Therefore, while intervals may vary from sample to sample and we do not know exactly where they lay in relation to the true popluation mean, we can at least have a certain degree of confidence that any sample has the possibility to be within the parameters of the popluation mean. Whether it does or does not can only be given confidence, not definition. Margin or error expands a point estimate to create the parameters of a confidence interval of the population mean. The margin of error provides more information about the possibility of an interval coming within certain proximity of the true mean. The margin of error requires specific calculation but ultimately defines the parameters of a confidence interval.
Margin of error involves sample size, standard deviation and z-score.
The larger the sample size, the lower the margin of error and therefore the shorter the confidence interval - this is the ideal relationship. The standard deviation of a sample size calculated with a z-score offers the margin of error. The margin of error is the arrangement of variables to support and contruct a confidence interval. When someone either computes or is given a confidence interval, another value can be compared to it to see what the likelihood is that the computed or given value will fall in the interval. The margin of error helps in computing the confidence interval.