I am getting a new error in the draggableProof problem. The warning message claims that "choose" isn't numeric in array slice. The "choose" reference is likely due to the "choose" prompt in the pop-up questions that precede the draggable proof problem.

I have declared "Context()->normalStrings;" throughout this problem. And the line code of 213 is beyond the length of my code block.

Any help would be most appreciated.

But I understand that this feature is not yet an official option for the version 2.13 release.

# DESCRIPTION Interpretation of the Confidence Interval

# Translate descriptions of critical points and function

# into correct notation.

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

# ENDDESCRIPTION

## DBsubject(Calculus-single variable)

## DBchapter(Differentiation)

## DBsection(Conceptual understanding of derivatives)

## Institution(Humboldt State University)

## Author(Tim Payer)

## KEYWORDS(derivative, translate, notation)

DOCUMENT();

loadMacros(

"PGstandard.pl",

"PGunion.pl",

"MathObjects.pl",

"parserPopUp.pl",

"unionTables.pl",

"niceTables.pl",

"PGML.pl",

"PGcourse.pl",

"draggableProof.pl",

);

TEXT(beginproblem());

#install_problem_grader(~~&std_problem_grader);

$showPartialCorrectAnswers = 1;

#Context("Numeric");

Context()->texStrings;

$popup1 = PopUp(

["choose", "A", "B", "C"

],"C");

$popup2 = PopUp(

["choose", "D", "E", "F", "G"

],"F");

$popup3 = PopUp(

["choose", "H", "I", "J", "K", "L"

],"H");

$CorrectProof = DraggableProof([

"95% confidence means that",

"95% of all guinea pig brain cells",

"sampled will form",

"confidence intervals that",

"contain ",

"the true mean count of ",

"the dendritic branch segments emanating from the brain cell."

],

[

"there is a 95% chance that",

"the sample mean count of the",

"will exist within",

"we have calculated."

],

SourceLabel => "Choose phrases from here...",

TargetLabel => "...to create the correct interpretation of confidence here.",

);

BEGIN_PGML

*Drawn from the Lecture Notes: Week 6 Day 1, Quiz 5 Prep.*

*11.3)* A dendritic tree is a branched structure that emanates from the body of a nerve cell. In a study of brain development, researchers examined brain tissue from seven adult guinea pigs. The investigators randomly selected nerve cells from a certain region of the brain and counted the number of dendritic branch segments emanating from each selected cell. A total of 36 cells were selected, and the resulting counts are given in the table below.

[@

DataTable(

[

[["38 25 35 48 17 26 $BR 47 24 38 38 49 41 $BR 35 44

45

31

32

59 $BR 42

35

33

53

24

26 $BR 28

35

26

29

26

26 $BR 38

25

28

46

39

53 ", ], ],

],

caption => ' The number of dendritic branches for 36 nerve cells. ',

midrules => 1,

align => '|p{1.3in}|',

);

@]***

Using [``\bar x = 35.67``], and [``sd = 9.99``] gives us [``SE_{\overline x} = \frac{9.99}{\sqrt{36}}=1.67``]

Then we obtain the confidence interval of [``35.67 \pm (2.042)(1.67)``]

or: [``32.3 < \mu < 39.1``]

*11.3a)* Choose the letter that best describes why the preceding analysis might be criticized. (Hint: Are the observations independent?) [___]{$popup1}

*A.)* The data is not large enough to ensure that we have a normal distribution.

*B.)* Seven rodents and 36 brain cells cannot form an even grouping of data. At least one rodent is over represented in the sample.

*C.)* The count of branch segments emanating from a nerve cell will vary over the rodents life. A single snap shot of a count of cells will not give a reliable comparison unless the specific age of the rodent is considered.

*11.3b)* Create 2 histograms of the sample data with R. Does the shape of these histograms support the criticism made in part a?

