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Re: [Phys-L] From a Math Prof (physics BS major) at my institution ( math challenge)




I just chatted briefly with the math class, and he commented that one of the student sequences (I haven't personally checked this) had one sequence that was all prime numbers, for which the odds is exceedingly low in a truly random sample. He thinks that student misunderstood the assignment, which in part was make-up a sequence that they thought would look random (I don't know how many such sequences they were to make up.)
Sent from my iPad

On Feb 21, 2014, at 9:45 PM, "Ian Sefton" <I.Sefton@physics.usyd.edu.au> wrote:


On 21/02/2014, at 12:49 AM, Jeffrey Schnick wrote:


So far the only general law of human behavior we've seen asserts that
people "religiously avoid" consecutive numbers when cooking up numbers ...

I wouldn't call it a law but I was operating on the hypothesis that in trying to cook up a random distribution of numbers people tend to shy away from nice round numbers like 10, 20, and 30.
...


I was thinking along the same lines (although I think "religiously" is a bit of an exaggeration).
So I used the good old chi-squared null-hypothesis thing to check out the following hypotheses:

1) People will tend to avoid numbers evenly divisible by 5 (which includes the next case)
2) People will tend to avoid numbers evenly divisible by 10.
3) People may be biassed in favour of (or against) primes.

I also checked a couple of other ideas but did not discover anything.

Results:
1) List 1: p = 0.0034; list 2: p = 0.81. We may be on to something here.

2) List 1: p = 3.560E-06 (wow!); but wait for it ... list 2: p = 0.019 (which lies within the traditional 5% boundary).

3) Exactly the same distribution of primes/non-primes occurred in both sets but there is nothing to get excited about; p = 0.69 in both cases.

Given that only one of the data sets was generated by people alone, I'm betting that was list 1. I am also suspicious that the generator of list 2 may not be truly "random".

Cheers
Ian




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