Date: Sep 23, 2013 4:22 AM
Author: Luis A. Afonso
Subject: A Confidence Interval *puzzle*
A Confidence Interval *puzzle*

Each experiment A, B, ... consists in:

____Firstly a Source-sample, X~ N(0, 1): 20 is obtained (exactly, Box-Muller) and the 95% CI W= [u, v] limited by

____u= msource - 1.959964 /sqrt(20)

____v= msource + 1.959964/sqrt(20)

Then

____10 times 40´000, total 400´000 similar-to-source-samples simulated X´~N(0, 1):20 each one the proportion of means found inside W.

______________________________MC_______ Exact______

A_____[-.5170, .3595]__________0.9351______0.9357______

B_____[-.4599, .4166]__________0.9485______0.9489______

C_____[-.4807, .3958]__________0.9458______0.9459______

D_____[-.3738, .5028]__________0.9406______0.9404______

E_____[-.4951, .3814]__________0.9420______0.9426______

F_____[-.4749, .4016]__________0.9469______0.9469______

The column *Exact* was obtained in order to compare the value. To this intent my Sep 24, 2012 7:37 PM was extended to include the two bounds (u´= u*sqrt(20), v´ = v*sqrt(20), routine <NSIDES>).

We ask: Why the values ARE NOT 0.95 ?

Luis A. Afonso