Confidence intervals
Confidence intervals and hypothesis tasting are the key elements of "Inferential statistics." A confidence interval answers the question "Based on sample data, what numbers would & would not be a reasonable guess for the mean of the population from which the sample came?"
The concept of a reasonable guess requires some definition. Often in business we only need to guess an upper or lower bound on a number: "the mean operating cost is under ˆ500 per day" or "the mean pages printed per ink cartridge is over 5000." Sometimes we need to guess both; this is what statisticians call a two sided interval: "the mean productivity is between 7 and 9 widgets per hour."
These types of guesses, called confidence intervals, quality as "reasonable" if they are calculated from sample
data using a procedure which, despite the inevitable uncertainty of
generalizing from a sample to its parent population, is nevertheless
guaranteed
to be correct in a specified proportions of applications, usually 90%
or
95%.
For technical reasons statisticians refuse to
call the
specified proportion the "probability" that the unknown population mean
is in the calculated interval, preferring the phrase "confidence
level,"
but for most practical purposes the difference is inconsequential.
Calculating Quick & Dirty Confidence Intervels with Excel