9. A primatologist believes that rhesus monkeys possess curiosity. She reasons that, if this is true, then they should prefer novel stimulation to repetitive stimulation. An experiment is conducted in which 12 rhesus monkeys are randomly selected from the university colony and taught to press two bars. Pressing bar 1 always produces the same sound, whereas bar 2 produces a novel sound each time it is pressed. After learning to press the bars, the monkeys are tested for 15 minutes. during which they have free access to both bars. The number of presses on each bar during the 15 minutes is recorded. The resulting data are as follows:

1. What is the alternative hypothesis? In this case, assume a non-directional hypothesis is appropriate because there is insufficient empirical basis to warrant a directional hypothesis.

h. What is the null hypothesis?

c. Using alpha = 0.05, what is your conclusion?

d. What error may you be making by your conclusion in part c?

e. To what population does your conclusion apply?

2. (21 pts) Refer to the data you collected for Homework 4 by flipping a fair coin 16 times (times five separate samples). If you didn't save these numbers, re-flip the coin so you have five samples, each with a count of the number of heads in 16 flips. For each of your 5 samples of 16 flips, use the binomial distribution to test the null hypothesis that the coin is fair, using a = .05 (two-tailed). (Note: the alternative hypothesis is that the coin is not fair.)

Make a little table listing the following information: the sample number (1 to 5), the number of heads for each sample, the final calculated p value, your decision about the null hypothesis, and the explicit reason for your decision, in terms of the decision rule. (Note: You don't necessarily have to show your work for the p value computation, but if your answer is wrong and you don't show your work, there will be no partial credit!) Finally, answer the following additional question: in general, what proportion of samples of fair coin flips should result in rejecting the null hypothesis (a = .05, two-tailed)?

3. (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 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:

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

1. What is the (non-directional) alternative hypothesis?
2. What is the null hypothesis appropriate for the non-directional alternative hypothesis?
3. 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)?
4. Using a = 0.052 tail, what is your conclusion about the null hypothesis? Justify your answer.
5. If you had set a = 0.012 tail, what would be your conclusion about the null hypothesis? Justify your answer.
6. To what population do the results apply?
7. What is the power of this experiment, for a = 0.052, and P _real = .10?
8. What is the probability of making a Type II error in this experiment when a = 0.052 and P _real = .10?
9. What is the power of this experiment, for a = 0.012 tail and P _real = .10?
10. What is the probability of making a Type II error in this experiment when a = 0.012 tan and P _real = .10?

K. What is the power of this experiment, for a = 0,052 tail and P _real = 0.30? As

L. What is the probability of making a Type II error in this experiment when a = 0.052, A and P _real = .30?

M. What is the power of this experiment, for a = 0.012w and P _real = .30?

N. What is the probability of making a Type II error in this experiment when a = 0.012 ,ii and P _real = .30?

4. (32 pts: 2 pts per sub-question.) Answer the following True-False questions. In your write-up, just list the sub-question letter (A-P) and whether the statement is True or False — no need to restate the question or to justify your answer.

1. If the number of trials in the binomial distribution increases by 1 (and P = .5), the probability of getting either of the most extreme possible outcomes is cut in half.
2. In the binomial distribution, as the probability of a "+" or "-" outcome differs more and more from .5, the shape of the distribution of probabilities for all possible outcomes always becomes less and less symmetrical.
3. In the sign test, the p value associated with a given number of "+" outcomes will be the same as the p value associated with the same number of "-" outcomes, when the test is two-tailed.
4. In the sign test, when the obtained result is exactly what would be expected by chance (like 7 successes out of 14 trials when P = .50), the p value (assuming you're doing a two-tailed test) will sometimes be greater than 1.00.
5. In the sign test, if N increases and alpha is made less stringent (like from .01 to .05), the number of different possible outcomes that allow rejection of Ho must increase.
6. In the sign test, if N decreases and the size of the effect of the independent variable decreases, the probability of a Type II error decreases.
7. In the sign test, as the numerical value of P _real gets closer to .5, the power of an experiment must always increase.
8. As power increases, the probability of correctly rejecting the null hypothesis decreases.
9. If a researcher fails to reject then null hypothesis, then she must "accept" the null hypothesis.
10. A researcher will always know when she has made a Type I error.
11. If the p value is less than the alpha level, the null hypothesis should be rejected.
12. It is impossible to make a Type I error when you retain the null hypothesis.
13. If a researcher uses a one-tailed test, it will be easier for her to reject the null hypothesis than if she uses a two-tailed test, assuming the effect is in the predicted direction.
14. All else being equal, if the N in the sign test increases, it becomes easier to reject the null hypothesis.
15. In a binomial distribution with 15 trials, increasing the alpha level from .01 to .05 means that fewer of the possible particular outcomes (like number of trials correct) will allow rejection of the null hypothesis.
16. All else being equal, if a researcher reduces the likelihood of making a Type I error by reducing the value of alpha, then she is more likely to make a Type II error

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