Homework: Confidence Survey
For this Critical Thinking homework, 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 A: Complete the following steps:
1) Define two sets to represent the two different opinions of the survey's respondents.
2) Create a Venn diagram to represent the results of this survey.
3) How many respondents believed that only lack of confidence affects students' ability to succeed in math?
4) How many respondents believed that only outside distractions affect students' ability to succeed in math?
5) How many respondents believed that neither lack of confidence nor outside distractions affect students' ability to succeed in math?
Part B: Based on your work in Part A, discuss the following:
1) Use an alternative method to define the sets in Part A.
2) Explain how you created the Venn's diagram. Describe how you found the numbers corresponding to each region.
3) Discuss how you can use set operations to answer questions three through five in Part I.
4) 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?
5) Discuss the advantages of using a Venn diagram to analyze the results of this survey.
6) Provide an example of a real-world survey that could be modeled using the Venn diagram.
Format your homework according to the following formatting requirements:
(1) The answer should be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides.
(2) The response also includes a cover page containing the title of the homework, the student's name, the course title, and the date. The cover page is not included in the required page length.
(3) Also include a reference page. The Citations and references should follow APA format. The reference page is not included in the required page length.