[@

DataTable(

[

[["Web Page Access: ", headerrow => 1], "Or the URL link: "],

[[" \\(\\rightarrow\\) users.humboldt.edu/tpayer $BR

\\(\\rightarrow\\) Stat_109 $BR

\\(\\rightarrow\\) Data Files $BR

\\(\\rightarrow\\) HW11.csv" ], htmlLink( "http://users.humboldt.edu/tpayer/Stat_109/Data%20Files/HW11.csv","HW11_Nerves_data_set" ) ],

],

caption => ' Access the HW11.csv MS Excel file at either location:',

midrules => 1,

align => '|p{2in}|p{2in}|',

);

@]***

Still need some help loading the data into R-Studio?

Try checking out the pdf file called "Loading_CSV_Files_in_R_Studio.pdf".

This document uses the HW 10 data set as an example.

Look in the folder:

*users.humboldt.edu/tpayer* [`\rightarrow`]

[`\rightarrow`] Stat 109 [`\rightarrow`] Loading_CSV_Files_in_R_Studio.pdf

[@

DataTable(

[

[["Create two histogram plots $BR with different bin widths." ], " Hints for R code: " ],

[["1.) The default display. $BR $BR

2.) The histogram bin span set to 1.5." ], " $BBOLD > attach(HW11) $BR > hist(Nerves) $BR > bins = seq(16.5, 61.5, by = 1.5 $BR > hist(Nerves, breaks = bins) $EBOLD" ],

],

caption => "Compare the distributions of two $BR histograms drawn from the same data set. ",

midrules => 1,

align => '|p{2.5in}|p{2.5in}|',

);

@]***

* Based on the comparison of your two histograms, select one of the four statements below that best explains the criticism made in part a above: [___]{$popup2}

*D.)* The data set does not pass normality, it is skewed left.

*E.)* The data set does not pass normality it is skewed right.

*F.)* The distribution shows 2 or perhaps 3 modes which may reflect the hierarchical structure in the data. That is, the different modes may represent different age classes of kinds of guinea pigs.

*G.)* There is always variation in a random selection of data. With such a small data set it is not unusual to see what looks like a blending of 2 or 3 modes within one normal distribution.

*11.3c)* Interpret the meaning of the confidence interval in the context of this problem. If we have 95% confidence then 95% of what must be true? Choose the one correct interpretation within the following list below: [___]{$popup3}

*H.)* 95% confidence means that 95% of all guinea pig brain cells sampled will form confidence intervals that bracket the true mean count of dendritic branch segments emanating from a guinea pig's brain cell.

*I.)* 95% confidence means that 95% of all guinea pigs will have a mean number of dendritic branch segments emanating from each selected brain cell that falls within the confidence interval that we have calculated.

*J.)* 95% confidence means that 95% of all dendritic branch segments emanating from each selected guinea pig brain cell will exist within the confidence interval that we have calculated.

*K.)* 95% confidence means that 95% of all sample means of the count of dendritic branch segments emanating from each selected guinea pig brain cell will exist within the confidence interval that we have calculated.

*L.)* 95% confidence means that 95% of all guinea pig brain cells sampled will form confidence intervals that bracket the sample mean count of dendritic branch segments emanating from a guinea pig's brain cell.

END_PGML

BEGIN_TEXT

$BBOLD 11.3c) $EBOLD Interpret the meaning of the confidence interval in the context of this problem. If we have 95% confidence then 95% of what must be true? $BR

$BR

Click and drag \{ $CorrectProof->numNeeded\} sentence framents from the left column to form a correct interpretation of the meaning of 95% confidence in the right column.

$PAR

\{ $CorrectProof->Print \}

END_TEXT

Context()->normalStrings;

# Answer Evaluation

ANS($CorrectProof->cmp);

BEGIN_PGML_SOLUTION

The correct answers are:

1. [@ $popup1->correct_ans("g'(12) = 0") @]*.

2. [@ $popup2->correct_ans("g'(14) < 0") @]*.

3. [@ $popup3->correct_ans("g'(15) = 0") @]*.

END_PGML_SOLUTION

ENDDOCUMENT();