Calculate Expected Comments and Confidence Interval Analysis

Q: Calculate Expected Comments and Confidence Interval Analysis

This question evaluates a data scientist's competency in statistical estimation and inference—specifically expectation of a count variable, sampling distributions and the Central Limit Theorem, choice between population and sample standard deviation, and construction and interpretation of confidence intervals.

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Question

Scenario

You are analyzing the distribution of comment counts per post for a social platform feature over a fixed time window. Let X be the random variable representing the number of comments on a post in this window. You either have a sample of n posts (sampled from all posts in the window) or access to the full population of posts in that window.

Tasks

Compute/define the expected value of the number of comments per post.
State the Central Limit Theorem (CLT) and explain its relevance to estimating the mean comments per post.
Explain when to use population standard deviation versus sample standard deviation for comment counts.
Construct and interpret a 95% confidence interval for the mean comments per post, stating assumptions, formulas, and any sample size requirements. Include brief derivations.

Calculate Expected Comments and Confidence Interval Analysis

Scenario

Tasks

Solution

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