# Re: st: binary proportions and sample size

 From Austin Nichols To statalist@hsphsun2.harvard.edu Subject Re: st: binary proportions and sample size Date Wed, 25 Mar 2009 18:05:46 -0400

```If you want a simple confidence interval, do:

clear
set obs 74
g ok=_n>4
g pw=900/74
g fpc=900
svyset [pw=pw], fpc(fpc)
svy:tab ok, ci

I don't understand this part:
"which is the probability that the problem-rate in the sample and in
the population are different - statistically significantly different"
unless you are looking for some Bayesian solution--the kinds of
probabilities you mention depend on the population proportion.

Or do you mean, what is the probability of rejecting the null of the
true proportion in the population at the 5% level given a sample of
74, in which case the answer is 5% (the size of your test).

Maybe you could rephrase your question...

On Wed, Mar 25, 2009 at 2:05 PM,  <nicola.baldini2@unibo.it> wrote:
> This is stupid question stemming from a practical problem. The problem sounds easy and familiar, but I don't have a statistical manual at hand and no idea about the keywords to refine a search for the solution on Statalist.
> I took a (let's say random) sample of 74 tools from a popolation of 900. I checked personally each of the 74 tools, and found that 4 of them have some problems (5,4%) and 70 are ok. Can I expect to find 49 (5,4% x 900) problems in the population (i.e. is the sample size big enough to say so) and can I attach a p-value to my expectations (i.e. which is the probability that the problem-rate in the sample and in the population are different - statistically significantly different)? (And, obviously, which Stata command will answer to my questions???)