Analyze Central Limit Theorem in User Comment Distribution

Q: Analyze Central Limit Theorem in User Comment Distribution

This question evaluates competence in inferential statistics — specifically the Central Limit Theorem, expectation estimation, the distinction between population and sample standard deviation, and construction of 95% confidence intervals for a per-user comment metric in the Statistics & Math domain.

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Question

Comments per User — CLT, Expectation, SD, and 95% CI

Context

You are measuring how many comments each user makes in a fixed time window (e.g., one week). Let X be the random variable "number of comments made by a randomly selected user in that window." You sample n users uniformly at random and record X1, X2, …, Xn.

Tasks

Central Limit Theorem (CLT): Explain how it applies to the sample mean of comments per user.
Expected Value: Define E[X] and explain how to compute/estimate the expected number of comments across all users.
Population vs. Sample Standard Deviation: Differentiate σ (population) from s (sample) in this context.
95% Confidence Interval: Construct a 95% CI for the mean number of comments.

Analyze Central Limit Theorem in User Comment Distribution

Comments per User — CLT, Expectation, SD, and 95% CI

Context

Tasks

Solution

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