Linear Regression Hypothesis Testing: Linear regression is a versatile tool for modeling relationships between variables. Hypothesis testing in linear regression helps us determine whether the relationships we observe are statistically significant. Share an example of a real-world scenario where hypothesis testing in linear regression could be valuable. Explain how you would formulate null and alternative hypotheses in this context and discuss the potential implications of your findings.

One-Way ANOVA Hypothesis Testing: One-way ANOVA is used to compare means across multiple groups or categories. Think about a research question where you might need to perform a one-way ANOVA. Describe the null hypothesis, alternative hypothesis, and the significance level you would choose. How would you interpret the results if you found significant differences between the groups? Additionally, consider the post-hoc tests that are often conducted after ANOVA. When and why might these tests be necessary?

Comparing Hypothesis Testing Methods: Compare and contrast hypothesis testing in one-way ANOVA and two sample means. What are the similarities and differences in terms of the underlying principles, assumptions, and practical applications? Discuss situations where you might choose one method over the other to answer specific research questions