Date:         Fri, 3 Feb 2006 11:20:42 -0600
Reply-To:     Robin High <robinh@UNLSERVE.UNL.EDU>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Robin High <robinh@UNLSERVE.UNL.EDU>
Subject:      Re: Constructing confidence interval
Comments: To: Steve Jones <st_jones77@YAHOO.COM>
In-Reply-To:  <d6721d19bd26a8761280f65c887984fd.43464@mygate.mailgate.org>
Content-Type: TEXT/PLAIN; charset=US-ASCII

On Thu, 2 Feb 2006, Steve Jones wrote:

> I am trying to construct a confidence interval for a proportion/mean
> calculated from a sample. Here are the details: I have a dataset
> consisting of about 80,000 observations. They are responders and non
> responders to a marketing campaign. Specifically, 20% are responders,
> the remaining 80% nonresponders.
>
> Now I take a RANDOM sample of just 5,000 observations. I found 5% of the
> sample to be responders. Now, have can I construct a confidence interval
> around the 5% response rate from the sample?
>

SJ

If you have a population with known proportion of responders (.2), the
variance of proportion of a RANDOM sample (normal approximation reasonable
since 5000*.2 >> 10), you have a std error (ignoring the fpc to be
conservative) of:

  std_err(p) = sqrt((0.2*(1-0.2))/5000) ~ .0113

which implies a 95% conf interval of your 'random' sample is about

 .05 +-.0226

which, for a population of 80000, is far, far away from the "known" value
of 0.2, leading to the conclusion, the 'random' sample is likely to not be
very random.

Robin H.
Univ. of Oregon