##DESCRIPTION ##KEYWORDS('statistics','Inference about a population') ## ## CMMK tagged this problem ## DBchapter('Inference About a Population') ## DBsection() ## Date('07/12/2005') ## Author('Cristina Murray-Krezan') ## Institution('UVa') ## TitleText1('Statistics for Management and Economics') ## EditionText1('6') ## AuthorText1('Keller, Warrack') ## Section1() ## Problem1() ##ENDDESCRIPTION DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGgraphmacros.pl", "PGnumericalmacros.pl", "PGstatisticsmacros.pl", "extraAnswerEvaluators.pl" ); TEXT(beginproblem()); $showPartialCorrectAnswers = 1; # install_problem_grader(~~&std_problem_grader);$n1 = random(35,51,2); $n2 = random(36,52,2);$xbar1 = random(50,60,0.1); $xbar2 = random(70,80,0.1);$s1 = random(5,6,0.1); $s2 = random(10,11,0.1);$df = $n1 +$n2 - 2; $sp2 = (($n1-1)*$s1**2 + ($n2-1)*$s2**2)/$df; $siglev = random(92,98,.5);$alpha = 0.01*(100-$siglev);$tcrit = tdistr($df,$alpha/2); $ucl = ($xbar1 - $xbar2) +$tcrit*sqrt($sp2*(1/$n1 + 1/$n2));$lcl = ($xbar1 -$xbar2) - $tcrit*sqrt($sp2*(1/$n1 + 1/$n2)); BEGIN_TEXT $PAR Two random samples are selected from two independent populations. A summary of the samples sizes, sample means, and sample standard deviations is given below:$PAR $\begin{array}{lll} n_1 = n1, & \bar{x}_1 = xbar1, & s_1 = s1 \\ n_2 = n2, & \bar{x}_2 = xbar2, & s_2 = s2 \\ \end{array}$ $PAR Find a$siglev$PERCENT confidence interval for the difference $$\mu_1 - \mu_2$$ of the means, assuming equal population variances.$PAR Confidence Interval = \{ ans_rule(25) \} $PAR END_TEXT ANS(interval_cmp("($lcl,\$ucl)", sloppy=>'yes')); ENDDOCUMENT(); # This should be the last executable line in the problem.