Question

Using an illustrative example, explain the difference between:

i) a 95% confidence interval for a population mean and

ii) a 95% tolerance interval based on a single sample.

Answer 1

A confidence interval is a range of values, derived from sample statistics, that is likely to contain the value of an unknown population parameter. Because of their random nature

A 95% confidence interval is a range of values that you can be 95% certain contains the true mean of the population. This is not the same as a range that contains 95% of the values

A tolerance interval is a range that is likely to contain a specified proportion of the population. To generate tolerance intervals, you must specify both the proportion of the population and a confidence level. The confidence level is the likelihood that the interval actually covers the proportion

tolerance interval bounds a selected proportion of a distribution
A tolerance interval can be seen as a statistical version of a probability interval. "In the parameters-known case, a 95% tolerance interval and a 95% prediction interval are the same