20 May Please define each of the following terms and pr

TASK1:

Answer the following with examples. Include peer-reviewed references.

Topics:

Chapter 9: “Hypothesis Test” 

Chapter 10: “Inference about Means and Proportions with Two Populations” 

Chapter 11: “Inference About Population Variances”

· Please define each of the following terms and provide a hypothetical example for each: hypothesis testing, null and alternative hypothesis, non-directional and directional hypothesis, type I error in testing a hypothesis, type II error in testing a hypothesis, probability of type I error (ɑ), probability of type II error (ß), power of the test and its significance, the critical value(s) in a test, p value (significance level).

· What is the difference between testing a hypothesis on a population and testing a hypothesis when comparing two populations? Provide hypothetical examples.

· What are the possible outcomes in testing a hypothesis? 

· What are the determinant factors in deciding the critical value(s) in testing a hypothesis?

· When is it appropriate to use the z statistic to test a hypothesis? 

· When is it appropriate to use the t statistic to test a hypothesis? 

· For each case, include the underlying assumptions, and the test statistic, for both testing a hypothesis on the mean of population, and testing hypothesis in comparing the value of the mean in a population with the value of the mean in another population. 

· What is the criterion for rejecting the null hypothesis for both non-directional and directional tests?

· How do you find the p value in each case? 

· Do not forget to discuss cases that involve proportion(s). 

· When is the chi squared statistic used to test hypotheses? Include underlying assumptions and the test statistic for testing hypotheses on a single population. 

· What is the criterion for rejecting the null hypothesis for both non-directional and directional tests? 

· How do you find the p value in each case?

TASK2:

Develop 8 page APA formatted paper.

Include Abstract, Introduction, Several Pragraphs, Tables, Conclusion and include 8 peer-reviewed references.

Please provide complete solutions to the following problems. Explain your work in detail and justify the use of the statistic in each case. You may start with a non-directional test and then do a directional test if applicable.

1. Problems 64 and 72 in the Supplementary Exercises presented at the end of Chapter 9.

2. Problems 41 and 44 in the Supplementary Exercises presented at the end of Chapter 10. In problem 41 you may assume that the distribution of data is normal.

3. Problem 27 in the Supplementary Exercises presented at the end of Chapter 11.

TASK3:

Answer the following with examples. Include peer-reviewed references.

Topics:

Chapter 13: Experimental Design and Analysis of Variance

· Explain how the F distribution is constructed by combining two chi squared distributions. 

· What are the properties of the F distribution? 

· Explain the objectives of ANOVA and how it is formulated. 

· What are the underlying assumptions? 

· What is the sum of the squares of errors and mean sum of squares of errors in ANOVA? 

· What is the test statistic in ANOVA? 

· What is the criterion for rejecting the null hypothesis? 

· How is the p value determined in an ANOVA formulation? 

· Provide a hypothetical example of ANOVA formulation.

· What is the objective of Fisher's post-hoc test? 

· How is it formulated? 

· Are they non-directional or directional tests? 

· What is the test statistic in Fisher’s test? 

· What are the expected outcomes of Fisher’s test?   

TEXTBOOK: Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., & Cochran, J. J. (2020). Statistics for business & economics (14th ed.). Cengage Learning