Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


Luis A. Afonso
Posts:
4,743
From:
LIsbon (Portugal)
Registered:
2/16/05


You NEVER know if a coin is FAIR!
Posted:
Aug 6, 2011 1:23 PM


You NEVER know if a coin is FAIR!
This is a rather trivial matter for a lot of people. However because statistical users largely exceed *abusers* I think the matter is not futile to present here. Users, a large amount of them, were persuaded that Statistics, in particular Significance Tests, is able to decide though a Null Hypotheses is true. The *abusers*, those who had got the true problem?s realm, say peremptory: NO, NEVER. To the *believers* I use to ask a simple question: How many finite flips should you perform in order that to be sure a coin is fair?. They are unable to get an answer: nobody does. In fact I propose that a person should find n such that an interval [0.5d , 0.5+d] which associated to the probability 1x : d=0, x= 0: IMPOSSIBLE.
Values: __________n____#heads interval___alpha_____C.V.__ _d=0.01__6765___[ 3315, 3450 ]____0.1_____1.645__ ________ 9604___[ 4706, 4898 ]____0.05____1.960__ _______12544___ [ 6147, 6397 ]____0.025___2.240__ _______16589___ [ 8129, 8461 ]____0.01____2.576__ _______19698___ [ 9652, 10046]___ 0.005___2.807__ _______27077___ [13268,13809]___ 0.001___3.291__
_d=0.0001__ _______67650627____[ 33818548, 33832078 ]_____ _______96040009____[ 48010400, 48029608 ]_____ ______125440007____[ 62707460, 62732548 ]_____ ______165894405____[ 82930613, 82963792 ]_____ ______196981224____[ 98470914, 98510310 ]_____ _____ 270767020___[ 135356434, 135410587 ]_____
___271 millions of trials, to achieve 0.5 +/ 0.001 with the probability 99.9% (!).
Luis A. Afonso
REM "YOUNEVER" CLS DEFDBL AZ COLOR 8 z(1) = 1.645: REM alpha/2:alpha = .1 z(2) = 1.96: REM alpha=0.05 z(3) = 2.24: REM =.025 z(4) = 2.576: REM =.010 z(5) = 2.807: REM =.005 z(6) = 3.291: REM =.001 PRINT : PRINT : PRINT COLOR 14 delta = .01 PRINT USING " d= #.#### "; delta COLOR 7 FOR zz = 1 TO 6 n = (.5 / delta) ^ 2 * z(zz) ^ 2 PRINT USING "############### "; n; REM u1 = (.5  delta) * n u2 = (.5 + delta) * n PRINT USING " ############ "; u1; u2 NEXT zz COLOR 14 delta = .001 PRINT USING " d= #.#### "; delta COLOR 7 FOR zz = 1 TO 6 n = (.5 / delta) ^ 2 * z(zz) ^ 2 PRINT USING "###############"; n; REM u1 = (.5  delta) * n u2 = (.5 + delta) * n PRINT USING " ############"; u1; u2 NEXT zz COLOR 14 delta = .0001 PRINT USING " d= #.#### "; delta COLOR 7 FOR zz = 1 TO 6 n = (.5 / delta) ^ 2 * z(zz) ^ 2 PRINT USING "###############"; n; REM u1 = (.5  delta) * n u2 = (.5 + delta) * n PRINT USING " ############"; u1; u2 NEXT zz LOCATE 15, 50 END



