Example ① How can you make a confidence interval narrower?
Solution:① Increase n (sample size). ② If there is no way to reduce σ, ① is the standard approach.
When n is multiplied by 4, the interval width becomes 1/2.
Solution:① Increase n (sample size). ② If there is no way to reduce σ, ① is the standard approach.
When n is multiplied by 4, the interval width becomes 1/2.
Key Point
- Error is proportional to σ/√n: quadrupling the sample halves the error
Practice Problems
- What happens to the confidence-interval width when the sample increases from 100 to 400?
Solutions and Explanations
- Solution:It becomes 1/2 as wide