View of /trunk/NationalProblemLibrary/Rochester/setStatistics7MultinomialContingency/ur_stt_7_6.pg

    1 ## DESCRIPTION
    2 ##   Multinomial Contingency
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Multinomial', 'Contingency', 'Hypothesis', 'Test Statistic', 'Critical Value')
    6 ## Tagged by nhamblet
    7 
    8 ## DBsubject('Statistics')
    9 ## DBchapter('Hypothesis Testing')
   10 ## DBsection('Multinomial Contingency')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Rochester')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGgraphmacros.pl",
   28 "PGnumericalmacros.pl",
   29 "PGstatisticsmacros.pl"
   30 );
   31 
   32 TEXT(beginproblem());
   33 $showPartialCorrectAnswers = 1;
   34 
   35 $s = random(100,300,1);
   36 $m[0] = random(int($s*0.13), int($s*0.25), 1);
   37 $w[0] = random(2,4,1);
   38 $m[1] = random(int($s*0.25), int($s*0.33), 1);
   39 $w[1] = random(2,5,1);
   40 $m[2] = random(int($s*0.1), int($s*0.15), 1);
   41 $w[2] = random(2,4,1);
   42 $m[3] = random(int($s*0.05), int($s*0.10), 1);
   43 $w[3] = random(2,4,1);
   44 $m[4] = random(int($s*0.1), int($s*0.15), 1);
   45 $w[4] = random(int($s*0.05), int($s*0.1), 1);
   46 
   47 $row_tot_m = $m[0]+$m[1]+$m[2]+$m[3]+$m[4];
   48 $row_tot_w = $w[0]+$w[1]+$w[2]+$w[3]+$w[4];
   49 $total = $row_tot_m + $row_tot_w;
   50 
   51 $stat = 0;
   52 for ($i=0; $i<5; $i++) {
   53   $col_tot[$i] = $m[$i] + $w[$i];
   54   $ex_m[$i] = $row_tot_m * $col_tot[$i] / $total;
   55   $ex_w[$i] = $row_tot_w * $col_tot[$i] / $total;
   56   $stat = $stat + ($m[$i]-$ex_m[$i])**2/$ex_m[$i] + ($w[$i]-$ex_w[$i])**2/$ex_w[$i];
   57 }
   58 
   59 $alpha = random(0.01, 0.025, 0.015);
   60 
   61 $crit = chisqrdistr(4, $alpha);
   62 
   63 $mc = new_multiple_choice();
   64 
   65 @ans = ('Yes','No');
   66 
   67 if ($stat > $crit) {$tag = 0;} else {$tag = 1;}
   68 
   69 $mc -> qa('Is there sufficient evidence to warrant the rejection of the claim that the
   70 gender of a professor is independent of the department?', $ans[$tag]);
   71 
   72 $mc -> extra($ans[1-$tag]);
   73 
   74 BEGIN_TEXT
   75 
   76 The number of men and women among professors in Math, Physics, Chemistry, Linguistics, and
   77 English departments of a certain college were counted, and the results are shown in the
   78 table below.
   79 
   80 \{begintable(6)\}
   81 \{row('Dept.', 'Math', 'Physics', 'Chemistry', 'Linguistics','English')\}
   82 \{row('Men', $m[0], $m[1], $m[2], $m[3], $m[4])\}
   83 \{row('Women', $w[0], $w[1], $w[2], $w[3], $w[4])\}
   84 \{endtable()\}
   85 
   86 Test the claim that the gender of a professor is independent of the department. Use the
   87 significance level \( \alpha = $alpha \) $BR
   88 
   89 The test statistic is \(\chi^2=\) \{ans_rule(10)\} $BR
   90 
   91 The critical value is \(\chi^2=\) \{ans_rule(10)\} $BR
   92 
   93 \{$mc->print_q()\}$BR
   94 \{$mc->print_a()\}$BR
   95 
   96 END_TEXT
   97 
   98 ANS(num_cmp($stat));
   99 ANS(num_cmp($crit));
  100 ANS(radio_cmp($mc->correct_ans));
  101 
  102 ENDDOCUMENT();       # This should be the last executable line in the problem.
  103