In a experiment on relaxation techniques, subject's brain signals were measured before and after the relaxation exercises with the following results:
Person 1 2 3 4 5
Before 32 38 66 49 29
After 26 36 59 52 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)

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

The population is normally distributed

This is a paired t test since sample size is very small and same population under two different conditions studied.

[tex]H_0: \bar x-\bar y =0\\H_a: \bar x >\bar y[/tex]

(Right tailed test)

Alpha = 5%

x y Diff

32 26 6

38 36 2

66 59 7

49 52 -3

29 24 5

Mean 3.4

Std dev 4.037325848

Mean difference = [tex]3.40[/tex]

n =5

Std deviation for difference = [tex]4.037326[/tex]

Test statistic t = mean difference / std dev for difference

= [tex]1.883[/tex]

p value =0.132

Since p >0.05 we accept null hypothesis.

There is no sufficient evidence to suggest that the relaxation exercise slowed the brain waves