How do I analyze survey data with a probability proportional to size sampling design?

This example is taken from Levy and Lemeshow’s
Sampling of Populations.

Page 353 cluster sampling with unequal probabilities:
probability proportional to size sampling
This example uses the hospslct
data set.
NOTE: The data step creating hspslct2 is necessary to create the
weight variable, w2star.

data hspslct2;
set hospslct;
/*n is 50*/
/*N_i is admiss*/
/* X is 7087, the total number of life-threatening conditions across all the hospitals*/
/*X_i is tl, the total number of life-threatening conditions for each hospital*/
if hospno = 2 then  tl = 785; 
if hospno = 5 then  tl = 3404; 
if hospno = 9 then  tl = 778; 
w2star = (admiss/50)*(7087/tl);
run;

proc surveymeans data = hspslct2 n = 4672 mean sum;
weight w2star;
cluster drawing;
var lifethrt dxdead;
run;

The SURVEYMEANS Procedure

            Data Summary

Number of Clusters                 5
Number of Observations            50
Sum of Weights            51344.9973

                               Statistics

                               Std Error
Variable            Mean         of Mean             Sum         Std Dev
------------------------------------------------------------------------
LIFETHRT        0.121904        0.021404     6259.175814     1276.638273
DXDEAD          0.034287        0.022991     1760.471466     1078.465840
------------------------------------------------------------------------