OPTIONS LINESIZE=88 PAGESIZE=53 NOCENTER NODATE NONUMBER NOFMTERR;
*************************************************************************;
* PROJECT NAME: Learning to Use SAS                                      ;
*             PROGRAM NAME        DATE                    PROGRAMMER     ;
TITLE1 "Source:lec24p5.sas   C:\ed\web\be691f\webready  11/30/98  EJS "  ;
* Description:     Program simulates 200 selections of a sample of n=7 from a ;
*     binomial distribution with n=7, p=.2, and compares it with a       ;
*     similar normal distribution with meand 0.2, and var 0.2(0.8)/7     ;
*     INPUT:  none                                                       ;
**    Output:  none                                                      ;
*************************************************************************;


  ***********************************;
  *** Generate 7 binomial RV and     ;
  *** estimate sample proportion     ;
  ***********************************;
DATA d;
  ***************************;
  *** Define macro variable *;
  ***  for probability of ill;
  ***************************;
  %LET p=0.2;
  %LET n=7;
  %LET ntrials=2000;

  DO I=1 to &ntrials;
    x_m=RANBIN(3333,7,&p)/&n;
    LABEL x_m= 'Sample proportion';
    OUTPUT;
  END;

PROC CHART;
  HBAR x_m /TYPE=PERCENT MIDPOINTS=-.25 TO 0.65 BY 0.05;
  TITLE2 "Figure 4.1.  Percent Frequency of Mean from Sample of N=7 from population with P=&p";
  TITLE3 "               based on &ntrials trials";

   *****************************************;
   *** Use Normal random number generator to;
   *** get sample of 200 observations from a ;
   *** normal distribution with mean 0.20   ;
   *** VAR= p(1-p)/n =0.2(0.8)/7=0.22857    ;
   ***  SE=0.151                            ;
   *** And plot histogram                   ;
   *****************************************;

DATA d2;
  DO i=1 to &ntrials;
    phat= &p + SQRT(&p*(1-&p)/&n)*RANNOR(223);
    OUTPUT;
  END;

PROC CHART;
  HBAR phat /TYPE=PERCENT MIDPOINTS=-.25 TO 0.65 BY 0.05;
  TITLE2 "Figure 4.2.  Chart of &ntrials random variables from a Normal Distribution mean=&p, SE=0.151";
RUN;