Question

194 pts.) A psychologist is interested in whether hypnosis affects brain dominance (that is, whether the left or right nemisphere 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 I, 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__ Condition 1 Condition 2 1 26 12 2 15 13 3 22 18 4 19 17 5 23 21 6 37 22 7 16 11 8 17 22 9 14 10 10 16 14 21 15 Answer the following questions and show your work for each mathematical questioni A. (3 pts) What is the (non-directional) alternative hypothesis? B. (3 pts) What is the null hypothesis? C. (6 pts) 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)?) Show your work. D. (3 pts) For a 0.05 . What is your conclusion about the null hypothesis? Justify your answer using the decision rule

Answer 1

A.

Alternative Hypothesis H0: The difference in relative dominance scores with and without hypnosis is not equal to 0.
Since the alternative hypothesis contains the term "not equal to", it is a non-directional alternative hypothesis.

B.

Null Hypothesis H0: The difference in relative dominance scores with and without hypnosis is equal to 0.

C.
Since same students were involved in both the test, it is a paired data and we should use paired samples t test.

The difference in scores (Condition1 - Condistion2) is,
14 2 4 2 2 15 5 -5 4 2 6

Mean difference , d = 4.636364

Standard deviation of differences, s = 5.643983

Standard error of mean difference, se = s / $\sqrt{n}$ = 5.643983 / $\sqrt{11}$ = 1.701725

Test statistic, t = (d - hypothesized difference)/se = (4.636364 - 0) / 1.701725 = 2.72

Degree of freedom = n-1 = 11 - 1 = 10

For two-tail test, p-value = 2 * P(t > 2.72) = 0.0216

D.

Since, p-value is less than 0.05 significance level, we reject null hypothesis H0 and conclude that there is significant evidence that the difference in relative dominance scores with and without hypnosis is not equal to 0.