How do you interpret a 95% confidence interval?
It is an interval for which we have 95% confidence that it includes the true parameter.
Many people think that a confidence interval says something about our confidence of the location of a parameter (like
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.