For a given confidence level and when σ is known, the margin of error in a confidence interval estimate
A) varies from sample to sample of the same size.
B) is the same for all samples of the same size.
C) increases as the sample size increases.
D) is independent of sample size.

Question

For a given confidence level and when σ is known, the margin of error in a confidence interval estimate
A) ​varies from sample to sample of the same size.
B) ​is the same for all samples of the same size.
C) ​increases as the sample size increases.
D) ​is independent of sample size.

Quizplus · Accepted Answer

When σ is known, the margin of error in a confidence interval estimate is calculated as follows: ME=z*σ/√n, where z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size. Since z and σ are constants for a given confidence level, the margin of error will be the same for all samples of the same size.

For a Given Confidence Level and When σ Is Known