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# Annotation of /trunk/NationalProblemLibrary/UVA-Stat/setStat212-Homework07/stat212-HW07-02.pg

 1 : jjholt 451 ## 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.