Narrow a confidence interval for a mean
Company: Google
Role: Data Scientist
Category: Statistics & Math
Difficulty: Medium
Interview Round: Technical Screen
You have a simple random sample with n = 100 and sample mean 100. The current 95% CI for the population mean is 100 ± 10, which a PM says is too wide. a) If you increase n to 10,000 and the sample standard deviation s is unchanged, compute the new 95% CI half‑width exactly and explain the 1/√n scaling. b) Without increasing n, list and justify at least four specific levers to narrow the CI (e.g., change confidence level α, reduce variance via paired designs/blocking/stratification, reduce measurement noise, transform the outcome), and explain trade‑offs/risks for each. c) Under what assumptions is tightening the CI by raising α misleading, and how would you communicate that risk to non‑statisticians?
Quick Answer: This question evaluates understanding of confidence intervals, the relationship between sample size and interval width, variance-reduction techniques, the impact of changing confidence levels, and the ability to communicate statistical risk and design-based trade-offs.