b) Reject the null hypothesis which states there is no change in brain waves in favor of the alternate which states the brain waves slowed after relaxation.
c) There is not enough information to make a conclusion.

Answer 1

b) Reject the null hypothesis which states there is no change in brain waves in favor of the alternate which states the brain waves slowed after relaxation.

Explanation:

Given the data:

Person 1 2 3 4 5

Before 31 38 62 52 28

After 27 36 58 49 24

H0 : μd = 0

H0 : μd ≠ 0

This is a dependent / paired sample t test:

The difference, d = (before - after) ;

d = 4, 2, 4, 3, 4

Sample size, n = 5

The test statistic : dbar ÷ (Sd/√n)

Mean of difference, dbar = Σd / n = (4+2+4+3+4) / 5 = 17 /5 = 3.4

Sd =standard deviation of difference = 0.894 (calculator)

Test statistic = 3.4 / (0.894/√5)

Test statistic = 3.4 / 0.3998089

Test statistic = 8.50

df = n - 1 = 5 - 1 = 4

α = 0.05

critical value (4, 0.05) = 2.776

Test statistic > Critical value ; Reject the Null