Question 1

What is a confidence interval?

Accepted Answer

A confidence interval is a range of values that likely contains the true population parameter. A 95% CI means if you repeated the sampling 100 times, about 95 of those intervals would contain the true value.

Question 2

What is the formula for a confidence interval?

Accepted Answer

For a mean: CI = x̄ ± Z × (σ/√n). For a proportion: CI = p̂ ± Z × √(p̂(1-p̂)/n). Where Z is the z-score for your confidence level, σ is the standard deviation, and n is the sample size.

Question 3

When should I use z-distribution vs t-distribution?

Accepted Answer

Use the z-distribution when the sample size is large (n ≥ 30) or the population standard deviation is known. Use the t-distribution for small samples (n < 30) with unknown population standard deviation.

Question 4

How do I interpret a 95% confidence interval?

Accepted Answer

A 95% confidence interval means you are 95% confident that the true population parameter falls within the calculated range. It does NOT mean there is a 95% probability the true value is in the range.