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Tue Jul 3 21:36:52 2007 UTC (5 years, 10 months ago) by jjholt
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```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());
35
36 \$mc[1] = new_multiple_choice();
37 \$mc[1]->qa('As a general rule, the normal distribution is
38 used to approximate the sampling distribution of the
39 sample proportion only if',
40     '\(np\) and \(n(1-p)\) are both greater than 5'
41 );
42 \$mc[1]->extra(
43     'the sample size \(n\) is greater than 30',
44     'the population proportion \(p\) is close to 0.50',
45     'the underlying population proportion is normal'
46 );
47
48
49 \$mc[2] = new_multiple_choice();
50 \$mc[2]->qa('If the standard error of the sampling
51 distribution of the sample proportion is 0.0229 for samples of
52 size 400, then the population proportion must be either',
53     '0.3 or 0.7'
54 );
55 \$mc[2]->extra(
56     '0.4 or 0.6',
57     '0.5 or 0.5',
58     '0.2 or 0.8'
59 );
60
61
62 \$mc[3] = new_multiple_choice();
63 \$mc[3]->qa('Given that \(X\) is a binomial random variable, the
64 binomial probability \(P(X \geq x)\) is approximated
65 by the area under a normal curve to the right of',
66     '\(x-0.5\)'
67 );
68 \$mc[3]->extra(
69     '\(x+0.5\)',
70     '\(x-1\)',
71     '\(x+1\)'
72 );
73
74
75 \$mc[4] = new_multiple_choice();
76 \$mc[4]->qa('A sample of size \(n\) is selected at random from
77 an infinite population.  As \(n\) increases, which of
78 the following statements is true?',
79     'The standard error of the sample mean decreases'
80 );
81 \$mc[4]->extra(
82     'The population standard deviation decreases',
83     'The population standard deviation increases',
84     'The standard error of the sample mean increases'
85 );
86
87 \$mc[5] = new_multiple_choice();
88 \$mc[5]->qa('Suppose that \(X\) is a binomial random variable with
89 n = 16 and p = 0.35.  Using normal approximation with continuity
90 correction, what is (approximately) \(P(X = 7)\)?',
91     '0.1589'
92 );
93 \$mc[5]->extra(
94     '0',
95     '0.1854',
96     '0.1740'
97 );
98
99
100 \$a = random(1,5,1);
101 \$b = random(1,5,1);
102 while (\$a==\$b){
103      \$b=random(1,5,1);
104 }
105
106
107 BEGIN_TEXT
108 \$PAR
109 \{ \$mc[\$a]->print_q() \}
110
111 \{ \$mc[\$a]->print_a() \}
112 \$PAR
113 \{ \$mc[\$b]->print_q() \}
114
115 \{ \$mc[\$b]->print_a() \}
116 \$PAR
117
118 END_TEXT
119