Central Limit Theorem (CLT) and Normal Distribution Questions
Understand the CLT: when you take multiple random samples and calculate their means, those sample means are normally distributed (bell-shaped) even if the underlying data isn't. Know that normal distribution is parameterized by mean and standard deviation. Appreciate why this matters: it allows you to estimate population characteristics from samples and construct confidence intervals.
EasyTechnical
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Define standard error in the context of estimating a population mean. Explain how the standard error differs from the sample standard deviation and how the standard error changes with sample size. Give a short numeric example: if sample sd = 10 and n = 25, compute the standard error and interpret it.
MediumTechnical
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Explain the finite population correction (FPC) factor and when it should be applied. Given a population of N = 5,000 users and a sample without replacement of n = 2,500 users, show how the standard error of the sample mean changes when applying FPC, assuming sample sd = 20.
MediumTechnical
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Design a small dashboard or slide for a non-technical stakeholder that demonstrates the CLT using company transaction data. Specify the plots and interactive elements you would include (e.g., slider for sample size), what each element communicates, and how you would explain the practical implications for estimating average transaction value.
MediumTechnical
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You run an A/B test to compare conversion rates: control has 200 conversions out of 10,000 visitors, treatment has 250 conversions out of 10,000 visitors. Using the CLT (normal approximation), compute the z-score and two-sided p-value for the difference in proportions. Then discuss whether the normal approximation is appropriate here and any caveats a data scientist should communicate.
HardTechnical
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The data you analyze appear to follow a Pareto distribution with tail exponent alpha ≈ 1.7 (so variance is infinite). Explain why the standard CLT does not apply and propose alternate inference strategies for estimating a central tendency and quantifying uncertainty in this setting.
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