Re: WHY IS SOUND to get C.V.´s from Mont Carlo

Let be the Hypotheses Test:
_____H0: m=0 , Ha: m =/0
for means m of normal samples WITH SD=1 with size n
----N(m,1):n
It should be noted that the source population as a
KNOWN MEAN that is equal to 1.

Procedure:
Because throughout the test I must admit that H0 is
true I construct an huge number N =1 million (or 4
millions, . . . ), of N(0,1):n samples and I evaluate
the mean of each one.
The set of N means is very similar to the analytical
Distribution Function of the statistics (the
Givenko-Cantelli theorem assures it).
Then I evaluate the quantiles
_____u = prob(mean)< alpha/2
_____v = prob (mean) > 1- alpha/2
that bounds the rejection region FOR ALL MEANS OF THE
SAMPLES OF SIZE n DRAWN FROM N(m,1).

I evaluate (other thread) this bounds for the
confidence levels 95% and 99%. They were:
__Size____
__15_____0.354, 0.646_______0.310, 0.689
__16_____0.359, 0.641_______0.316, 0.684
__17_____0.363, 0.637_______0.322, 0.678
__18_____0.367, 0.633_______0.327, 0.674
__19_____0.370, 0.630_______0.331, 0.669
__20_____0.374, 0.626_______ 0.335, 0.665

This values are ABSOLUTELLY EQUAL TO THOSE OBTAINED
BY THEORY.


____licas (Luis A. Afonso)


These "confidence intervals" are not equal to those obtained by theory. The exact 1-alpha level confidence intervals on the population mean for samples of size n with sigma known and equal to one are

xbar +/- z(1-alpha/2)/sqrt(n).

Jack
.