Construct a 95% Confidence Interval for Comment Counts
Overview
This question evaluates understanding of statistical inference, specifically construction of a 95% confidence interval for a population mean, properties of the sampling distribution via the Central Limit Theorem, and computation and interpretation of the 95th percentile for skewed count data.
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Aug 4, 2025, 10:55 AM
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Comment Activity Analysis: Mean CI, Sampling Distribution, and 95th Percentile
Context
You have a simple random sample of users with their comment counts (non-negative integers, often right-skewed). You want to:
- Construct a 95% confidence interval (CI) for the population mean comments per user.
- Describe the sampling distribution of the sample mean and how sample size affects its variance.
- Compute and interpret the 95th percentile of the comment-count distribution.
Assume independent and identically distributed (i.i.d.) observations from a much larger population, and apply the Central Limit Theorem (CLT) where appropriate.
Tasks
- How do you construct a 95% CI for the population mean from the sample?
- What is the sampling distribution of the sample mean, and how does n affect its variance?
- How do you compute and interpret the 95th percentile of the comment distribution?
Solution
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