/* module Confidence Interval: */

/*  : 1,2,5 */

data one;
  do j = 1 to 300;
    do i = 1 to 100;
      x = rannor(23);
      output;
    end;
  end;
run;

proc means clm alpha=0.05 data=one;
  by j;
  var x;
  output out=two lclm=lowLim uclm=upLim;
run;
proc print data=two;
  var lowLim upLim;
run;

/*  : 3 */
* The expected value of rannor is 0, and 0 is
* the population mean of a standard normal population.

/*  : 4 */
* 15 of the 300 C.I.'s don't include the population mean.
* That agrees with the alpha of .05.

/*  : 5 */
* 15 of the 300 C.I.'s don't include the population mean.
* That agrees with the alpha of .05.
* The intervals will tend to be smaller, inversely
* proportional to the square-root of n.

/*  : 6 */
* We estimate that mu lies between -.02 and .16,
* with a 5% chance that mu is not in that
* interval.