I have a survey with yes\no responses and I am trying to determine the
margin of error.  I would like to be able to say that the mean yes is
within +/- X percent 95 times out of 100 but I don't know how to
calculate X.

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Clarification of Question by michaelw2000-ga on 11 Nov 2002 18:15 PST

Okay I figured out the answer, the formula is 1/SQRT(N) where N is the
sample size.  New question: Do midsized companies (5MM-50MM in annual
sales) host their own e-commerce websites or do they use hosting
services?

Hi michaelw2000,
The concept of the margin of error is closely related to the concept
of the confidence interval.  When you say that the margin of error of
your survey is X, you are in fact saying that you are 95% confident
that the true mean is within the interval between sample (mean - X)
and sample (mean + X).
Since in your question, you're interested in calculating the margin of
error at the 95% confidence interval, we shall use figures relating to
that.  If you'd like to use figures for other confidence interval, you
can substitute them later.
As you might know, 95% of a normal curve lie within 1.96 standard
deviations from the mean.  The formula for calculating the margin of
error of a sample proportion is given by:
margin of error = 1.96 * squrt[phat*(1-phat)/n]

where phat represents the sample proportion, n represents the sample
size, and squrt represents the square root symbol.

Here's an example problem to illustrate how to use this formula:
Question: A random survey of 867 registered voters found that 63%
favored Proposition A. What is the margin of error of this survey?
Answer: Margin of error = 1.96 * squrt(0.63*0.47/867)
                        = 1.96 * 0.0164
                        = 0.032
So the answer to the above problem is 3%.

I hope that this answered your question.  If you need clarification,
please ask for it before rating this answer and I will be happy to
clarify.
secret901-ga

Links:
http://www.cate.org/sms99/apst99/ymmsum99/ymm12121.htm
http://www.robertniles.com/stats/margin.shtml
http://www.amstat.org/sections/srms/brochures/margin.pdf

Search strategy:
binomial "margin of error"
"margin of error" proportion

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Clarification of Answer by secret901-ga on 11 Nov 2002 18:29 PST

Dear michaelw2000-ga,
Unfortunately, I have embarked on answering your question before you
wrote your clarification, thus I was unable to know that you have
found what you were looking for.  The formula that you cited is only a
rough approximation of the formula that I cited.
Since I do not believe that I can answer the alternate question that
you posed satisfactorily, please let me know if I should remove my
current answer.

Regards,
secret901-ga

As to your second question -- it depends. Some host their own, others
outsource it.  Depends upon the company.

There are advantages and disadvantages both ways -- personally I
prefer to outsource it if you can find a company you trust who is
dependable. It makes them responsible for the considerable maintenance
and upkeep and also limits your exposure from a security standpoint by
keeping the website very distinct from your corporate network.

Hosting your own has the advantage of maintaining greater local
control and if you already have the IT staff and resources to support
it (including appropriate inbound bandwidth) it may make sense to do
so rather than paying an outside company to do it.

-Coach-

I suspect there is something phony about margin of error in polls. The
wording of the question is more important than the sample size in
getting an accurate estimation of public opinion. Since the wording is
subjective; math fails.  Neil