Question

Why can you never really have 100% confidence of correctly estimating the population characteristic of interest?

Answer 1

Answer: because you are working with a sample

Explanation: Since you are working with a sample and not all the population, you are generalizing the characteristic to the rest of the people, which can or cannot be accurate. This is way you never have 100% confidence, you are estimating, which is a generalization that can be wrong.

In statistics, especially in social studies, you have a standard error that indicates the accuracy of your estimation. We use the standard error to know exactly how accurate is this sample measurement to the whole population. Also, you have the confidence interval, which indicates you how confident can you be that your estimation is correct.

Answer 2

In statistics, a confidence interval (CI) is a kind of interval estimate of a population parameter and is used to indicate the reliability of an estimate. It is an observed interval (i.e. it is calculated from the observations), in principle different from sample to sample, that frequently includes the parameter of interest, if the experiment is repeated. How frequently the observed interval contains the parameter is determined by the confidence level or confidence coefficient.