# How do you interpret a 95% confidence interval?

##### 1 Answer

It is an interval for which we have 95% confidence that it includes the true parameter.

#### Explanation:

Many people think that a confidence interval says something about our confidence of the location of a parameter (like *actually* refers to is the confidence of the interval *itself*.

The width of a confidence interval is proportional to the estimate we get for

#hat mu +- t_(alpha/2)sqrt(hat sigma^2 /n)#

In turn, our estimate for

Consider holding a single 95% C.I. fixed, and then repeating the experiment several times, getting several new

What we're really saying is that, any time we perform the experiment, the interval we calculate has a 95% chance of including the parameter, rather than the parameter having a 95% chance of being in any one randomly calculated interval. More specifically, if the experiment were repeated several times, then 95% of the C.I.'s obtained would cover the true parameter value.

It's not an easy concept to wrap your head around, it's true; but give it some time. Remember: it's not a 95% chance that a dart will hit the board, but rather a 95% chance that a board will fall on the dart.