But how do you explain that you win 95% of the time?
On Monday, November 18, 2002, at 11:10 AM, Elliot Cramer wrote:
Alan McLean <[EMAIL PROTECTED]> wrote:
: The use of the t distribution in inference on the mean is on the whole
: straightforward; my question relates to the theory underlying this use.
: If Z = (X - mu)/sigma is ~ N(0, 1), then is T = (X - mu)/s (where s is
: the sample SD based on a simple random sample of size n) ~ t(n-1)?
YES
: My second question is on the matter of confidence intervals. In my
: Whatever is said in the text books, this is understood by most people as
: a statement that "mu lies in the interval with probability 0.95" - or
: something very close to this. In effect, we define a secondary notional
: variable Y which imagines that we could find out the 'true' value of mu;
: Y = 1 if this true value is in the confidence interval, = 0 otherwise -
: and we estimate the probability that Y = 1 as 0.95.
: So my question is: how do YOU explain to students what a confidence
: interval REALLY is?
I treat it as a bet where on repeated samples I bet that mu is in the
region. I win 95% of the time
..
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