**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**

The margin of error depends on two characteristics of the sample and one judgment call. The two characteristics of the sample are the number of observations and how much those observations vary from one another. Small samples and heterogeneous observations require a big margin of error, which means not much power to exclude unreasonable guesses.

The judgment call is known as the "confidence level." In practice, the confidence level chosen is almost always 95%. Choosing a confidence level of 90% means a more lenient standard of what is a "reasonable guess." The margin of error for 90% confidence is larger, so fewer guesses can be ruled out. Conversely, choosing a confidence level of 99% means a smaller margin of error and a stricter standard for a "reasonable guess."

**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__