Minimum sample size
Work back from the precision you need to n; since it is a minimum, always round up.
Worked example
How large must the sample be so that the 99% confidence interval for μ is at most ±3.0 wide? σ = 5, z = 2.576.
Worked solution
- 1.n ≥ (z · σ / E)² = (2.576 · 5 / 3.0)² = 18.43
- 2.Round up: n = 19
Typical mistake: Rounding down; a minimum size is always rounded up.
Your turn
Three problems of exactly this type, each time with new numbers. Comma or point; fractions like 1/6 work too.
Task
How large must the sample be so that the 99% confidence interval for μ is at most ±1.5 wide? σ = 15, z = 2.576.
Minimum n
Comma or point; fractions like 1/6 work too.
Formulas for this topic
- σ known: x̄ ± z · σ / √n
- σ unknown: x̄ ± t(n − 1) · s / √n
- Minimum n for margin E: n ≥ (z · σ / E)², round up
Typical mistake: Rounding down; a minimum size is always rounded up.
Frequently asked questions
What is the typical mistake in "Minimum sample size"?
Rounding down; a minimum size is always rounded up.
When do I use t instead of z?
When σ is unknown and estimated by s from the sample, especially for small samples.