One of the most exciting areas of mathematics involves the application of statistics to real-world settings to make informed decisions. In this task you will design, implement, and analyze the results of an original investigation comparing two groups in order to answer a question. You will collect, display, and interpret your data. Select one of the following topics as a base for your original investigation:

• Mathematics education: Design an investigation that compares two pedagogical approaches or one that allows you to compare two subgroups.
• Observational study: Design an investigation that focuses on some type of observable behavior.

Task:

A.  Design an investigation that details the following six components:

Note: If one or more of the following components do not apply to your investigation, explain why each does not apply in a way that fully demonstrates your understanding of the missing component.

• Statement of purpose
• Identification of a target population
• Description of sampling methodology (random sampling or random assignment)
• Description of sample(s)
• Identify the independent and dependent variables
• Identification of baseline or control group

B. Describe the methodology that will be used to implement the investigation. The methodology should include the following three components:

• Materials used during the investigation
• Method of data collection
• Timeline for data collection

C.  Analyze the results from the implemented investigation. Your analysis should include the following components:

1.  Statistical results presented using the following formats:

• Table or listing of the data collected by the candidate through random sampling or random assignment of treatments
• Graphical representation of the data collected

2.  Interpretation of results

• Interpret data representations created as part of an investigation.

D. Discuss the feasibility of using a computer-based simulation to model the system that was studied, based on the results of the investigation.

E.  When you use sources, include all in-text citations and references in APA format.