** Using WeBWorK **

NAMED_WEIGHTED_ANS(pnot => $popup6->cmp->withPostFilter(

  AnswerHints(

   '0'=>"The proportion is not zero.",

   Compute("$phat")=>"Sample data should not be used in the hypothesis statement.",

   '80%'=>"Percents are not the same as proportions.",

   '0.80'=>"Yes.",

  )), 7 );

##DESCRIPTION

##  Hypothesis test on one proportion.

##ENDDESCRIPTION

##KEYWORDS('confidence interval', 'confidence interpretation')

## DBsubject('Statisitics')

## DBchapter('confidence intervals')

## DBsection('Real Numbers')

## Date('11/7/2016')

## Author('Tim Payer')

# DESCRIPTION  CI on mu for t-intervals and Chi-intervals

# Find the associated probability given mu and sigma.

# Use correct notation.

# WeBWorK problem written by TimPayer <tsp1@humboldt.edu>

# ENDDESCRIPTION

## DBsubject(Probability)

## DBchapter(Random variables)

## DBsection(Expectation)

## Institution(Humboldt State University)

## Author(Tim Payer)

## KEYWORDS(probability, translate, notation)

DOCUMENT();

loadMacros(

"PGstandard.pl",

"PGunion.pl",

"PGnumericalmacros.pl",

"PGstatisticsmacros.pl",

"MathObjects.pl",

"parserPopUp.pl",

"PGML.pl",

"unionTables.pl",

"niceTables.pl",

"PGcourse.pl",

"PGchoicemacros.pl",

  "answerHints.pl",

"weightedGrader.pl"

);

install_weighted_grader();

#Text(beginproblem());   #uncomment

install_problem_grader(~~&std_problem_grader);

$showPartialCorrectAnswers = 1;

Context("Numeric");

Context()->flags->set(

  tolerance => 0.01,

  tolType => "absolute",

);

### Prob 14B.1) ########

$po = 0.8;

$n = random(65, 110,1);

$dd = random(0.60, 0.80, 0.01) ;

$y1 = floor($n*$dd);

$y = Compute("$y1");

$phat1 =$y/$n;

$phat = sprintf("%0.4f",$phat1);

#$phat1 =Compute("$phat2");

$fat ="\frac{$y}{$n}";

$pnp = Compute("$po*$n*(1-$po)");

$zsam =Compute("($phat-$po)/sqrt($po*(1-$po)/$n)");

$alfa = list_random('10%', '5%', '1%', '0.5%', '0.01%', '0.005%', '0.001%');

$popup0 = PopUp(

["Choose:",  'has', 'does not have' ], 'has');

$popup1 = PopUp(

["?",  '=', 'not =', ' < ', ' >', '< or =', '> or =' ], '> or =');

$popup13 = PopUp(

["Choose:",  'mu', 'eta', 'p', 'sigma', 'x-bar' ,'x-tilde', 'p-hat', 'sd' ], 'mu');

$popup2 = PopUp(

["Choose:",  'mean', 'median', 'proportion', 'variance', 'standard deviation','percentage'], 'proportion');

$popup3 = PopUp(

["Choose:",  'survive.', 'die.', 'survive will exceed 80%.', 'die will exceed 80%.',  'survive will be about 80%.', 'die will be about 80%.',  'survive will be less than 80%.', 'die will be less than 80%.', 'survive will exceed '.$phat.'.', 'die will exceed '.$phat.'.', 'survive will be about '.$phat.'.', 'die will be about '.$phat.'.', 'survive will be less than '.$phat.'.', 'die will be less than '.$phat.'.'], 'die.');

$popup4 = PopUp(

["Choose:",  'mu', 'eta', 'p', 'sigma', 'x-bar' ,'x-tilde', 'p-hat', 'sd' ], 'p');

$popup5 = PopUp(

["Choose:",  '=', 'not =', '< ', '>', '< or =', '> or =' ], '=');

$popup6 = PopUp(

["Choose:",  '0', $phat1, '80%', '0.80'], '0.80');

$popup7 = PopUp(

["Choose:",  'mu', 'eta', 'p', 'sigma', 'x-bar' ,'x-tilde', 'p-hat', 'sd' ], 'p');

$popup8 = PopUp(

["Choose:",  '=', 'not =', '<', '>', '< or =', '> or =' ], '<');

$popup9 = PopUp(

["Choose:",  '0', $phat, '80%', '0.80'], '0.80');

$poplos = PopUp(

["alpha ?",  "0.20", "0.10", "0.05",  "0.025",  "0.02", "0.01",  "0.005",  "0.002", "0.001","0.0005",  "0.0001", "0.00005", "0.00001", "0.000005"], '0.05');

$popup10 = PopUp(

["Choose:",  'upper tailed', 'lower tailed', 'two tailed'], 'upper tailed');

$popup11 = PopUp(

["?",  '-', '+', '+ or -'], '+');

$popup12 = PopUp(

["Z-Critical?", "1.282", "1.645","1.960", "2.326", "2.576", "3.090", "3.291", "3.891", "4.491"], "1.645");

