# Population Variances

## Inference About Population Variances

__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 Pagraphs, 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.

- Problems 64 and 72 in the Supplementary Exercises presented at the end of Chapter 9.
- 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.
- 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*(14

^{th}ed.). Cengage Learning