View of /trunk/rochester_problib/setStatistics3Estimates/ur_stt_3_19.pg

    1 ##DESCRIPTION
    2 ##KEYWORDS('')
    3 ##
    4 ##ENDDESCRIPTION
    5 
    6 DOCUMENT();        # This should be the first executable line in the problem.
    7 
    8 loadMacros(
    9 "PG.pl",
   10 "PGbasicmacros.pl",
   11 "PGchoicemacros.pl",
   12 "PGanswermacros.pl",
   13 "PGnumericalmacros.pl",
   14 "PGstatisticsmacros.pl"
   15 );
   16 
   17 TEXT(beginproblem());
   18 $showPartialCorrectAnswers = 1;
   19 
   20 $b = random(.01,.09,.005);
   21 $p = random(.1,.9,.1);
   22 $q = 1-$p;
   23 
   24 @conf = ("\(80\\%\)",
   25    "\(90\\%\)",
   26    "\(95\\%\)",
   27    "\(98\\%\)",
   28    "\(99\\%\)");
   29 @slice = NchooseK(5,1);
   30 @sconf = @conf[@slice];
   31 
   32 $z1 = normal_distr(.4);
   33 $z2 = normal_distr(.45);
   34 $z3 = normal_distr(.475);
   35 $z4 = normal_distr(.49);
   36 $z5 = normal_distr(.495);
   37 
   38 @z = ($z1, $z2, $z3, $z4, $z5);
   39 @sz = @z[@slice];
   40 
   41 $ans1 = ($sz[0]**2*.25)/$b**2;
   42 $ans2 = ($sz[0]**2*$p*$q)/$b**2;
   43 
   44 BEGIN_TEXT
   45 A random sample of elementary school children in New York state is to be
   46 selected to estimate the proportion \(p\) who have received a medical
   47 examination during the past year.  An interval estimate of the proportion \(p\)
   48 with a bound of \($b\) and $sconf[0] confidence is required. $PAR
   49 (a) \( \ \) Assuming no prior information about \(p\) is available,
   50 approximately how large of a sample size is needed? $BR
   51 \( n = \) \{ans_rule(10)\} $PAR
   52 (b) \( \ \) If a planning study indicates that \(p\) is around \($p\),
   53 approximately how large of a sample size is needed? $BR
   54 \( n = \) \{ans_rule(10)\}
   55 END_TEXT
   56 ANS(num_cmp($ans1, tol=>3));
   57 ANS(num_cmp($ans2, tol=>3));
   58 
   59 ENDDOCUMENT();       # This should be the last executable line in the problem.