For this Critical Thinking assignment, you will analyze survey results using concepts from set theory.

A survey of 500 high school math teachers was conducted to determine what affects students’ ability to succeed in math. The study found that 340 respondents believed that lack of confidence affects students’ ability to succeed in math, while 225 believed that a plethora of outside distractions affects students’ ability to succeed in this subject. There were 65 respondents who believed both, lack of confidence and outside distractions, affect students’ ability to succeed in math.

**Part I: Complete the following steps:**

- Define two sets to represent the two different opinions of the survey’s respondents.
- Create a Venn diagram to represent the results of this survey.

How many respondents believed that only lack of confidence affects students’ ability to succeed in math? - How many respondents believed that only outside distractions affect students’ ability to succeed in math?
- How many respondents believed that neither lack of confidence nor outside distractions affect students’ ability to succeed in math?

**Part II: Based on your work in Part I, discuss the following:**

- Use an alternative method to define the sets in Part I.
- Explain how you created the Venn’s diagram. Describe how you found the numbers corresponding to each region.
- Discuss how you can use set operations to answer questions three through five in Part I.
- Discuss how the numbers on the Venn diagram would have changed if the total respondents who believed that lack of confidence affects students’ ability to succeed in math decreased to 300. What would this imply for the answers to questions three through five in Part I?
- Discuss the advantages of using a Venn diagram to analyze the results of this survey.
- Provide an example of a real-world survey that could be modeled using the Venn diagram below.

**Requirements:**

You must submit two files for this assignment. The first file should contain the computations, graphs, diagrams, etc., associated with the questions in Part I. This file may be formatted as a numbered list of answers. Unless stated in the problem, a narrative discussion is not required, but you must provide enough information to show how you arrived at the answer.

The second file should be a 2-3-page narrative paper, written in APA format, associated with the situation described in Part II. Specific requirements for the paper are provided below:

- Your paper should be 2-3 pages in length (not counting the title page and references page) and should cite and integrate at least two credible outside sources. The CSU Global Library is a great place to find resources. Your textbook is a credible resource.
- Include a title page, introduction, body, conclusion, and a reference page.
- The introduction should describe or summarize the topic or problem. It might discuss the general applications of the topic or it might introduce the unique terminology associated with the topic.
- The body of your paper should address the questions posed in the problem. Explain how you approached and answered the question or solved the problem, and, for each question, show all steps involved. Be sure this is in paragraph format, not numbered answers like a homework assignment.
- The conclusion should summarize your thoughts about what you have determined from your analysis in completing the assignment. Nothing new should be introduced in the conclusion that was not previously discussed in the body paragraphs.

- Include any tables of data or calculations, calculated values, and/or graphs referenced in the paper. (Note: The minimum required length excludes any tables, graphs, etc.)
- Document formatting, citations, and style should conform to the
__CSU Global Writing Center (Links to an external site.)__. A short summary containing much that you need to know about paper formatting, citations, and references is contained in the__Template Paper (Links to an external site.)__. If you need assistance with your writing style or you need writing tips or tutorials, visit the__CSU-Global Writing Center (Links to an external site.)__.

**References**

(Adapted from) GlobeNewswire, Inc. (2018). __Lack of confidence biggest stumbling block to performing well in math, national survey of high school math teachers reveals. (Links to an external site.)__ *Society for Industrial and Applied Mathematics*.