----- Original Message -----
From: KazakOR <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Saturday, November 20, 1999 10:07 PM
Subject: Help out an English Major, please!
> The city in which I live has a population of 126,635. I wish to sample
this
> city and generate poll results with a margin of error of 3.5%. How many
people
> must I contact to arrive at this confidence level?
>
> Thanks for any help! BTW, this is not homework; I'm 38 and am arguing
with my
> statistics major wife who is probably right in the first place.
The big point here is that the size of the city *does*not*matter*,
unless the indicated sample size is rather close to the population size - a
very rare occurrence. BTW, mentioning the city size does rather support your
claim that it is not a homework problem; few instructors would be evil
enough to deliberately throw in a red herring like that until the class were
advanced enough to recognize it as such. (_I_ might be...)
What does matter somewhat is the outcome; however, this dependency is
very "flat" betwen (say) 25-75 and 75-25 splits, and the figures for that
range are conservative if the error is given as a proportion of the
population. (What is less often mentioned is that if the incidence of (say)
potential serial killers in the population is 0.0001%, you do not want to
know that to within plus-or-minus 5% !)
The estimate you generate will be a random variable, randomized by the
sampling process. What matters most of all in sample size determination is
the "confidence level" - the proportion of all possible random samples that
give an estimate within the desired margin of error of the true population
proportion. Traditionally this is 95%; there are good reasons for using a
standard confidence level here, so we shall stick with it.
This being the case, to a good approximation you need roughly (100/p)^2
samples to estimate to within plus or minus p% at a 95% confidence level.
This comes out as around 816 people. As this is way less than the population
of the city, that figure may be ignored. As we are using several
approximations here, and the 3.5% presumably does not have any great implied
precision, you would probably use 800, 900, or 1000 in practice. Indeed, I
would hazard a guess that the 3.5% figure comes from a conservative rounding
of the 3.16% margin of error obtained from a sample size of 1000 and 95%
confidence level (this is rather an industry standard).
-Robert Dawson
PS: As a matter of basic courtesy, please refrain in future from mangling
your
email address when asking others for favors. "Defense of elitism" as per
your sig is all very well, but it should not mean that the rest of us -
especially when helping you out - should have to do silly walks to defend
the Elite from spam. I am posting this reply to Edstat-L only; my mailer
does not recognize "aol.comnojunk" as a valid domain. If you miss it, too
bad.
