Question

Briefly describe the conflict between confidence level and margin of error when constructing a confidence interval for a population mean from a sample. How do you resolve this conflict?

Answer 1

Confidence level is nothing but the probability that a result is significant. Using this confidence level we generally construct the condfidence limits. This level determines the distance for how close the confidence limits are to sample mean when we are going to find out an interval estimate of the true population mean.

The Ci is of the form In that case the margin of error is

where =1-confidence level, known, = upper the quantile of N(0,1).

Evidently keeping fixed, if we increase confidence level then becomes smaller resulting in larger . Hence the CI will be wider, which is quit sensible since the confidence probability of true mean to be included within that CI becomes larger.

Here generally we take confidence level=95%. and accordinglu=y we find the margin of error and the CI