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



Not being familiar with random number tests, I had to take a simple (and
crude) test. If the numbers are truly random and have been arranged in
numerical order, then the first column would be expected the have numbers
from 1 - 7, with successive columns having numbers between 8 - 14, 15 - 21,
22 - 28, and 29 - 35.

So a very simple test is to simply count the number of times that numbers in
each column exceed (or fall below) the expected column limits. For the
first set of numbers, I find that the column limits were exceeded,
respectively, 5, 8, 6, 4, and 5 times (for the last column I counted the
number of times the listed number fell below the lower column limit). Doing
this for the second set of numbers produced the excess numbers 8, 11, 10, 4,
and 7 (again, for the last column I counted the number of times the listed
number fell below the lower column limit).

Clearly the second set of numbers failed the column limit tests more often
and should be (i.e. "probably is") the student list.

Don

Dr. Donald Polvani
Anne Arundel Community College
Adjunct Faculty, Physics (Retired)
Arnold, MD

--Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Rauber, Joel
Sent: Monday, February 17, 2014 2:08 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] From a Math Prof (physics BS major) at my institution
( math challenge)

Before giving it away, both lists are in numerical order smallest to
largest; so that has been ordered after the numbers were generated.

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Jeffrey Schnick
Sent: Monday, February 17, 2014 11:32 AM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] From a Math Prof (physics BS major) at my institution
( math challenge)

Each set of five numbers in the first set is listed in numerical order from
smallest to largest. Thus, I think the first group was student generated.

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Paul Nord
Sent: Monday, February 17, 2014 12:28 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] From a Math Prof (physics BS major) at my
institution ( math challenge)

That's easy.

The first group is the real lottery numbers. It is more uniformly
distributed.

In the second set, the student-generated numbers, numbers in the 20's
are much preferred.

Paul


On Feb 17, 2014, at 10:33 AM, Rauber, Joel <Joel.Rauber@SDSTATE.EDU>
wrote:

The below may be tangentially related to discussions of entropy (See
subject heading)


I asked my Math 316 (Discrete Math) to randomly pick 5 numbers from
1 to
35. This is the same as the "South Dakota Cash Lottery" that has
drawings twice a week. I told them that I would compare their
"random" numbers to actual numbers drawn in the lottery. They were
instructed to try to make their numbers as random as possible so they
looked just like the real random numbers. I had 21 responses, they
are in one of the two lists below. The other list is the numbers
drawn in the lottery from Dec 7, 2013 to Feb 15, 2014. Can you tell
which list is the student's list? Hint: there is an easy, almost trivial,
way to do this, or least to locate the most likely student list.


02-06-07-25-34
03-09-12-15-34
06-16-21-28-32
06-10-13-21-23
04-18-26-27-34
03-06-17-27-32
03-11-21-22-35
01-02-08-17-27
07-12-14-24-31
03-07-14-18-27
07-13-22-25-31
07-12-23-31-32
04-17-18-22-35
08-15-17-20-25
12-16-18-29-34
02-07-11-16-21
08-23-24-32-35
17-19-23-29-31
09-16-27-28-32
06-15-19-26-32
06-13-15-23-31



11-17-19-28-31
03-11-29-32-35
14-21-24-28-33
09-14-22-23-31
03-21-26-30-31
05-15-20-27-29
02-23-24-25-26
07-13-20-24-25
03-23-26-27-28
06-20-21-26-29
01-10-14-19-35
12-18-27-32-35
02-06-24-27-28
03-08-11-21-30
09-14-20-25-31
04-13-19-21-28
10-11-12-21-31
02-07-11-20-24
06-17-25-29-30
13-23-24-26-34
09-17-21-25-26
_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l

_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l
_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l
_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l