View of /trunk/NationalProblemLibrary/UVA-Stat/setStat212-Homework07/stat212-HW07-01.pg

    1 ## DESCRIPTION
    2 ##  Statistics: Continuous Probability Distributions
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('statistics', 'continuous probability distributions', 'probability distributions')
    6 ## CMMK tagged this problem.
    7 
    8 ## DBchapter('What is Statistics?')
    9 ## DBsection()
   10 ## Date('6/17/2005')
   11 ## Author('Cristina Murray-Krezan')
   12 ## Institution('UVA')
   13 ## TitleText1('Statistics for Management and Economics')
   14 ## EditionText1('6')
   15 ## AuthorText1('Keller, Warrack')
   16 ## Section1()
   17 ## Problem1()
   18 
   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 );
   31 
   32 TEXT(beginproblem());
   33 $showPartialCorrectAnswers = 0;
   34 install_problem_grader(~~&std_problem_grader);
   35 
   36 $mc[1] = new_multiple_choice();
   37 $mc[1]->qa('As a general rule, the normal distribution is
   38 used to approximate the sampling distribution of the
   39 sample proportion only if',
   40     '\(np\) and \(n(1-p)\) are both greater than 5'
   41 );
   42 $mc[1]->extra(
   43     'the sample size \(n\) is greater than 30',
   44     'the population proportion \(p\) is close to 0.50',
   45     'the underlying population proportion is normal'
   46 );
   47 
   48 
   49 $mc[2] = new_multiple_choice();
   50 $mc[2]->qa('If the standard error of the sampling
   51 distribution of the sample proportion is 0.0229 for samples of
   52 size 400, then the population proportion must be either',
   53     '0.3 or 0.7'
   54 );
   55 $mc[2]->extra(
   56     '0.4 or 0.6',
   57     '0.5 or 0.5',
   58     '0.2 or 0.8'
   59 );
   60 
   61 
   62 $mc[3] = new_multiple_choice();
   63 $mc[3]->qa('Given that \(X\) is a binomial random variable, the
   64 binomial probability \(P(X \geq x)\) is approximated
   65 by the area under a normal curve to the right of',
   66     '\(x-0.5\)'
   67 );
   68 $mc[3]->extra(
   69     '\(x+0.5\)',
   70     '\(x-1\)',
   71     '\(x+1\)'
   72 );
   73 
   74 
   75 $mc[4] = new_multiple_choice();
   76 $mc[4]->qa('A sample of size \(n\) is selected at random from
   77 an infinite population.  As \(n\) increases, which of
   78 the following statements is true?',
   79     'The standard error of the sample mean decreases'
   80 );
   81 $mc[4]->extra(
   82     'The population standard deviation decreases',
   83     'The population standard deviation increases',
   84     'The standard error of the sample mean increases'
   85 );
   86 
   87 $mc[5] = new_multiple_choice();
   88 $mc[5]->qa('Suppose that \(X\) is a binomial random variable with
   89 n = 16 and p = 0.35.  Using normal approximation with continuity
   90 correction, what is (approximately) \(P(X = 7)\)?',
   91     '0.1589'
   92 );
   93 $mc[5]->extra(
   94     '0',
   95     '0.1854',
   96     '0.1740'
   97 );
   98 
   99 
  100 $a = random(1,5,1);
  101 $b = random(1,5,1);
  102 while ($a==$b){
  103      $b=random(1,5,1);
  104 }
  105 
  106 
  107 BEGIN_TEXT
  108 $PAR
  109 \{ $mc[$a]->print_q() \}
  110 
  111 \{ $mc[$a]->print_a() \}
  112 $PAR
  113 \{ $mc[$b]->print_q() \}
  114 
  115 \{ $mc[$b]->print_a() \}
  116 $PAR
  117 
  118 END_TEXT
  119 
  120 ANS(radio_cmp($mc[$a]->correct_ans));
  121 ANS(radio_cmp($mc[$b]->correct_ans));
  122 
  123 ENDDOCUMENT();       # This should be the last executable line in the problem.