Calculate Expected Comments and Confidence Interval Analysis
Overview
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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Aug 4, 2025, 10:55 AM
Data Scientist
Onsite
Statistics & Math
0
0
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.
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