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| 1 : | amanda | 29 | ##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 : | |||
| 8 : | loadMacros( | ||
| 9 : | "PG.pl", | ||
| 10 : | "PGbasicmacros.pl", | ||
| 11 : | "PGchoicemacros.pl", | ||
| 12 : | "PGanswermacros.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 : | amanda | 30 | (a) \( \ \) the degree of freedom \( \ \) \{ans_rule(10)\} $PAR |
| 59 : | (b) \( \ \) the critical \(t\) value \( \ \) \{ans_rule(10)\} $PAR | ||
| 60 : | amanda | 29 | (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)); | ||
| 71 : | ANS(radio_cmp($mc->correct_ans)); | ||
| 72 : | |||
| 73 : | ENDDOCUMENT(); # This should be the last executable line in the problem. |
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