What are some common assumptions that underlie hypothesis testing for paired data, multiple population means, and variance comparisons? Discuss the potential consequences of violating these assumptions and suggest possible remedies. Additionally, provide examples of situations where each of these statistical tests may be appropriate, and explain why. Finally, what are some practical limitations or considerations when interpreting the results of these tests? How can Python be used to develop a useful tool in this context?

Prepare your answer as follows:

Provide a professionally written answer, anchored in scholarly work.

Create a diagram, table, or other visual prop to help explain your answer and include $12$sentences describing the visual.

Include a Jupyter notebook with the relevant Python code you created.

Record a short $2-$ to $3-$minute video $($using tools like Zoom or Loom$)$ in which you explain your answer and code. Use an online video platform such as Loom, YouTube, or Vimeo to upload your completed video. Include the link to the video in your answer.