Q: What is the difference between CI, PI, and TI? A: CI estimates the mean, PI predicts a new value, and TI covers most of the population with a specific confidence level.
Q: When do we use z vs. t in the CI formula? A: Use z if σ (population SD) is known or n is large (≥ 30); use t if σ is unknown and n is small.
Q: What is the margin of error? A: It’s the amount added/subtracted from the sample mean to build a confidence interval. It shrinks as sample size increases.
Q: What does 95% confidence really mean? A: If you repeated your sampling many times, 95% of those intervals would contain the true population mean μ.
Q: Why is k (TI) larger than t or z? A: Because tolerance intervals cover most individual values, not just the mean. It requires wider bounds to include that range.
Q: Why do we rarely use CI for variance in finance? A: Most financial models focus on estimating parameters (like regression coefficients), not σ². But in engineering, it's more common.