Why this chapter matters
Inference depends on how sample statistics vary across repeated samples, and the CLT explains why normal-based methods often work.
What you will learn
- Differentiate a population distribution from a sampling distribution.
- Compute standard errors for sample means and proportions under assumptions.
- Use CLT conditions to justify approximate normal inference.
Lessons in this chapter
- Sampling distributionsDescribe the long-run distribution of a statistic across repeated samples.
- CLT for sample meansApply normal approximation to x-bar with known or estimated spread behavior. Read the full guide →
- Sampling distribution of p-hatUse success-failure checks and standard error for proportions.
- Interpreting standard errorConnect sample size changes to precision changes.
Study task
Compare standard errors for sample sizes 25, 100, and 400 from the same population standard deviation, and explain the pattern.
Chapter checkpoint
How does doubling sample size affect standard error for a mean?
Standard error scales by 1 over square root of n, so doubling n multiplies standard error by 1/sqrt(2), about 0.707.