Construct a 95% Confidence Interval for Comment Counts

Quick Overview

This interview question evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer for Construct a 95% Confidence Interval for Comment Counts states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

Construct a 95% Confidence Interval for Comment Counts

Company: Meta

Role: Data Scientist

Category: Statistics & Math

Difficulty: medium

Interview Round: Onsite

##### Scenario You are analyzing comment activity to distinguish between genuine users and potential fake accounts. ##### Question Given a sample of comment counts per user, how would you construct a 95% confidence interval for the population mean? What is the sampling distribution of the sample mean and how does sample size affect its variance? How do you compute and interpret the 95th percentile of the comment distribution? ##### Hints Apply the Central Limit Theorem, standard-error = σ/√n, and percentile definition to articulate assumptions and impact of sample size.

Quick Answer: This interview question evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer for Construct a 95% Confidence Interval for Comment Counts states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

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Aug 4, 2025, 10:55 AM
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Construct a 95% Confidence Interval for Comment Counts

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:

  1. Construct a 95% confidence interval (CI) for the population mean comments per user.
  2. Describe the sampling distribution of the sample mean and how sample size affects its variance.
  3. 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

  1. How do you construct a 95% CI for the population mean from the sample?
  2. What is the sampling distribution of the sample mean, and how does n affect its variance?
  3. How do you compute and interpret the 95th percentile of the comment distribution?

Clarifying Questions to Ask Guidance

  • Clarify the random variables, distributional assumptions, independence assumptions, and desired output.
  • Show enough derivation for the interviewer to follow the reasoning.
  • Explain how you would validate the result with simulation or sensitivity checks.

What a Strong Answer Covers Guidance

  • A correct setup with definitions, formulas, and boundary conditions.
  • A step-by-step derivation or estimation plan.
  • Interpretation of the result, including uncertainty and practical limitations.
  • Checks for assumptions, edge cases, and numerical stability.

Follow-up Questions Guidance

  • How would the result change if the assumptions were relaxed?
  • Can you verify the answer with a simulation?
  • What is the most likely source of estimation error?
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