View of /trunk/NationalProblemLibrary/UVA-Stat/setStat212-Homework07/stat212-HW07-02.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('The finite population correction factor should not be used when:',
   38      'we are sampling from an infinite population'
   39 );
   40 $mc[1]->extra(
   41     'we are sampling from a finite population',
   42     'sample size is greater than 1$PERCENT of the population size',
   43 );
   44 
   45 $mc[1]->makeLast(
   46     'None of the above statements is correct'
   47 );
   48 
   49 
   50 $mc[2] = new_multiple_choice();
   51 $mc[2]->qa('If two populations are normally distributed, the
   52 sampling distribution of the sample mean difference \(\bar{X_1}-\bar{X_2}\) will be:',
   53     'normally distributed'
   54 );
   55 $mc[2]->extra(
   56     'approximately normally distributed',
   57     'normally distributed only if both sample sizes are greater than 30',
   58     'normally distributed only if both population sizes are greater than 30'
   59 );
   60 
   61 
   62 $mc[3] = new_multiple_choice();
   63 $mc[3]->qa('Given a binomial distribution with \(n\) trials and
   64 probability \(p\) of success on any trial, a conventional rule
   65 of thumb is that the normal distribution will provide an adequate
   66 approximation of the binomial distribution if',
   67     '\(np \geq 5\) and \(n(1-p) \geq 5\)'
   68 );
   69 $mc[3]->extra(
   70     '\(np \leq 5\) and \(n(1-p) \leq 5\)',
   71     '\(np \geq 5\) and \(n(1-p) \leq 5\)',
   72     '\(np \leq 5\) and \(n(1-p) \geq 5\)'
   73 );
   74 
   75 
   76 $mc[4] = new_multiple_choice();
   77 $mc[4]->qa('If two random samples of sizes \(n_1\) and \(n_2\) are
   78 selected independently from two populations with means \(\mu_1\)
   79 and \(\mu_2\), then the mean of the sampling distribution of the
   80 sample mean difference, \(\bar{X_1}-\bar{X_2}\), equals',
   81     '\(\mu_1 - \mu_2\)'
   82 );
   83 $mc[4]->extra(
   84     '\(\mu_1 + \mu_2\)',
   85     '\(\mu_1 / \mu_2\)',
   86     '\(\mu_1\mu_2\)'
   87 );
   88 
   89 
   90 $mc[5] = new_multiple_choice();
   91 $mc[5]->qa('If two random samples of sizes \(n_1\) and \(n_2\) are
   92 selected independently from two populations with variances \(\sigma_1^2\)
   93 and \(\sigma_2^2\), then the standard error of the sampling distribution
   94 of the sample mean difference, \(\bar{X_1}-\bar{X_2}\), equals',
   95     '\(\displaystyle \sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}\)'
   96 );
   97 $mc[5]->extra(
   98     '\(\displaystyle \sqrt{\frac{\sigma_1^2 - \sigma_2^2}{n_1 n_2}}\)',
   99     '\(\displaystyle \sqrt{\frac{\sigma_1^2 + \sigma_2^2}{n_1 n_2}}\)',
  100     '\(\displaystyle \sqrt{\frac{\sigma_1^2}{n_1}-\frac{\sigma_2^2}{n_2}}\)'
  101 );
  102 
  103 
  104 $a = random(1,5,1);
  105 $b = random(1,5,1);
  106 while ($a==$b){
  107      $b=random(1,5,1);
  108 }
  109 
  110 
  111 BEGIN_TEXT
  112 $PAR
  113 \{ $mc[$a]->print_q() \}
  114 
  115 \{ $mc[$a]->print_a() \}
  116 $PAR
  117 \{ $mc[$b]->print_q() \}
  118 
  119 \{ $mc[$b]->print_a() \}
  120 $PAR
  121 
  122 END_TEXT
  123 
  124 ANS(radio_cmp($mc[$a]->correct_ans));
  125 ANS(radio_cmp($mc[$b]->correct_ans));
  126 
  127 ENDDOCUMENT();       # This should be the last executable line in the problem.