The margin of error refers to the 95% confidence interval of a poll, and provides a false sense of reliability of a poll since one out of twenty times the true value will lie outside the confidence interval. From: Encyclopedia of Social Measurement,
2005
Stephen C. Loftus, in
Basic Statistics with R, 2022The idea of interval estimates
12.5 Creating confidence intervals
Generally speaking, our confidence intervals for our parameters will be of the form
Point Estimate ± Margin of Error similar to the interval estimates we talked about above. While the exact form of our confidence intervals will vary depending on what parameter we are doing confidence intervals for, we can see the process of making confidence intervals and how they are connected to the probability of being “right.” Specifically, we will look at this through calculating our confidence interval for the population proportion p.
For our confidence interval to be “right” [1−α]100% of the time, we need the interval to have a lower bound and upper bound calculated from our sample such that
P[Lower