1. SAS procedure for the C.I. of a population average PROC MEANS DATA = data-name N MEAN STD CLM ALPHA=value MAXDEC = number; VAR measurement-variable; RUN; Where ALPHA=value is the (1-confidence level) value. (Thus ALPHA=0.05 for a 95% C.I., ALPHA =0.1. for a 90% CI, ALPHA=0.01 for a 99% C.I. ) CLM is the option for C.I.’s MAXDEC = number defines how many decimal numbers (typically 1 to 4)

2. SAS example proc means data=dist n mean std clm alpha=0.05 maxdec=4 ; var x; title “C.I. for population average"; run; C.I. for population average The MEANS Procedure Analysis Variable : x Lower 95% Upper 95% N Mean Std Dev CL for Mean CL for Mean ________________________________________________________ 100 34.9956 5.2118 33.9614 36.0297 ________________________________________________________

3. SAS example: Parking meter collections In May 1978 Brink’s Inc. was awarded a contract to collect coins from some 70,000 parking meters in New York City for delivery to the City Department of Finance. Sometime later the City became suspicious that not all of the money collected was being returned to the city. In April of 1978 five Brink's collectors were arrested and charged with grand larceny. They were subsequently convicted. The city sued Brink's for negligent supervision of its employees, seeking to recover the amount stolen. The data was provided by the City's attorney. The average of the monthly amount of money collected from different contractors was $1,688,567. The data about the money collected from Brink’s employees can be analyzed and compared with the monthly average from different collectors.

4. SAS output for Brink’s data Collections for parking meters The MEANS Procedure Analysis Variable : con Monthly collections by Brink’s contractors Lower 90% Upper 90% N Mean Std Dev CL for Mean CL for Mean ------------------------------------------------------------------------------------- 24 1588309.7083 172926.9350 1527812.5066 1648806.9101 ------------------------------------------------------------------------------------- The 90% C.I. suggests that the money collected by the Brink’s employees were on average less than the money collected by other contractors. The average of the monthly amount of money collected from different contractors was $1,688,567, which does not lie in the C.I. computed above. Maybe there were some employees that kept the money collected from the parking meters. However the data analysis does not provide a conclusive evidence!