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# View of /trunk/rochester_problib/setStatistics4HypothesisTesting/ur_stt_4_15.pg

Tue Jul 3 13:40:26 2001 UTC (11 years, 10 months ago) by amanda
File size: 2172 byte(s)
fixed typos and spacing


    1 ##DESCRIPTION
2 ##KEYWORDS('small sample','hypothesis testing','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 $showPartialCorrectAnswers = 1; 20 21$n = random(3,20,1);
22 $mean = random(80,95,1); 23$s = random(5,15,1);
24 $eff = random(90,99,1); 25$e = $eff/100; 26$alpha = random(.01,.05,.04);
27 $m =$mean/100;
28 $s1 =$s/100;
29
30 $df =$n-1;
31 $t = tdistr($df, $alpha); 32$test = ($m-$e)/($s1/sqrt$n);
33
34 $mc = new_multiple_choice(); 35 36 @ans = ("We can reject the null hypothesis that $$\mu = e$$ and accept that $$\mu 37 > e$$, that is, the bug repellent is effective. ", 38 "There is not sufficient evidence to reject the null hypothesis that $$\mu = 39 e$$. "); 40 41 if ($test > $t ) {$tag = 0;} else {$tag = 1;} 42 43$mc -> qa('The final conclustion is', $ans[$tag]);
44
45 $mc -> extra($ans[1-$tag]); 46 47 BEGIN_TEXT 48 The effectiveness of a new bug repellent is tested on $$n$$ subjects for a 10 49 hour period. Based on the number and location of the bug bites, the percentage 50 of surface area exposed protected from bites was calculated for each of the 51 subjects. The results were as follows:$PAR
52 $$\overline{x} = mean$$ $PERCENT, $$\ s = s$$$PERCENT $PAR 53 The new repellent is considered effective if it provides a percent 54 repellency of at least $$eff$$. Using $$\alpha = alpha$$, construct a 55 hypothesis test with null hypothesis $$\mu = e$$ and alternative hypothesis $$\mu>e$$ to determine 56 whether the mean repellency of the new bug relellent is greater than $$eff$$ by computing the following: 57$PAR
58 (a) $$\$$ the degree of freedom $$\$$ \{ans_rule(10)\} $PAR 59 (b) $$\$$ the critical $$t$$ value $$\$$ \{ans_rule(10)\}$PAR
60 (c) $$\$$ the test statistics $$\$$ \{ans_rule(10)\} $PAR 61$PAR
62
63 \{ $mc->print_q() \} 64$PAR
65 \{ $mc->print_a() \} 66 67 END_TEXT 68 ANS(num_cmp($df));
69 ANS(num_cmp($t, tol=>.002)); 70 ANS(num_cmp($test));