9 Jun
2015
9 Jun
'15
11:25 a.m.
I ran a simple simulation in R:
p = 0.5
v = rbinom(n = 1000000, size = 1672, p)
v = v/1672
mean(v >= .5633)
[1] 0
So, the estimated p-value is 0 (or p < 0.001).
I also estimated the following based on 21% unsigned ballots: 7,962 people
who cast a vote, 6,290 of those people signed their ballot, and 3,152 of
the signers casted a NO vote. If those estimates are close, then if you
combine the NO votes from the signed (3,152) and unsigned (942) ballots,
you have a NO vote cast by 51.4% of all voters.
The 3,152 NO votes is a rough midpoint of the possible range of NO votes
from signed voters that would round to 50.1% (3149 to 3154 votes). A range
of possible percentages for NO votes from all voters (signed and unsigned)
would be from 51.38% to 51.44%.
Bob
+++
Robert C. delMas, Ph.D.
Associate Professor
Quantitative Methods in Education
Department of Educational Psychology
University of Minnesota
168 Education Sciences Building
56 East River Road
Minneapolis, MN 55455
On Tue, Jun 9, 2015 at 8:52 AM, Kevin Rees <krees(a)ma.org> wrote:
Happy summer everyone,
I thought I would send out a message I received yesterday. A local
journalist reached out to me (I taught his daughters) with the following
question, and I thought it was a nice problem to send out to everyone.
Even though our school year is over, I've sent it along to my students to
see if anyone is interested to try and answer this question for him, or
even to possibly present to the local town council.
Enjoy!
In 2007, Ross Valley residents voted on a flood tax. You had to sign the
ballot (which was unusual) and 21% of the ballots were not signed and
thrown out. The "valid" votes were split essentially 50-50 (50.1%
"no" vs.
49.9% "yes") but the 1,672 tossed out votes were 56.33% "no" and
43.67%
"yes." Assuming there is no reason why the unsigned ballots would be more
likely "yes" or "no, " can you calculate the odds of this 56.33-43.67
split
for a 50-50 event? Many of us suspect foul play, and the matter is of
urgency now as the tax money is about to be used to tear up San Anselmo's
Memorial Park. Your names will NOT be used; it's purely my mathematical
curiosity. Thanks. -- Barry
Kevin
--
Kevin Rees
Math Department Chair
Marin Academy
www.ma.org
415-482-3260
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