$pop14 = PopUp(

["LOS ??",  "20%","10%", "5%", "2.5%", "2%", "1%", "0.5%", "0.2%", "0.1%", "0.05%", "0.01%", "0.005%", "0.001%", "0.0005%" ], "5%");

$pop15 = PopUp(

["reject ?", "reject", "do not reject"], "reject");

$pop16 = PopUp(

["?", ">", "<"], ">");

$pop17 = PopUp(

["?", ">", "<"], ">");

$pop18 = PopUp(

["?", "-", "+", "+ or -"], "+");

$pop19 = PopUp(

["Z-Critical?", "1.282", "1.645","1.960", "2.326", "2.576", "3.090", "3.291", "3.891", "4.491"], "1.645");

$pop20 = PopUp(

["?", ">", "<"], "<");

$pop21 = PopUp(

["which bracketed p-value?",

"(p > 0.20)","(p > 0.10)","(0.10 < p < 0.20)", "(0.05 < p < 0.10)", "(0.025 < p < 0.05)", "(0.02 < p < 0.05)", "(0.01 < p < 0.025)","(0.01 < p < 0.02)",  "(0.005 < p < 0.01)", "(0.002 < p < 0.01)", "(0.001 < p < 0.005)", "(0.001 < p < 0.002)",  "(0.0005 < p < 0.001)", "(0.0001 < p < 0.001)", "(0.00005 < p < 0.0005)",  "(0.00001 < p < 0.0001)", "(0.000005 < p < 0.00005)","(p < 0.00001)", "(p < 0.000005)"], "(p < 0.000005)" );

$pop22 = PopUp(

["?", ">", "<"], "<");

$pop23 = PopUp(

["alpha ?",  "0.20", "0.10", "0.05",  "0.025",  "0.02", "0.01",  "0.005",  "0.002", "0.001","0.0005",  "0.0001", "0.00005", "0.00001", "0.000005"], "0.05");

$pop24 = PopUp(

["?", "decreased", "increased", "remained consistent with the incidence"], "increased");

####  Begin Problem...

 

BEGIN_PGML 

   *Drawn from Lecture Notes: Week 7 Day 3.*  

*14B.2)* In Virginia the big eared bat's population has dropped to a near endangered level of 10,000 due to White Nose Syndrome (WNS). WNS is a fungus the grows on the bats nose and wing tips of the blighted bat and has a mortality rate of 80% for all bats who catch the fungus. In an effort to treat WNS, biologists dusted an anti-fungal powder on a random sample of [$n] bats with WNS and yet [$y] of these bats still died. Was the anti-fungal powder effective in reducing the mortality rate for the big eared bat? Test the hypothesis at the [$alfa] LOS.  

fat = [`[$fat]`]

 

*14B.2) Step 1*  Preliminary check on sample size.  

 

Is [``n \cdot p_o(1-p_o) \ge 10``] ?  

 

Then   [``n \cdot p_o(1-p_o) ``] = [______] [$popup1->menu]* [``\Large{\text{10}}``] 

 

We conclude that this data set [$popup0->menu]* an ample sample for hypothesis testing on one proportion.

END_PGML 

BEGIN_TEXT

$PAR

$PAR

\{

DataTable(

[

['$BBOLD Note! $EBOLD Because of the limitations in software most special characters can not be included in a "pop-up" answer format and yet they are needed for the hypothesis formation. The pop-up selections will be in the text-form for the special characters embedded within the pop-up answer. Use the table at the right as a guide if needed.','  ',[image( "Symbol_translation.png", width=>165, height=>290, tex_size=>700 ) ] ,image( "Z_Table.png", width=>235, height=>212, tex_size=>700 ),]

  ], 

  caption => 'English text equivalence with special symbols, and an abbreviated Z-table: ',

  midrules=>0, 

  align => 'p{3in} p{0.1in} p{2in}p{3in}'

);

\}

$PAR

END_TEXT

BEGIN_PGML 

*14B.2) Step 2*  Make selections that will create the best declaration of variable for the biologist's hypothesis.  

 

[$popup13->menu]* = The [$popup2->menu]* of bats with WNS treated with anti-fungal powder that [$popup3->menu("pdes")]*

 

*14B.2) Step 3*  Make selections that will create the correct hypothesis and LOS statement for Sicher's hypothesis. 

 

[``\Large{H_o:}``] [$popup4->menu]* [$popup5->menu]* [$popup6->menu("pnot")]*  

 

[``\Large{H_a:}``] [$popup7->menu]* [$popup8->menu]* [$popup9->menu]*

 

[``\Large{\alpha =}``] [$poplos->menu]*

*14B.1) Step 4*  The decision line for this hypothesis test is: [$popup10->menu]*  

 

*14B.1) Step 5*  The Z-critical value for this hypothesis test is:  

 

Z-critical = [$popup11->menu]* [$popup12->menu]*   

 

*14B.1) Step 6*  The statistical conclusion for this hypothesis test is:  

At the [$pop14->menu]*  LOS we [$pop15->menu]*  the null hypothesis of  [``\large{H_o  }``], because:

 

