## PSY 520 Graduate Statistics Assignments GCU

### Module 5 Exercises

#### Grand Canyon University: PSY-520: Graduate Statistics 2014 Chapter 10:

- 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.
- 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 was conducted in which 12 rhesus monkeys were randomly selected from the university colony and taught me 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, assuming 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 ? = 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?

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 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 ? = 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:

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 ?²

c. µ and µ

d. ? and ?

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 ? = 8? Use ? = 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.

- What is the alternative hypothesis? In this case, assuming a non-directional hypothesis is appropriate because there are insufficient theoretical and empirical bases to warrant a directional hypothesis.
- What is the null hypothesis?
- What do you conclude about the student’s technique? Use ? = 0.052 tail.

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 ? = 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.

#### PSY 520 Week 1 Discussion 1 Latest-GCU

Review the levels of measurement terms in the Statistics Visual Learner media piece. Compare and contrast Stevens’s four scales of measurement, and explain when each type of scale should be used.

#### PSY 520 Week 1 Discussion 2 Latest-GCU

The professor teaching a large introductory class gives a final exam that has alternate forms, A, B, and C. A student taking the exam using Form B is upset because she claims that Form B is much harder than Forms A and C. Discuss how percentile point data might be useful to determine if the student is correct.

#### PSY 520 Week 2 Discussion 1 Latest-GCU

The process of random sampling guarantees that the sample selected will be representative of the population. Is this statement true? Discuss.

#### PSY 520 Week 2 Discussion 2 Latest-GCU

Review the video on Normal Distribution in the Calculations section of the Statistics Visual Learner media piece.

Bob compares his SAT Verbal score of 400 to Marge’s ACT Verbal score of 20. I beat you, he exclaims.

My score is 20 times your score! Although his multiplication is good, his logic is faulty. Explain why.

#### PSY 520 Week 3 Discussion 1 Latest-GCU

Review the video Linear Correlation in the Calculations section of the Statistics Visual Learner media piece.

It is sometimes said that the higher the correlation between two variables, the more likely the relationship is causal. Do you think this is correct Discuss?

#### PSY 520 Week 3 Discussion 2 Latest-GCU

Discuss the strengths and weaknesses of correlational and regression studies; discuss concepts such as positive and negative correlations, correlation coefficients, confounding, and causality.

#### PSY 520 Week 4 Discussion 1 Latest-GCU

Explain why there is an inverse relationship between committing a Type I error and committing a Type II error. What is the best way to reduce both kinds of error?

#### PSY 520 Week 4 Discussion 2 Latest-GCU

Review the term Significance Test in the Statistics Visual Learner media piece.

When a newspaper or magazine article reports the results of a study and draws a conclusion without also reporting whether the results are statistically significant, what are the possible reasons for doing so? How seriously should you take the conclusion offered in such a study?

#### PSY 520 Week 5 Discussion 1 Latest-GCU

Explain why using the t statistic may be an appropriate alternative to using a z-score (use the concept of estimated standard error to justify your answer).

#### PSY 520 Week 5 Discussion 2 Latest-GCU

Discuss how the t-test for correlated groups and the t-test for single samples are alike and different.

#### PSY 520 Week 6 Discussion 1 Latest-GCU

Review the four ANOVA videos in the Calculations section of the Statistics Visual Learner media piece.

Explain the major differences between analyzing a one-way ANOVA versus a two-factor ANOVA, and explain why factorial designs with two or more independent variables (or factors) can become very difficult to interpret.

#### PSY 520 Week 6 Discussion 2 Latest-GCU

Explain how the ANOVA technique avoids the problem of the inflated probability of making Type I error that would arise using the alternative method of comparing groups two at a time using the t-test for independent groups.

#### PSY 520 Week 7 Discussion 1 Latest-GCU

Review the three Non-parametric test videos in the Calculations section of the Statistics Visual Learner media piece.

A researcher is examining preferences among four new flavors of ice cream. A sample of n = 80 people is obtained. Each person tastes all four flavors and then picks a favorite. The distribution of preferences is as follows. Do these data indicate any significance preferences among the four flavors Test at the .05 level of significance?

