Asked by Robert Schofield on Jul 05, 2024
Verified
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.
Confidence Interval
A stretch of numerical indicators, obtained from sample statistics, envisaged to hold the secret value of a population characteristic.
Margin of Error
An expression of the amount of random sampling error in a survey's results, indicating a confidence interval within which the true value lies.
σ
Symbol representing the standard deviation of a population in statistics.
- Absorb the mechanisms by which sample size and confidence levels dictate the margin of error and the construction of confidence intervals for population means and proportions.
Verified Answer
VV
Valerie ValadezJul 12, 2024
Final Answer :
B
Explanation :
When σ is known, the margin of error is based on the sample size and the confidence level, and is independent of the population size or variability. Therefore, the margin of error would be the same for all samples of the same size and the same confidence level.
Learning Objectives
- Absorb the mechanisms by which sample size and confidence levels dictate the margin of error and the construction of confidence intervals for population means and proportions.