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    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
25 loadMacros(
26 "PG.pl",
27 "PGbasicmacros.pl",
28 "PGchoicemacros.pl",
29 "PGanswermacros.pl",
30 "PGgraphmacros.pl",
31 "PGnumericalmacros.pl",
32 "PGstatisticsmacros.pl",
33 "PGauxiliaryFunctions.pl",
34 "extraAnswerEvaluators.pl"
35 );
36
37
38
39 TEXT(beginproblem());
40 $showPartialCorrectAnswers = 1; 41 # install_problem_grader(~~&std_problem_grader); 42 43$n = random(40,50,1);
44 $k = random(5,9,1); 45$sse = random(1200,1500,1);
46 $ssr = random(800,900,1); 47$sst = $ssr +$sse;
48
49 $r2 = 0.0001*floor(10000*($ssr/$sst) + 0.5); 50$multr = 0.0001*floor(10000*sqrt($r2) + 0.5); 51$adjr2 = 0.0001*floor(10000*(1 - ( ($sse/($n-$k-1))/($sst/($n-1)) )) + 0.5);; 52$obs = $n; 53$se = 0.01*floor(100*sqrt($sse/($n-$k-1))+0.5); 54 55$dfreg = $k; 56$dfres = $n-$k-1;
57 $dftot =$n-1;
58
59 $msr = 0.01*floor(100*$ssr/$dfreg + 0.5); 60$mse = 0.01*floor(100*$sse/$dfres + 0.5);
61 $f = 0.01*floor(100*$msr/$mse + 0.5);; 62$fsig = fprob($dfreg,$dfres,$f); 63 64 65 BEGIN_TEXT 66 67 Below is partial Excel output from a multiple regression: 68 $69 \begin{array}{|l|r|r|r|r|r|} \hline 70 \multicolumn{2}{|c|}{\mbox{Regression Statistics}} & & & & \\ \hline 71 \mbox{Multiple R} & multr & & & & \\ \hline 72 \mbox{R Square} & r2 & & & & \\ \hline 73 \mbox{Adjusted R Square} & adjr2 & & & & \\ \hline 74 \mbox{Standard Error} & se & & & & \\ \hline 75 \mbox{Observations} & obs & & & & \\ \hline 76 & & & & & \\ \hline 77 \mbox{ANOVA} & & & & & \\ \hline 78 & \mbox{df} &\mbox{SS} &\mbox{MS} &\mbox{F} &\mbox{Significance F} \\ \hline 79 \mbox{Regression} & dfreg & ssr & msr & f & fsig\\ \hline 80 \mbox{Residual} & dfres & sse & mse & & \\ \hline 81 \mbox{Total} & dftot & sst & & & \\ \hline 82 \end{array} 83$ 84$PAR
85 Determine each of the following from the output:
86 $PAR 87 88 $$R^2$$ = \{ ans_rule(15) \} 89 90$PAR
91
92 $$s_{\epsilon}$$ = \{ ans_rule(15) \}
93
94 $PAR 95 96 MSR = \{ ans_rule(15) \} 97 98$PAR
99
100 END_TEXT
101
102 ANS(num_cmp($r2)); 103 ANS(num_cmp($se));
104 ANS(num_cmp(\$msr));
105
106 ENDDOCUMENT();       # This should be the last executable line in the problem.


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