Ice Cream Flavor | |||

A | B | C | D |

12 | 18 | 28 | 22 |

#### PSY 520 Week 7 Discussion 2 Latest-GCU

Is it true that parametric tests are generally more powerful than nonparametric tests? If so, give two reasons why you might choose to use a nonparametric test instead of a parametric test.

#### PSY 520 Week 8 Discussion 1 Latest-GCU

To determine whether a new sleeping pill has an effect that varies with dosage, a researcher randomly assigns adult insomniacs, in equal numbers, to receive either 4 or 8 grams of the sleeping pill. The amount of sleeping time is measured for each subject during an 8-hour period after the administration of the dosage. What type of design is this, and what type of statistic is needed to analyze the data?

#### PSY 520 Week 8 Discussion 2 Latest-GCU

Dr. Bill Board designs a 2 X 2 between-subjects factorial design, where Factor A is word frequency (low or high) and Factor B is category cues (no queues or cues). Assume that the data are intervals. What type of statistic is needed to analyze the data?

#### PSY 520 Week 2 Exercise Latest-GCU

Details:

Complete the following exercises from Review Questions located at the end of each chapter and put them into a Word document to be submitted as directed by the instructor.

- Chapter 1, numbers 1.8 and 1.9
- Chapter 2, numbers 2.14, 2.17, and 2.18
- Chapter 3, numbers 3.13, 3.14, 3.18, and 3.19
- Chapter 4, numbers 4.9, 4.14, 4.17, and 4.19

Show all relevant work; use the equation editor in Microsoft Word when necessary.

#### PSY 520 Week 3 Probability Project Latest-GCU

Details:

Use the document “Probability Project” to complete the assignment.

While APA format is not required for the body of this assignment, solid academic writing is expected, and documentation of sources should be presented using APA formatting guidelines, which can be found in the APA Style Guide, located in the Student Success Center.

#### Topic 3 – Probability Project

Directions

Use the following information to complete the assignment. While APA format is not required for the body of this assignment, solid academic writing is expected, and documentation of sources should be presented using APA formatting guidelines, which can be found in the APA Style Guide, located in the Student Success Center. PSY 520 Graduate Statistics Essay Assignments

There are many misconceptions about probability which may include the following.

- All events are equally likely
- Later events may be affected by or compensate for earlier ones
- When determining probability from statistical data, sample size is irrelevant
- Results of games of skill are unaffected by the nature of the participants
- “LuckyUnlucky” numbers can influence random events
- In random event involving selection, results are dependent on number rather than rations
- If events are random then the results of a series of independent events are equally likely

The following statements are all incorrect. Explain the statements and the errors fully using the probability rules discussed in topic two.

- I have flipped an unbiased coin three times and got heads, it is more likely to get tails the next time I flip it.
- The Rovers play Mustangs. The Rovers can win, lose, or draw, so the probability that they win is 13.
- I roll two dice and add the results. The probability of getting a total of 6 is 112 because there are 12 different possibilities and 6 is one of them.
- Mr. Purple has to have a major operation. 90% of the people who have this operation make a complete recovery. There is a 90% chance that Mr. Purple will make a complete recovery if he has this operation.
- I flip two coins. The probability of getting heads and tails is 13 because I can get Heads and Heads, Heads and Tails, or Tails and Tails.
- 13 is an unlucky number so you are less likely to win raffles with ticket number 13 than with a different dumber.

#### PSY 520 Week 3 Exercise Latest-GCU

Details

Complete the following exercises located at the end of each chapter and put them into a Word document to be submitted as directed by the instructor.

Show all relevant work; use the equation editor in Microsoft Word when necessary.

- Chapter 6, numbers 6.7, 6.10, and 6.11
- Chapter 7, numbers 7.8, 7.10, and 7.13

#### PSY 520 Week 4 Exercise Latest-GCU

Details:

Complete the following exercises located at the end of each chapter and put them into a Word document to be submitted as directed by the instructor.

Show all relevant work; use the equation editor in Microsoft Word when necessary.

- Chapter 9, numbers 9.7, 9.8, 9.9, 9.13, and 9.14
- Chapter 10, numbers 10.9, 10.10, 10.11, and 10.12
- Chapter 11, numbers 11.11, 11.19, and 11.20
- Chapter 12, numbers 12.7, 12.8, and 12.10