Question

An experimenter flips a coin 100 times and gets 32 heads. Test the claim that the coin is fair against the two-sided claim that it is not fair at the level α=.01.

a) H_o: p = .5, H_a: p ≠ .5; z = -3.60; Reject H_o at the 1% significance level.

b) H_o: p = .5, H_a: p < .5; z = -3.86; Reject H_o at the 1% significance level.

c) H_o: p = .5, H_a: p ≠ .5; z = -3.60; Fail to reject H_o at the 1% significance level.

d) H_o: p = .5, H_a: p ≠ .5; z = -3.86; Reject H_o at the 1% significance level.

e) H_o: p = .5, H_a: p < .5; z = -3.60; Fail to reject H_o at the 1% significance level.

Part 2

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	31	38	66	51	32
After	26	35	57	51	26

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) There is not enough information to make a conclusion.

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

c) 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.

Answer 1

Ans:

1)

z=(0.32-0.5)/SQRT(0.5*(1-0.5)/100)

z=-3.60

critical z values=+/-2.58

H_o: p = .5, H_a: p ≠ .5; z = -3.60; Reject H_o at the 1% significance level.

2)

Person	1	2	3	4	5
Before	31	38	66	51	32
After	26	35	57	51	26
d	5	3	9	0	6
d-bar	4.6
sd	3.362

Test statistic:

t=(4.6-0)/(3.362/SQRT(5))

t=3.06

df=5-1=4

p-value=tdist(3.06,4,1)=0.0188

As,p-value<0.05,we reject the null hypothesis.

Correct option is:

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.