END_PGML

BEGIN_TEXT

$BR

$PAR

\{

DataTable(

[

[' Z Notational $BR Support: $BR $BR Numeric $BR Validation: ',' \(\hspace{10pt}\)  \(\large{Z_{sample}}\) \(\hspace{2pt}\) '.$pop16->menu.' \(\hspace{2pt}\) \(\large{Z_{critical}}\) $BR $BR '.$zsam->ans_rule(5).' '.$pop17->menu.''.$pop18->menu.''.$pop19->menu.'' ],

  ], 

  caption => '  ',

  midrules=>0, 

  align => 'p{1.2in}p{7in}'

);

\}

$PAR

\{

DataTable(

[

['p-Notational $BR Support: $BR $BR Numeric $BR Validation: ',' \(\hspace{115pt}\) \(\Large{p} \hspace{2pt}\) '.$pop20->menu.'\(\hspace{2pt} \Large{\alpha}\) $BR $BR '.$pop21->menu.''.$pop22->menu.''.$pop23->menu.'' ],

  ], 

  caption => '  ',

  midrules=>0, 

  align => 'p{1.2in}p{7in}'

);

\}

$PAR

$BR

END_TEXT

BEGIN_PGML

*14B.1) Step 7*   Write an English sentence conclusion.  

 

The evidence supports the case that peanut allergies among children under 18 years of age has  [$pop24->menu]* since 1997.

END_PGML

#Adapted weighted answers values:  

## Problems 13.1 ##

WEIGHTED_ANS( ($pnp)->cmp, 7 );

WEIGHTED_ANS( ($popup1)->cmp, 1 );

WEIGHTED_ANS( ($popup0)->cmp, 1 );

WEIGHTED_ANS( ($popup13)->cmp, 4 );

WEIGHTED_ANS( ($popup2)->cmp, 4 );

NAMED_WEIGHTED_ANS(pdes => $popup3->cmp->withPostFilter(

  AnswerHints(

      "survive." => "No. Just what kind of rate is being measured?",

   "die." => "Yes!",

   "survive will exceed 80%." => "Survival rates are not sought, and do not restrict your variable declaration to a quantity.",

   "die will exceed 80%." => "Do not restrict your variable declaration to a quantity.",

   "survive will be about 80%." => "Survival rates are not sought, and do not restrict your variable declaration to a quantity.",

   "die will be about 80%." => "Do not restrict your variable declaration to a quantity.",

"survive will be less than 80%." => "Survival rates are not sought, and do not restrict your variable declaration to a quantity.",

 "die will be less than 80%." => "Do not restrict your variable declaration to a quantity.",

   'survive will exceed '.$phat.'.' => "Survival rates are not sought, and do not restrict your variable declaration to a quantity.",

   'die will exceed '.$phat.'.'=> "Do not restrict your variable declaration to a quantity.",

   'survive will be about '.$phat.'.' => "Survival rates are not sought, and do not restrict your variable declaration to a quantity.",

   'die will be about '.$phat.'.' => "Do not restrict your variable declaration to a quantity.",

'survive will be less than '.$phat.'.' => "Survival rates are not sought, and do not restrict your variable declaration to a quantity.",

 'die will be less than '.$phat.'.' => "Do not restrict your variable declaration to a quantity.",

  )), 7 );

WEIGHTED_ANS( ($popup4)->cmp, 4 );

WEIGHTED_ANS( ($popup5)->cmp, 1 );

NAMED_WEIGHTED_ANS(pnot => $popup6->cmp->withPostFilter(

  AnswerHints(

   '0'=>"The proportion is not zero.",

   Compute("$phat")=>"Sample data should not be used in the hypothesis statement.",

   '80%'=>"Percents are not the same as proportions.",

   '0.80'=>"Yes.",

  )), 7 );

WEIGHTED_ANS( ($popup7)->cmp, 3 );

WEIGHTED_ANS( ($popup8)->cmp, 3 );

WEIGHTED_ANS( ($popup9)->cmp, 4 );

WEIGHTED_ANS( ($poplos)->cmp, 1 );

WEIGHTED_ANS( ($popup10)->cmp, 4 );

WEIGHTED_ANS( ($popup11)->cmp, 2 );

WEIGHTED_ANS( ($popup12)->cmp, 4 );

WEIGHTED_ANS( ($pop14)->cmp, 1 );

WEIGHTED_ANS( ($pop15)->cmp, 4 );

WEIGHTED_ANS( ($pop16)->cmp, 1 );

WEIGHTED_ANS( ($zsam)->cmp, 16 );

WEIGHTED_ANS( ($pop17)->cmp, 2 );

WEIGHTED_ANS( ($pop18)->cmp, 3 );

WEIGHTED_ANS( ($pop19)->cmp, 4 );

WEIGHTED_ANS( ($pop20)->cmp, 2 );

WEIGHTED_ANS( ($pop21)->cmp, 7 );

WEIGHTED_ANS( ($pop22)->cmp, 1 );

WEIGHTED_ANS( ($pop23)->cmp, 3 );

WEIGHTED_ANS( ($pop24)->cmp, 3 );

BEGIN_PGML_SOLUTION

The correct answers are coming....in 2017, Hah!

END_PGML_SOLUTION

ENDDOCUMENT();