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| 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. |
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