View of /trunk/NationalProblemLibrary/UVA-Stat/setStat212-Homework11/stat212-HW11-20.pg

    1 ##DESCRIPTION
    2 ##KEYWORDS('statistics','Inference about a population')
    3 ##
    4 ## CMMK tagged this problem
    5 
    6 ## DBchapter('Inference About a Population')
    7 ## DBsection()
    8 ## Date('07/12/2005')
    9 ## Author('Cristina Murray-Krezan')
   10 ## Institution('UVa')
   11 ## TitleText1('Statistics for Management and Economics')
   12 ## EditionText1('6')
   13 ## AuthorText1('Keller, Warrack')
   14 ## Section1()
   15 ## Problem1()
   16 
   17 
   18 ##ENDDESCRIPTION
   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 "PGnumericalmacros.pl",
   28 "PGstatisticsmacros.pl",
   29 "PGauxiliaryFunctions.pl",
   30 "extraAnswerEvaluators.pl"
   31 );
   32 
   33 
   34 TEXT(beginproblem());
   35 $showPartialCorrectAnswers = 1;
   36 # install_problem_grader(~~&std_problem_grader);
   37 
   38 $pval = 0;
   39 while ($pval < 0.003) {
   40 
   41 $n1 = random(80,100,1);
   42 $n2 = random(80,100,1);
   43 $x1 = $n1 - random(25,35);
   44 $x2 = $n2 - random(40,50);
   45 
   46 $phat1 = $x1/$n1;
   47 $phat2 = $x2/$n2;
   48 
   49 $alpha = random(0.01,0.10,0.001);
   50 
   51 $zcrit = udistr($alpha);
   52 $se = sqrt( $phat1*(1-$phat1)/$n1 + $phat2*(1-$phat2)/$n2 );
   53 $zstat = (($phat1-$phat2)-.05)/$se;
   54 $pval = uprob($zstat);
   55 }
   56 
   57 $mc = new_multiple_choice();
   58 
   59 @ans = ("Reject \(H_0\).", "Do Not Reject \(H_0\).",
   60         "Reject \(H_1\).", "Do Not Reject \(H_1\).");
   61 
   62 if ($pval < $alpha) {$tag = 0;} else {$tag = 1;}
   63 
   64 $mc -> qa('D. Your decision for the hypothesis test:', $ans[$tag]);
   65 
   66 $mc -> extra($ans[1-$tag],$ans[2],$ans[3]);
   67 
   68 BEGIN_TEXT
   69 $PAR
   70 A marketing research firm suspects that a particular product
   71 has higher name recognition among college graduates than among
   72 high school graduates.  A sample from each population is selected,
   73 and each asked if they have heard of the product in question.
   74 A summary of the sample sizes and number of each group
   75 answering ``yes'' are given below:
   76 $PAR
   77 \[
   78 \begin{array}{lll}
   79 \mbox{College Grads (Pop. 1)}: & n_1 = $n1, & x_1 = $x1 \\
   80 \mbox{High School Grads (Pop. 2)}: & n_2 = $n2, & x_2 = $x2 \\
   81 \end{array}
   82 \]
   83 $PAR
   84 The company making the product is willing to increase marketing
   85 targeted at high school graduates if the difference between the
   86 two groups is at least 5$PERCENT.
   87 Is there evidence, at an \(\alpha = $alpha\) level of significance,
   88 to support such an increase in marketing?
   89 Carry out an appropriate
   90 hypothesis test, filling in the information requested.
   91 $PAR
   92 
   93 A. The value of the standardized test statistic: \{ ans_rule(25) \}
   94 $PAR
   95 $BBOLD Note:$EBOLD For the next part, your answer should use interval notation.  An
   96 answer of the form \((-\infty, a)\) is expressed (-infty, a), an answer of the
   97 form \((b, \infty)\) is expressed (b, infty), and an answer of the
   98 form \((-\infty, a) \cup (b, \infty)\) is expressed (-infty, a)U(b, infty).
   99 $PAR
  100 B. The rejection region for the standardized test statistic: \{ ans_rule(25) \} $PAR
  101 $PAR
  102 C. The p-value is \{ ans_rule(25) \} $PAR
  103 
  104 \{ $mc ->print_q() \} $BR
  105 \{ $mc ->print_a() \}
  106 
  107 END_TEXT
  108 
  109 ANS(num_cmp($zstat));
  110 ANS(interval_cmp("($zcrit,infty)", sloppy=>'yes'));
  111 ANS(num_cmp($pval,tol=>0.005));
  112 ANS(radio_cmp($mc->correct_ans));
  113 
  114 ENDDOCUMENT();       # This should be the last executable line in the problem.