it's most easily explained for sigma known where xbar is within two sigma of mu 95% of the time. first put in mu with a two sigma band. Next put in a xbar with its confidence interval at both extremes of the band where it JUST includes mu and within which xbar must be 95% of them time
On Mon, 18 Nov 2002, Alan McLean wrote: > 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 > > > > > > .. > > .. > > ================================================================= > > Instructions for joining and leaving this list, remarks about the > > problem of INAPPROPRIATE MESSAGES, and archives are available at: > > .. http://jse.stat.ncsu.edu/ . > > ================================================================= > > . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
