NORTHCENTRAL UNIVERSITY

Course: EDR7101

Instructor: Dr. Wallace

Assignment 5: Week 5 Word Problems

Gregory Nelson

Problem Set Week 5 Chapters 7 & 8

2.) Describe the distribution of the sample means (shaped expected standard value and standard error) for sample of n = 36 selected from a population with a mean of u = 100 and standard deviation of Q = 12.

By the central limit theorem we know that the sample mean X bar will be approximately normal with the mean of the random variable X, , and standard deviation /n. for a value of the approximation will be excellent. Hence X bar will be bell-shaped with and x bar / (which is it's standard error).

6.) For a population mean of u = 70 and standard deviation of Q = 20 how much error, on average would you expect between the sample mean (M) and the population mean for each of the sample size?

1. n = 4 scores
2. n = 16 scores
3. n = 25 scores

Additional Items:

1. Many novice researchers have the understanding as sample size increases the standard deviation decreases. Use the Central Limit Theorem and the definition of parametric values to concisely explain why this understanding by novice researchers is false.
2. Often a sample mean is reported +/- the standard deviation. Instead of the standard deviation, the value reported should be the standard error of the mean. Concisely explain why the standard error of the mean is a more appropriated value to report in this case. Chapter 8:4.) If the alpha level is change from @ = .05 to @ = .01,
3. What happens to the boundaries for the critical region?
4. What happens to the probability of a type I error?

6.) Childhood participation in sports, cultural groups and youth groups appears to be related to improved self esteem for adolescents (McGee, Williams, Howden Champman, Martin, & Kawachi, 2006). In a representative study, a sample of n = 100 adolescents with a history of group participation is given a standardized self esteem questionnaire. For the general population of adolescents, scores on questionnaire form a normal distribution with a mean of u = 40 and a standard deviation of Q = 12. The sample of the group participation adolescents had an average of M = 43.84.

1. Does this sample provide enough evidence to conclude that the self esteem scores for these adolescents are significantly different from those of the general population? Use a two tailed test with @ = .01.
2. Compute Cohens d to measure the size of the difference.
3. Write a sentence describing the outcome of the hypothesis test and the measure of effect size as it would appear in a research report.

10.) Miller (2008) examined the energy drink consumption of college undergraduate and found that male uses energy drinks significantly more than females. To further investigate this phenomenon, suppose that a research selects a random sample of n = 36 male undergraduates and a sample of n = 25 females. On average, the male reported consuming M = 1.28. Assume that the overall level of consumption for college undergraduates averages u = 1.85 energy drinks per month, and the distribution of the monthly consumption scores is approximately normal with standard deviation of Q = 1.2.

1. Did the sample of males consume significantly more energy drinks than the overall population average? Use the one tailed test with @ = .01.
2. Did the sample of females consume significantly fewer energy drinks than the overall population average? Use the one tailed test with @ = .01.

14.) A psychologist is investigating the hypothesis that children who grew up as the only child in the household develop different personality characteristics than those who grew up in larger families. A sample of n = 30 only children is obtained and each child is given a standardized personality test. For the general population, scores on a test from a normal distribution with a mean of u = 50 and a standard deviation of Q = 15. If the mean for the sample is M = 58, can the research conclude that there is a significant difference in personality between only children and the rest of the population? Used a two tailed test with @ = .05.

20.) Briefly explain how increasing sample size influences each of the following. Assume that all other factors or held constant.

1. The size of the z - score in a hypothesis test.
2. The size of Cohens d.
3. The power of a hypothesis test.

Additional Item:

1. Chapter 8 is crucially important for the understanding of most of the rest of this course. Too often students focus on the calculations and not the underlying concepts and principles. Please write a narrative indicating an understanding of the underlying process of hypothesis testing. Do not focus on the calculation of z-testing but rather the fundamentals of hypothesis testing. Be sure to address the following topics:
2. the four fundamental steps in hypothesis testing,
3. type I and type II errors, the relationship of alpha to type I and type II errors,
4. the critical regions (how it is established and how it relates to alpha), and
5. the decision, effect size, and how related to hypothesis testing and power.

References

Gravetter, F. J., & Wallnau, L. B. (2013).Statistics for the behavioral sciences (9th Ed.).Belmont, CA: Wadsworth Cengage Learning