Date:         Sat, 9 Dec 2006 10:41:03 -0500
Reply-To:     Statisticsdoc <statisticsdoc@cox.net>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         Statisticsdoc <statisticsdoc@cox.net>
Subject:      Re: guessing mean of bounded variable with 1:30 sampling ratio
Comments: To: nicola.baldini2@unibo.it
In-Reply-To:  <7.0.0.16.2.20061201115818.021fb5e0@unibo.it>
Content-Type: text/plain; charset="us-ascii"

Nicola,

You have the Central Limit Theorem working for you here.  Even though the
distribution of individual cases is not normal, the distribution of sample
means (with a sample size of 400) will approximate the normal distribution
and should provide you with a reasonable estimate of the population mean and
the standard error of the means of samples of 400 cases.

HTH,

Stephen Brand

For personalized and professional consultation in statistics and research
design, visit
www.statisticsdoc.com


-----Original Message-----
From: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU]On Behalf Of
Nicola Baldini
Sent: Friday, December 08, 2006 6:11 AM
To: SPSSX-L@LISTSERV.UGA.EDU
Subject: guessing mean of bounded variable with 1:30 sampling ratio


I have a population of N=12000. I want to know the mean (and possibly the
standard deviation) of a variable x, bounded between 1 and 7. I took a
(let's suppose random) sample of n=400 and estimated mean = 3.14 (standard
error = .15) and standard deviation = 2.28. The sample strongly departs from
normality. Can I trust such estimates? How much? Can I attach a p-value to
them? I need to state formally that, despite a ridicolous response rate, my
research is not that bad.
Nicola