[rochester] / trunk / rochester_problib / setStatistics4HypothesisTesting / ur_stt_4_15.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

# Annotation of /trunk/rochester_problib/setStatistics4HypothesisTesting/ur_stt_4_15.pg

 1 : amanda 29 ##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 : amanda 30 (a) $$\$$ the degree of freedom $$\$$ \{ans_rule(10)\} $PAR 59 : (b) $$\$$ the critical $$t$$ value $$\$$ \{ans_rule(10)\}$PAR 60 : amanda 29 (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.