Question

Consider the phrase "confidence interval" - what does the word "confidence" imply and what is the information provided by the word "interval"?

Answer 1

In statistics, the confidence or confidence level indicates the probability, with which the estimation of the location of a statistical parameter (e.g. an arithmetic mean) in a sample survey is also true for the population. Degree of confidence represents the probability that the confidence interval captures the true population parameter.

The typical confidence level is used as 95%, a calculated statistical value that was based on a sample, would also be true for the whole population within the established confidence level – with a 95% chance. In other words: the 0.95 chances out of 1 that the arithmetic mean (or other sample value ) of a population is exactly within the margins of error which were established for the survey based on a sample. Conversely, there is a chance that for many times repeated surveys with new samples, in 5 cases out of 100, one would calculate an arithmetic mean which does not fall within in the margin of error. The result of the survey would indeed be correct for the respondents themselves, but not representative for the surveyed group.

An interval (related to confidence) in statistics  is defined by two numbers, between which a population parameter is said to lie. For example, a <= μ <= b is an interval estimate for the population mean μ. It indicates that the population mean would lie between a and  b.