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# View of /trunk/rochester_problib/setStatistics3Estimates/ur_stt_3_5.pg

Thu Jun 28 18:00:51 2001 UTC (11 years, 10 months ago) by amanda
File size: 1780 byte(s)
new problems


    1 ##DESCRIPTION
2 ##KEYWORDS('large sample', 'confidence interval', 'statistics')
3 ##
4 ##ENDDESCRIPTION
5
6 DOCUMENT();        # This should be the first executable line in the problem.
7
9 "PG.pl",
10 "PGbasicmacros.pl",
11 "PGchoicemacros.pl",
13 "PGnumericalmacros.pl",
14 "PGstatisticsmacros.pl",
15 "PGauxiliaryFunctions.pl"
16 );
17
18 TEXT(beginproblem());
19 $showPartialCorrectAnswers = 1; 20 21 for ($i=0; $i<4;$i++) {
22   $n[$i] = random(70,120,5);
23   $x[$i] = random(1,105,.1);
24   $s[$i] = random(2,5, .01);
25 }
26
27 @conf = (90,95,99);
28 @a = (1.645,1.96,2.575);
29 @slice = NchooseK(3,1);
30 @sconf = @conf[@slice];
31 @sa = @a[@slice];
32
33 for ($i=0;$i<4; $i++) { 34$ans1[$i] =$x[$i] -$sa[0]*($s[$i]/sqrt $n[$i]);
35   $ans2[$i] = $x[$i] + $sa[0]*($s[$i]/sqrt$n[$i]); 36 } 37 38 BEGIN_TEXT 39 A random sample of $$n$$ measurements was selected from a population with unknown mean $$\mu$$ and 40 standard deviation $$\sigma$$. Calculate a $$sconf[0] \\%$$ confidence interval for $$\mu$$ for each of the 41 following situations:$PAR
42 (a) $$\$$ $$n = n[0], \ \overline{x} = x[0], \ s = s[0]$$ $BR 43 \{ans_rule(20)\} $$\leq \mu \leq$$ \{ans_rule(20)\}$PAR
44 (b) $$\$$ $$n = n[1], \ \overline{x} = x[1], \ s = s[1]$$ $BR 45 \{ans_rule(20)\} $$\leq \mu \leq$$ \{ans_rule(20)\}$PAR
46 (c) $$\$$ $$n = n[2], \ \overline{x} = x[2], \ s = s[2]$$ $BR 47 \{ans_rule(20)\} $$\leq \mu \leq$$ \{ans_rule(20)\}$PAR
48 (d) $$\$$ $$n = n[3], \ \overline{x} = x[3], \ s = s[3]$$ $BR 49 \{ans_rule(20)\} $$\leq \mu \leq$$ \{ans_rule(20)\} 50 END_TEXT 51 ANS(num_cmp($ans1[0]));
52 ANS(num_cmp($ans2[0])); 53 ANS(num_cmp($ans1[1]));
54 ANS(num_cmp($ans2[1])); 55 ANS(num_cmp($ans1[2]));
56 ANS(num_cmp($ans2[2])); 57 ANS(num_cmp($ans1[3]));
58 ANS(num_cmp(\$ans2[3]));
59
60 ENDDOCUMENT();       # This should be the last executable line in the problem.