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From: Greegor on 16 Jul 2010 18:59
> 55% of the votes in the entire school

55% of 1000 votes? 550 actual votes? How can that be?

> But only 100 students will show up to vote.

> underdog (the one with 45% support) will win?

45% "support" is not 45% of VOTES

Contradictions and incorrect comparisons (votes to "support")
From: Joel Koltner on 16 Jul 2010 19:10
"Michael Robinson" <kellrobinson(a)yahoo.com> wrote in message
news:By40o.9949$KT3.3413(a)newsfe13.iad...
> The simple fact is that the book's naively constructed simulation solution
> will give an answer that approaches validity only assuming very large school
> population (and there's no point in doing a sim then because you already
> know the answer).

I think the problem is more aimed at trying to get people to realize that a
small sampling size (with large populations) can lead to outcomes with
likelihoods may be further away from the "expected" 45% than one might intuit.

Although things like, "How many people in the room do you neeed to have a
50/50 chance of having the same birthday as someone else?" might be better for
that.

> For any school population where the outcome is worth calculating -- say, a
> few hundred students -- the suggested sim is dead wrong. The "underdog's"
> chance of winning varies. Always less than 45%, approaching zero as the
> school pop approaches 109 or 108. While the sim always returns values
> centering around 45%.

Maybe they're hoping you'll start noticing the pattern of the returned values
and recognize something that looks like a binomial distribution?

It does seem as though the original problem statement is aimed more at, e.g.,
liberal arts majors where they don't expect to teach them much actual math,
but at least figure they should be able to come up with some sort of
simulation that suggests one outcome or another. (...of course, one then
might be worried when those folks then start building, e.g., climate
"simulators"... :-) )

---Joel

From: Michael Robinson on 16 Jul 2010 19:37

"Tim Wescott" <tim(a)seemywebsite.com> wrote in message
news:IvKdncVn0bH5S93RnZ2dnUVZ_tqdnZ2d(a)web-ster.com...
> Are you saying that the 1600 student school that I attended makes
> calculations about it somehow not worthwhile?
>

Hey, not trying to ruffle your feathers.
In a school with 1600 students, an underdog candidate with 45% support from
the student body has
about a .127 chance of winning an election that only 100 students vote in, a
chance of .175 to at least tie.
Of course his chances would be much worse in an election with high
participation -- he'd be sure to lose.
Interestingly, even if the school had a million students and 100
participated in the election, he'd still have only about
..136 chance of winning (.183 of tying). So yeah, 1600 and a million aren't
all that different.
Okay, I admit I cheated -- I used an online calculator.



From: Michael Robinson on 16 Jul 2010 19:39

"Bill Sloman" <bill.sloman(a)ieee.org> wrote in message
news:1d191484-6c12-4546-a609-fe32f7aadb54(a)n8g2000prh.googlegroups.com...
On Jul 17, 8:12 am, "amdx" <a...(a)knology.net> wrote:
> > Doing this by simulation makes no sense unless the aim of the exercise
> > is
> > to teach the student how to do Monte Carlo simulation, or to help them
> > get
> > a feel for that 16% probability of a wrong vote.
>
> Oh, so Obama's election was just a statistical anomaly.
> I feel so much better now.

Actually, the US electors who got out to vote for Obama represent a
very large "school", and the likelysampling error on the result was
about 0.12% of his winning margin - 9,522,083 - out of 131,257,328
votes cast. The square root of 131,257,328 is about 11,457.

http://en.wikipedia.org/wiki/United_States_presidential_election,_2008

He won quite decisively - the biggest margin of any non-incumbent
candidate so far.

--
Bill Sloman, Nijmegen

Oh boy, you're asking for it Bill. Jim's going to come out with his gun.


From: Artemus on 16 Jul 2010 20:10

"Michael Robinson" <kellrobinson(a)n_o_s_p_a_m.n_o_s_p_a_m.yahoo.com> wrote in message
news:l6adnZjIINVRA93RnZ2dnUVZ_u2dnZ2d(a)giganews.com...
>
> More options Jul 16, 1:24 pm
> Newsgroups: sci.math
> From: gearhead <nos...(a)billburg.com>
> Date: Fri, 16 Jul 2010 10:24:41 -0700 (PDT)
> Local: Fri, Jul 16 2010 1:24 pm
> Subject: stats/probability question
> Reply | Reply to author | Forward | Print | Individual message | Show
> original | Remove | Report this message | Find messages by this author
>
> I'm an engineering undergrad in an intro stats course. We had a
> question in the book that's really dumb.
>
> problem as stated:
>
> Your candidate has 55% of the votes in the entire school. But
> only
> 100 students will show up to vote. What is the probability that the
> underdog (the one with 45% support) will win? To find out, set up a
> simulation.
> a) Describe how you will simulate a component and its outcomes.
> b) Describe how you will simulate a trial.
> c) Describe the response variable.
>
> The answer in the back of the book says using a two digit random
> number to determine each vote (00-54 for your candidate, 55-99 for the
> underdog) you would run a string of trials with 100 votes to each
> trial.
>
> Now, this is one misconceived exercise. Let me explain why.
>
> Say the school has 1000 students. If all of them show up, the
> underdog has 0% chance of winning. If exactly one voter shows up,
> underdog has 45% chance of winning. In an election where 100 voters
> show up, underdog's chance of winning the election HAS to lie
> somewhere between 0% and 45%. No ifs, ands or buts.

You're assuming that for *every* case of 100 randomly selected voters
it is *impossible* for more than 45 of them to be underdog supporters.
It is possible, albeit the probability is low, that 100% of them are
underdog supporters.

> The probability of a win for underdog can never exceed 45%. When the
> exercise asks "how often will the underdog win" I interpret that as
> meaning what are his chances, i.e., the probability that he will win.
> But if you run a simulation, you can get anything, including results
> above 45%. I don't think simulating has any validity here, at least
> the procedure suggested in the answer key. That is a lot of
> simulating to do by hand,

By hand???? This is trivial using a spreadsheet.

> 100 per trial, but it is nowhere close to
> even starting to answer the actual question. You would first of all
> have to know the population of the school and then do some very
> demanding simulations that would only be practical on a computer.
>
> Practical considerations aside, the question is
> meaningless unless know something about the magnitude of the
> school population.
> Consider: if the total population is 108, the underdog cannot win,
> because he only has 49 (48.6 rounded up) supporters total. Chance of
> winning 0%. Period. "Underdog" has NO CHANCE of winning the
> election. But if you run a simulation the way the book suggests, he's
> going to win some. In fact he wins about half.

My simulations show the underdog wins 44.96% of the time over 10,000
runs. The max votes he got on any one run was 66.
Art



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