st: correct confidence intervals of -mean- ?

[Dirk Enzmann <dirk.enzmann@uni-hamburg.de>]

Very carefully I want to ask: Are the confidence intervals given by 
-mean- really correct?
Below I compare the results of -mean- with the results of a different 
procedure:
* --------------------------------------
sysuse auto, clear
mean price, over(rep78)

local df = e(df_r)
display "degrees of freedom = n-1 = `df'"
* Note that here df is the number of the total sample - 1!

* alternative route:
collapse (mean) mprice=price (sd) sdprice=price (count) nprice=price if 
(rep78 < .), by(rep78)
* calculate the confidence intervals the -mean- way:
gen ci95la = mprice - invttail(`df',.025)*sdprice/sqrt(nprice)
gen ci95ua = mprice + invttail(`df',.025)*sdprice/sqrt(nprice)
* calculate the confidence intervals a different way:
gen ci95lb = mprice - invttail(nprice-1,.025)*sdprice/sqrt(nprice)
gen ci95ub = mprice + invttail(nprice-1,.025)*sdprice/sqrt(nprice)
* compare both sets of confidence intervals (..a vs ..b):
list
* --------------------------------------

My question: Which procedure is correct?

*************************************************
Dr. Dirk Enzmann
Institute of Criminal Sciences
Dept. of Criminology
Schlueterstr. 28
D-20146 Hamburg
Germany

phone: +49-(0)40-42838.7498 (office)
       +49-(0)40-42838.4591 (Mrs Billon)
fax:   +49-(0)40-42838.2344
email: dirk.enzmann@uni-hamburg.de
www: 
http://www2.jura.uni-hamburg.de/instkrim/kriminologie/Mitarbeiter/Enzmann/Enzmann.html
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