CONFIDENCE:
Confidence interval for a population mean
Classification:
Microsoft Excel Data Analysis
The
CONFIDENCE function calculates a value that you can use to create a confidence
interval for the population mean based on the sample mean. This definition
amounts to a mouthful, but in practice what the CONFIDENCE function does is
straightforward.
Suppose
that, based on a sample, you calculate that the mean salary for a chief
financial officer for a particular industry equals $100,000. You might wonder
how close this sample mean is to the actual population mean.
Specifically,
you might want to know what range of salaries, working at a 95-percent
confidence level, includes the population mean.
The
CONFIDENCE function calculates the number that you use to create this interval
using the syntax
=CONFIDENCE(alpha,standard_dev,size)
where alpha
equals 1 minus the confidence level, standard_dev equals the standard
deviation of the population, and size equals the number of values in
your sample.
If the
standard deviation for the population equals $20,000 and the sample size equals
100, use the formula
=CONFIDENCE(1-.95,20000,100)
The
function returns the value $3920 (rounded to the nearest dollar). This interval
suggests that if the average chief financial officer’s salary in your sample
equals $100,000, there’s a 95-percent chance that the population mean of the
chief financial officers’ salaries falls within the range $96,080 to $103,920.
