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Luis A. Afonso
Posts:
4,518
From:
LIsbon (Portugal)
Registered:
2/16/05


A Confidence Interval *puzzle*
Posted:
Sep 23, 2013 4:22 AM


A Confidence Interval *puzzle*
Each experiment A, B, ... consists in:
____Firstly a Sourcesample, X~ N(0, 1): 20 is obtained (exactly, BoxMuller) 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 similartosourcesamples 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



