Construct a 95% Confidence Interval for Comment Counts

Q: Construct a 95% Confidence Interval for Comment Counts

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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Question

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?

Construct a 95% Confidence Interval for Comment Counts

Comment Activity Analysis: Mean CI, Sampling Distribution, and 95th Percentile

Context

Tasks

Solution

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