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st: binary proportions and sample size

Subject   st: binary proportions and sample size
Date   Wed, 25 Mar 2009 19:05:04 +0100

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???)
Many thanks in advance for your help,

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