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

Tue Jul 3 21:36:52 2007 UTC (5 years, 10 months ago) by jjholt
File size: 3519 byte(s)
Added stat problems.  Tags to be fixed soon.


    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
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.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.