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The concept of a 95% Confidence Interval (95% CI) is one that is
somewhat elusive.
This is primarily due to the fact that many students of statistics are
simply required to memorize its definition without fully understanding
its implications. Here we will try to cover both the definition as
well as what the definition actually implies.

The definition that students are required to memorize is:

If the procedure for computing a 95% confidence interval is used over and
over, 95% of the time the interval will contain the true parameter value.

Students are then told that this definition does not mean that an
interval has a 95% chance of containing the true parameter value.
The reason that this is true, is because a 95% confidence interval will either contain
the true parameter value of interest or it will not (thus, the probability of
containing the true value is either 1 or 0). However, you have a 95%
chance of creating one that does. In other words, this is similar to saying, "you have a 50% of getting a heads in a coin toss,
however, once you toss the coin, you either have a head or a tail". Thus,
you have a 95% chance of creating a 95% CI for a parameter that contains the
true value. However, once you've done it, your CI either covers the parameter
or it doesn't.

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Frank Starmer
2004-05-19