37 pts) A psychologist is interested in whether hypnosis affects brain dominance (that is, whether the left or right hemisphere of the brain is dominant). Eleven college students from the freshman class are randomly sampled for an experiment. The experiment has two conditions that are given on different days. In condition 1, the students are hypnotized and then given a test that measures the relative dominance of the right and left hemispheres. The higher the score, the more dominant is the right hemisphere. In condition 2, the same students are given the test again, only this time they are not hypnotized but are in their normal state of consciousness. The following scores are obtained:

Student

1

2

3

4

5

6

7

8

9

10

11

Condition 1

26

15

22

19

23

37

16

17

14

16

21

Condition 2

12

13

18

17

21

22

18

22

10

14

15

Answer the following questions and show your work for each mathematical question:

What is the (non-directional) alternative hypothesis?

What is the null hypothesis appropriate for the non-directional alternative hypothesis?

What is the p value? In other words, what is the probability of getting a result as extreme or more extreme as the observed result purely by chance (2-tailed)?

Using ( = 0.052 tail, what is your conclusion about the null hypothesis? Justify your answer.

If you had set ( = 0.012 tail, what would be your conclusion about the null hypothesis? Justify your answer.

To what population do the results apply?

What is the power of this experiment, for ( = 0.052 tail and Preal = .10?

What is the probability of making a Type II error in this experiment when ( = 0.052 tail and Preal = .10?

What is the power of this experiment, for ( = 0.012 tail and Preal = .10?

What is the probability of making a Type II error in this experiment when ( = 0.012 tail and Preal = .10?

What is the power of this experiment, for ( = 0.052 tail and Preal = .30?

What is the probability of making a Type II error in this experiment when ( = 0.052 tail and Preal = .30?

What is the power of this experiment, for ( = 0.012 tail and Preal = .40?

What is the probability of making a Type II error in this experiment when ( = 0.012 tail and Preal = .40?