In a experiment on relaxation techniques, subject\'s brain signals were measured

ID: 3364412 • Letter: I

Question

In a experiment on relaxation techniques, subject's brain signals were measured before and after the relaxation exercises with the following results:

Is there sufficient evidence to suggest that the relaxation exercise slowed the brain waves? (Use =0.05)

a) There is not enough information to make a conclusion.

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) Fail to reject the null hypothesis which states there is no change in brain waves.

Person 1 2 3 4 5 Before 32 37 60 51 31 After 26 35 58 49 27

Explanation / Answer

This is a paired t test.

General procedure is taking the difference (di = beforei – afteri ) and taking the mean value of the differences(d) and testing the hypothesis.

H0 : d = 0

H1: d 0

t = d/s.e(d)

Using MS excel, data -> data analysis -> t-Test: Paired Two Sample for Means

The output is :

t-Test: Paired Two Sample for Means

before

after

Mean

42.2

Variance

162.7

197.5

Observations

Pearson Correlation

0.99577426

Hypothesized Mean Difference

t Stat

P(T<=t) one-tail

0.00806504

t Critical one-tail

2.13184678

P(T<=t) two-tail

0.01613009

t Critical two-tail

2.77644511

From the alternate hypothesis, we know that it is a two tailed test.

Since P(T<=t) two-tail (0.0161) < 0.05, we 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.

Note: the reason to use paired t test is because there is a strong correlation between before and after relaxation.