1. Critique the following statement. Indicate whether it is true or false and explain the rationale for your answer. (3 points)

A statement that "the 95% confidence interval for the population mean is (275, 325)" means that 95% of the population values are between 275 and 325.

2. As a research project a statistics student wants to construct a 95% confidence interval for the mean height of students enrolled at Maricopa College. She knows that heights are normally distributed with a standard deviation of 4 inches. What is the minimum sample size needed to ensure the margin of error does not exceed 0.5 inches? Include the calculations in your answer. (3 points)

3. When would it be appropriate to use a t-interval instead of a z-interval to determine a confidence interval? What makes t the better choice in this instance?

4. Identify the three components of a Confidence Interval. Explain what each represents and the relationship between them.

5. Describe a potential issue with public opinion polls that fail to include a margin of error when reporting the results. Why is it important to include that information?

6. What are the assumptions that need to be satisfied in order to use a t-test to test the significance of an observed difference between a known population mean and the mean of a set of sample data?

7. Summarize the similarities and differences between the critical value approach and the p-value approach to hypothesis testing. What information does the p-value approach provide that may be lacking when using the critical value approach?

8. Given a statistically significant outcome and rejection of the null hypothesis, why is the alternative hypothesis then said to be "supported" but is not said to be "proven"?

9. Why does "statistical significance" not necessarily also indicate "practical significance"? What is the difference between them?

10. Give an original example showing how a one-sample test of a population proportion could be used to answer a research question. Provide a brief summary of the research scenario, being sure to identify both the independent and dependent variables, and correctly state the null and alternative hypotheses in both words and symbols.

11. Assume you've conducted a statistical test and found a statistically significant difference between the means of two groups. Why is it important to also report the effect size?

12. Use an original example to illustrate the difference between a Type I error and a Type II error.

13. Use original examples to distinguish between a "between-subjects" design and a "within-subjects" design. Explain how participants might be selected in each case.

14. Explain what is meant by power of a statistical test. Why do researchers generally want to have maximum power in their tests, i.e., why does it matter?

15. Give an original example showing how a test of means with two independent samples could be used to answer a research question. Provide a brief summary of the research scenario, being sure to identify both the independent and dependent variables, and correctly state the null and alternative hypotheses in both words and symbols.

16. Describe the issue that would arise if several t-tests were used to conduct pairwise comparisons of three or more means. Why is ANOVA the better choice in this case?

17. Analysis of variance, as the name suggests, analyzes variance estimates in order to draw conclusions about differences between means. What is the logic for this? I.e., how does looking at variances lead to a decision about means?

18. How does a two-way ANOVA differ from a one-way ANOVA? What additional information does a two-way ANOVA provide the researcher?

19. Provide an original example of a research question that could be answered by a one-way ANOVA. Identify the independent and dependent variables and explain why the scenario is appropriate for a one-way ANOVA.

20. Provide an original example of a research question that could be answered by a two-way ANOVA. Identify the independent and dependent variables and explain why the scenario is appropriate for a two-way ANOVA.