View of /trunk/rochester_problib/setStatistics4HypothesisTesting/ur_stt_4_15.pg

    1 ##DESCRIPTION
    2 ##KEYWORDS('small sample','hypothesis testing','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(3,20,1);
   22 $mean = random(80,95,1);
   23 $s = random(5,15,1);
   24 $eff = random(90,99,1);
   25 $e = $eff/100;
   26 $alpha = random(.01,.05,.04);
   27 $m = $mean/100;
   28 $s1 = $s/100;
   29 
   30 $df = $n-1;
   31 $t = tdistr($df, $alpha);
   32 $test = ($m-$e)/($s1/sqrt $n);
   33 
   34 $mc = new_multiple_choice();
   35 
   36 @ans = ("We can reject the null hypothesis that \( \mu = $e\) and accept that \( \mu
   37   > $e\), that is, the bug repellent is effective. ",
   38         "There is not sufficient evidence to reject the null hypothesis that \( \mu =
   39   $e\). ");
   40 
   41 if ($test > $t ) {$tag = 0;} else {$tag = 1;}
   42 
   43 $mc -> qa('The final conclustion is', $ans[$tag]);
   44 
   45 $mc -> extra($ans[1-$tag]);
   46 
   47 BEGIN_TEXT
   48 The effectiveness of a new bug repellent is tested on \($n\) subjects for a 10
   49 hour period.  Based on the number and location of the bug bites, the percentage
   50 of surface area exposed protected from bites was calculated for each of the
   51 subjects.  The results were as follows: $PAR
   52 \( \overline{x} = $mean \) $PERCENT, \( \ s = $s \)$PERCENT $PAR
   53 The new repellent is considered effective if it provides a percent
   54 repellency of at least \($eff\).  Using \(\alpha = $alpha \), construct a
   55 hypothesis test with null hypothesis \(\mu = $e\) and alternative hypothesis \(\mu>$e\) to determine
   56 whether the mean repellency of the new bug relellent is greater than \($eff\) by computing the following:
   57 $PAR
   58 (a) \( \ \) the degree of freedom \( \ \) \{ans_rule(10)\} $PAR
   59 (b) \( \ \) the critical \(t\) value \( \ \) \{ans_rule(10)\} $PAR
   60 (c) \( \ \) the test statistics \( \ \) \{ans_rule(10)\} $PAR
   61 $PAR
   62 
   63 \{ $mc->print_q() \}
   64 $PAR
   65 \{ $mc->print_a() \}
   66 
   67 END_TEXT
   68 ANS(num_cmp($df));
   69 ANS(num_cmp($t, tol=>.002));
   70 ANS(num_cmp($test));
   71 ANS(radio_cmp($mc->correct_ans));
   72 
   73 ENDDOCUMENT();       # This should be the last executable line in the problem.