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Math 120 Project: A Study Comparing Two Populations

Project Overview You will formulate a question about two populations, and then seek to answer that question based on data you gather by using the methods of statistical inference we have learned in this class. Experimental Design • You will determine a question to ask regarding two populations and one variable to compare between those two populations. • You will collect samples from the two populations in order to answer your question. • Using the methods discussed in this class, you will analyze the data you collected in your samples. • You will write a report detailing the process described above and then draw conclusions based that data and process. Other Considerations • If data is collected from human subjects, privacy must be maintained at all times. In fact, in some circumstances, the release of

personal data could be considered a violation of school rules. • If data is collected on human subjects without their knowledge, you must clear your procedure with me beforehand. • Where feasible, you should try to meet the assumptions of the test you are planning to use (e.g., n > 30 for comparing means, 10 in

each category for proportions). That said, your sampling technique will almost certainly NOT be a simple random sample. (Samples of convenience will be acceptable for the purposes of this project, but extra credit may be given for more effective sampling techniques).

The Report Format and Style The report must have the following attributes: • It must be typed, single spaced. • It should have a cover page. • It should have each of the following sections, clearly labeled, in the order given: A. The Abstract (no more than one page) A one page (at most!) overview covering the crucial points of the study from beginning to conclusion (i.e. each section below). Note: This is not an introduction, but rather a synopsis/summary of your work. B. Methods (≈ 1 page, plus the original data sheets) 1. The question: Clearly state the question you are trying to answer. Clearly define the populations in question and the variable you

are studying for the two populations. 2. Sampling: A careful description of how you obtained the samples. Include sample sizes. Be very specific. Using vocabulary from

the class, what sampling method did you use? 3. Hypothesis Test: Complete all of the steps of a hypothesis test (i.e. state hypotheses, assumptions, p-value, decision, and

conclusion) 4. Confidence Interval: Include a confidence interval and its interpretation in context. 5. Data: The original page(s) you used to record the data and a summary of the counts. This does NOT have to be typed.

This is the section of the test with the single most amount of points. Be sure this is accurate!

C. Results (≈ 1 page) 1. Discuss your results:

a. Discuss the decision and conclusion of your hypothesis test in non-technical language as if explaining this to a person who has not taken statistics.

b. Include an easy-to-understand explanation of what the p-value you found actually represents. 2. Discuss the viability of your data and conclusion. Some considerations:

a. Give a detailed discussion of sources of bias that might be present due to your sampling method and other factors present in your data. Use specific terminology from the class as a part of this discussion.

b. Should you use this sample data to make inferences about the two populations as a whole? Explain your reasoning. 3. What would you do it differently if you were performing a formal study to be submitted to a scholarly journal D. Conclusion (at least 1 paragraph)

Give a final, overall summary of your study and results based on the discussion above.

Working with others You may discuss any topic with other students. However, only you may collect the data, do the calculations, and write the report. Due Date: See syllabus.

Grade Sheet for Math 120 Project

Format (10)

____ 3 Clearly delineated sections

____ 2 Cover page

____ 5 Typed, single spaced

Abstract (10)

____ 10 Completeness in summarizing key

points of the entire project

**0 points if written as introductory paragraph(s)

Study (40)

____ 5 Clearly Stated Question

____ 10 Describe Sampling Method (specific)

____ 20 Significance Test/Confidence Interval

____ 5 Original Data Sheet(s)

**maximum score of 15/40 if no two populations

Discussion (35)

____ 10 Interpretation of p-value/

interpretation of test conclusion

____ 10 Discussion of sources of bias

____ 15 Realistic evaluation of the study and

discussion of necessary changes

Conclusion (5)

____ 5 Overall summary of the study

____ Points deducted

____ Bonus points for difficulty/originality

_____ 100 Total Points

Grade Sheet for Math 120 Project

Format (10)

____ 3 Clearly delineated sections

____ 2 Cover page

____ 5 Typed, single spaced

Abstract (10)

____ 10 Completeness in summarizing key

points of the entire project

**0 points if written as introductory paragraph(s)

Study (40)

____ 5 Clearly Stated Question

____ 10 Describe Sampling Method (specific)

____ 20 Significance Test/Confidence Interval

____ 5 Original Data Sheet(s)

**maximum score of 15/40 if no two populations

Discussion (35)

____ 10 Interpretation of p-value/

interpretation of test conclusion

____ 10 Discussion of sources of bias

____ 15 Realistic evaluation of the study and

discussion of necessary changes

Conclusion (5)

____ 5 Overall summary of the study

____ Points deducted

____ Bonus points for difficulty/originality

_____ 100 Total Points

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