```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
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