View of /trunk/rochester_problib/setStatistics4HypothesisTesting/ur_stt_4_17a.pg

    1 ##DESCRIPTION
    2 ##KEYWORDS('hypothesis testing','population proportion','statistics')
    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 "PGauxiliaryFunctions.pl"
   16 );
   17 
   18 TEXT(beginproblem());
   19 $showPartialCorrectAnswers = 1;
   20 
   21 $n = random(90,150,10);
   22 $phat = random(.60,.80,.01);
   23 
   24 for ($i=0; $i<3; $i++) {
   25   $p[$i] = random(.50,.70,.05);
   26   $a[$i] = random(.01,.05,.04);
   27   $q[$i] = 1-$p[$i];
   28   $sd[$i] = sqrt ($p[$i]*$q[$i]/$n);
   29   $z[$i] = ($phat-$p[$i])/$sd[$i];
   30 }
   31 for ($i=0; $i<2; $i++) {
   32   $t[$i] = udistr($a[$i]);
   33 }
   34 $t[2] = udistr(($a[2]/2));
   35 if ($z[0] > $t[0] ) {$tag1 = 0;} else {$tag1 = 1;}
   36 if ($z[1] < -$t[1]) {$tag2 = 0;} else {$tag2 = 1;}
   37 if ($z[2] < -$t[2] or $z[2] > $t[2]) {$tag3 = 0;} else {$tag3 = 1;}
   38 $mc1 = new_multiple_choice();
   39 
   40 @ans1 = ("We can reject the null hypothesis that \( p = $p[0]\) and accept that \( p > $p[0]\). ",
   41         "There is not sufficient evidence to reject the null hypothesis that \( p = $p[0]\). ");
   42 
   43 $mc1 -> qa('The final conclustion is', $ans1[$tag1]);
   44 
   45 $mc1 -> extra($ans1[1-$tag1]);
   46 
   47 $mc2 = new_multiple_choice();
   48 
   49 @ans2 = ("We can reject the null hypothesis that \( p = $p[1]\) and accept that \( p < $p[1]\). ",
   50         "There is not sufficient evidence to reject the null hypothesis that \( p = $p[1]\). ");
   51 
   52 $mc2 -> qa('The final conclustion is', $ans2[$tag2]);
   53 
   54 $mc2 -> extra($ans2[1-$tag2]);
   55 
   56 $mc3 = new_multiple_choice();
   57 
   58 @ans3 = ("We can reject the null hypothesis that \( p = $p[2]\) and accept that \( p \ne $p[2]\). ",
   59         "There is not sufficient evidence to reject the null hypothesis that \( p = $p[2]\). ");
   60 
   61 $mc3 -> qa('The final conclustion is', $ans3[$tag3]);
   62 
   63 $mc3 -> extra($ans3[1-$tag3]);
   64 
   65 BEGIN_TEXT
   66 A random sample of \($n\) observations is selected from a binomial population with unknown
   67 probability of success \(p\).  The computed value of \(\hat{p}\) is \($phat\).
   68 $BR
   69 (1) \( \ \) Test \(H_0: p = $p[0]\) against \(H_a: p > $p[0] \).  Use \(\alpha = $a[0] \). $PAR
   70 test statistic \(z = \) \{ans_rule(10)\} $PAR
   71 critical \(z\) score \( \ \) \{ans_rule(10)\} $BR
   72 \{ $mc1->print_q() \}
   73 $BR
   74 \{ $mc1->print_a() \}$BR
   75 (2) \( \ \) Test \(H_0: p = $p[1]\) against \(H_a: p < $p[1] \).  Use \(\alpha = $a[1] \). $PAR
   76 test statistic \(z = \) \{ans_rule(10)\} $PAR
   77 critical \(z\) score \( \ \) \{ans_rule(10)\} $BR
   78 \{ $mc2->print_q() \}
   79 $BR
   80 \{ $mc2->print_a() \}$BR
   81 (3) \( \ \) Test \(H_0: p = $p[2]\) against \(H_a: p \ne $p[2] \).  Use \(\alpha = $a[2] \). $PAR
   82 test statistic \(z = \) \{ans_rule(10)\} $PAR
   83 positive critical \(z\) score \( \ \) \{ans_rule(10)\} $PAR
   84 negative critical \(z\) score \( \ \) \{ans_rule(10)\} $BR
   85 \{ $mc3->print_q() \}
   86 $BR
   87 \{ $mc3->print_a() \}
   88 
   89 END_TEXT
   90 ANS(num_cmp($z[0]));
   91 ANS(num_cmp($t[0], tol=>.01));
   92 ANS(radio_cmp($mc1->correct_ans));
   93 ANS(num_cmp($z[1]));
   94 ANS(num_cmp(-$t[1], tol=>.01));
   95 ANS(radio_cmp($mc2->correct_ans));
   96 ANS(num_cmp($z[2]));
   97 ANS(num_cmp($t[2], tol=>.01));
   98 ANS(num_cmp(-$t[2], tol=>.01));
   99 ANS(radio_cmp($mc3->correct_ans));
  100 
  101 ENDDOCUMENT();       # This should be the last executable line in the problem.