# Graduate Statistics

3. Explain in your own words why it is important to know the possible errors we might make when rejecting or failing to reject the null hypothesis.

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:

Subject Bar 1 Bar 2

1 20 40

2 18 25

3 24 38

4 14 27

5 5 31

6 26 21

7 15 32

8 29 38

9 15 25

10 9 18

11 25 32

12 31 28

a. 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.

b. What is the null hypothesis?

c. Using α = 0.052 tail, what is your conclusion?

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

e. To what population does your conclusion apply?

13. A researcher is interested in determining whether acupuncture affects pain tolerance. An experiment is performed in which 15 students are randomly chosen from a large pool of university undergraduate volunteers. Each subject serves in two conditions. In both conditions, each subject receives a short-duration electric shock to the pulp of a tooth. The shock intensity

is set to produce a moderate level of pain to the unanesthetized subject. After the shock is terminated, each subject rates the perceived level of pain on a scale of 0–10, with 10 being the highest level. In the experimental condition, each subject receives the appropriate acupuncture treatment prior to receiving the shock. The control condition is made as similar to the experimental condition as possible, except a placebo treatment is given instead of acupuncture. The two conditions are run on separate days at the same time of day. The pain ratings in the accompanying table are obtained.

a. What is the alternative hypothesis? Assume a non-directional hypothesis is appropriate.

b. What is the null hypothesis?

c. Using α = 0.052 tail, what is your conclusion?

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

e. To what population does your conclusion apply?

Subject Acupuncture Placebo

1 4 6

2 2 5

3 1 5

4 5 3

5 3 6

6 2 4

7 3 7

8 2 6

9 1 8

10 4 3

11 3 7

12 4 8

13 5 3

14 2 5

Chapter 12:

3. How are sampling distributions generated using the empirical sampling approach?

5. What are the assumptions underlying the use of the z test?

8. How do each of the following differ?

a. s and s

b. s² and σ²

c. µ and µ

d. σ and σ

16. How does increasing the N of an experiment affect the following?

a. Power

b. Beta

c. Alpha

d. Size of real effect

20. A set of sample scores from an experiment has an N = 30 and an obt = 19.

a. Can we reject the null hypothesis that the sample is a random sample from a normal population with µ = 22 and σ = 8? Use α = 0.011 tail. Assume the sample mean is in the correct direction.

b. What is the power of the experiment to detect a real effect such that µreal = 20?

c. What is the power to detect a µreal = 20 if N is increased to 100?

d. What value does N have to equal to achieve a power of 0.8000 to detect a µreal = 20? Use the nearest table value for zobt.

21. On the basis of her newly developed technique, a student believes she can reduce the amount of time schizophrenics spend in an institution. As director of training at a nearby institution, you agree to let her try her method on 20 schizophrenics, randomly sampled from your institution. The mean duration that schizophrenics stay at your institution is 85 weeks, with a standard deviation of 15 weeks. The scores are normally distributed. The results of the experiment

show that the patients treated by the student stay a mean duration of 78 weeks, with a standard deviation of 20 weeks.

a. What is the alternative hypothesis? In this case, assume a non-directional hypothesis is appropriate because there are insufficient theoretical and empirical bases to warrant a directional hypothesis.

b. What is the null hypothesis?

c. What do you conclude about the student’s technique? Use α = 0.052 tail.

25. A physical education professor believes that exercise can slow the aging process. For the past 10 years, he has been conducting an exercise class for 14 individuals who are currently 50 years old. Normally, as one ages, maximum oxygen consumption decreases. The national norm for maximum oxygen consumption in 50-year-old individuals is 30 milliliters per kilogram per minute, with a standard deviation of 8.6. The mean of the 14 individuals is 40 milliliters per kilogram per minute. What do you conclude? Use α = 0.051 tail.

References

Academic Web Services (n.d.). The Visual Learner – Statistics. Retrieved from: http://lc.gcumedia.com/hlt362v/the-visual-learner/the-visual-learner-v2.1.html.

Pagano, R. (2013). Understanding Statistics in the Behavioral Sciences (10th ed.). Wadsworth-Cengage Learning