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
0 practiced
Explain the rule-of-thumb for when the sampling distribution of a sample proportion p-hat can be approximated by a normal distribution. State the conditions involving n and p, and give a short example to check validity: n = 200, observed p-hat = 0.02. Is the normal approximation reasonable here?
MediumTechnical
0 practiced
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.
EasyTechnical
0 practiced
You have a vector of sample means from repeated experiments. Explain how to interpret a Q-Q plot that compares these sample means to a theoretical normal distribution. What specific patterns in the Q-Q plot indicate approximate normality, light tails, heavy tails, or skewness?
HardTechnical
0 practiced
Sketch (no long formal derivation required) why maximum likelihood estimators (MLEs) are asymptotically normal. State the asymptotic variance in terms of the Fisher information and explain how the CLT underpins this result. Describe one implication for constructing confidence intervals for parameters estimated by MLE.
HardTechnical
0 practiced
A non-technical stakeholder interprets a 95% CI for average daily active users (DAU) as saying there is a 95% chance the true DAU lies within the interval. Draft a concise explanation (3-5 sentences) correcting this interpretation and propose three practical ways you would present uncertainty to reduce misinterpretation and support decision making.
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