Statistics · Maths EE idea · Solid
How quickly does the central limit theorem kick in?
A research question to start from
How large must a sample be for the mean of skewed data to be approximately normal, and how does skewness affect the answer?
A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.
Why it works as a maths EE
Turns 'n ≥ 30' into a question you can investigate and argue about.
Mathematics you would need
- Sampling distributions
- Moment generating functions (or simulation)
- Skewness
- Measuring closeness of distributions
Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.
One possible line of attack
- Define a measure of how close a distribution is to normal.
- Compute sampling distributions for exponential and other skewed parents.
- Relate the required n to skewness and evaluate the rule of thumb.
Scope and difficulty
Solid. Solid.
Pitfalls
- Pictures without a measure.
- Treating 30 as a law.
Where to start reading
Search a library catalogue or a university's open lecture notes for: central limit theorem rate of convergence skewness; Berry-Esseen. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).