[npl] / trunk / NationalProblemLibrary / UVA-Stat / setStat212-Homework12 / stat212-HW12-16.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

# View of /trunk/NationalProblemLibrary/UVA-Stat/setStat212-Homework12/stat212-HW12-16.pg

Thu Jul 5 01:59:02 2007 UTC (5 years, 11 months ago) by jjholt
File size: 2556 byte(s)
Consolidated tags.


    1 ## DESCRIPTION
2 ##  Statistics: Sampling Distributions
3 ## ENDDESCRIPTION
4 ##DESCRIPTION
5 ##KEYWORDS('statistics','hypothesis testing')
6 ##
7 ## naw tagged this problem
8
9 ## DBchapter('Hypothesis Testing')
10 ## DBsection('Common Large-Sample Tests')
11 ## Date('7/8/2005')
12 ## Author('Nolan A. Wages')
13 ## Institution('University of Virgnia')
14 ## TitleText1('Mathematical Statistics')
15 ## EditionText1('4')
16 ## AuthorText1('Wackerly, Mendenhall, Scheaffer')
17 ## Section1('10.3')
18 ## Problem1('20')
19
20
21 ##ENDDESCRIPTION
22
23 DOCUMENT();        # This should be the first executable line in the problem.
24
26 "PG.pl",
27 "PGbasicmacros.pl",
28 "PGchoicemacros.pl",
30 "PGgraphmacros.pl",
31 "PGnumericalmacros.pl",
32 "PGstatisticsmacros.pl",
33 "PGauxiliaryFunctions.pl",
35 );
36
37
38
39 TEXT(beginproblem());
40 $showPartialCorrectAnswers = 0; 41 install_problem_grader(~~&std_problem_grader); 42 43$x[1] = random(-3,-1,1);
44 $x[2] = random(0,3,1); 45$x[3] = random(4,6,1);
46 $x[4] = random(7,9,1); 47$x[5] = random(9,12,1);
48
49 $y[1] = 3 + random(-3,-1,1); 50$y[2] = 6 + random(0,3,1);
51 $y[3] = 9 + random(4,6,1); 52$y[4] = 12 + random(6,8,1);
53 $y[5] = 15 + random(8,12,1); 54 55$n = 5;
56
57 $xbar = ($x[1]+$x[2]+$x[3]+$x[4]+$x[5])/$n; 58$ybar = ($y[1]+$y[2]+$y[3]+$y[4]+$y[5])/$n;
59
60 $sx = sqrt( (($x[1]-$xbar)**2 + ($x[2]-$xbar)**2 + ($x[3]-$xbar)**2 + ($x[4]-$xbar)**2 + ($x[5]-$xbar)**2)/($n-1) );
61 $sy = sqrt( (($y[1]-$ybar)**2 + ($y[2]-$ybar)**2 + ($y[3]-$ybar)**2 + ($y[4]-$ybar)**2 + ($y[5]-$ybar)**2)/($n-1) );
62
63 $cov = ( ($x[1]-$xbar)*($y[1]-$ybar) + ($x[2]-$xbar)*($y[2]-$ybar) + ($x[3]-$xbar)*($y[3]-$ybar) 64 + ($x[4]-$xbar)*($y[4]-$ybar) + ($x[5]-$xbar)*($y[5]-$ybar) )/($n-1);
65
66 $b1 =$cov/$sx**2; 67$b0 = $ybar -$b1*$xbar; 68 69$sse = ($n-1)*($sy**2 - ($cov/$sx)**2);
70 $se = sqrt($sse/($n-2)); 71$r2 = ($cov/($sx*$sy))**2; 72 73$x1 = random(1,5,1);
74 $x2 = random(6,10,1); 75 76$yhat1 = $b0 +$b1*$x1; 77$yhat2 = $b0 +$b1*$x2; 78 79 80 BEGIN_TEXT 81 82 Find the least-squares regression line 83 $$\hat{y} = b_0 + b_1 x$$ through the points 84 85 $86 (x[1],y[1]), (x[2],y[2]), (x[3],y[3]), (x[4],y[4]), (x[5],y[5]), 87$ 88 and then use it to find point estimates $$\hat{y}$$ corresponding to 89 $$x = x1$$ and $$x = x2$$. 90$PAR
91
92 For $$x = x1$$, $$\hat{y}$$  = \{ ans_rule(15) \}
93
94 $PAR 95 96 For $$x = x2$$, $$\hat{y}$$ = \{ ans_rule(15) \} 97 98$PAR
99
100 END_TEXT
101
102 ANS(num_cmp($yhat1)); 103 ANS(num_cmp($yhat2));
104
105 ENDDOCUMENT();       # This should be the last executable line in the problem.