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/ . =================================================================
