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GOAL: Explore the use of hypothesis testing and regression analysis in real-worl
GOAL: Explore the use of hypothesis testing and regression analysis in real-world scenarios.
Demonstrate the ability to use critical thinking and effective communication skills.
1. Given an article describing the results of a statistical study:
Read the article and comment on the analysis performed by the authors of the study.
Explain the process of hypothesis testing and describe its use in the study.
2. Given two sets of potentially related data:
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(a) Perform hypothesis testing to a given level of significance, including:
i. Form a hypothesis the data might or might not support in. Determine the null and alternative hypotheses for your analysis ili. Using the data, determine the test statistic and p-value iv. Make a decision regarding the null hypothesis
v. Summarize the results of your hypothesis test
(b) Make and defend a statement about the correlation between the two sets of data, includ-ing:
i. Create two scatter plots of the provided data with each set of data alternatively the explanatory and response variables, or use the provided scatter plots in Microsoft Excel
in. Make a statement about the linear correlation between the two variables ili. Use technology to find a best-fit line for each scatter plot, including the correlation
coefficient (r) and the coefficient of determination (72)
iv. Use the correlation coefficient and coefficient of determination to defend your
statement about the linear correlation between the two variables
v. Use technology to find a curve with a better visual fit for each scatter plot vi. Summarize your results
Part 1 contains instructions on how to do regression analysis
Part 2 of this project will use the study “Driver education and teen crashes and traffic violations in the first two years of driving in a graduated licensing system” performed by Duane F. Shell, et al., available online at https: //doi.org/10.1016/j.aap.2015.05.011.
Part 3 of this project will use data from the National Safety Council regarding fatal automobile accidents and bicycle deaths and injuries.
As it is primarily an essay with some mathematics and figures added, you may either use a word processor and write it in MLA format, or you may use IATEX. Whichever you choose to use, your final essay must be submitted in PDF format. Also, attach any scratch work paper you have to this packet and turn it in to me at the final exam.
For proper MLA formatting, refer to the Online Writing Lab (OWL) at Purdue (https://owl.
purdue.edu/ow1/research_and_citation/mla_style/mla_formatting_and_style_guide/ mla_formatting_and_style_guide. htm1). If you use IT Xinstead, it will properly format
Part 1 Linear Regression Instructions
We will use MS Excel to perform the regression analysis on the file “Project Dataxisx”.
Select the left-hand plot.
Select the “+” box above the paintbrush to open the “Chart Elements” menu.
Open the “Trendline” submenu by selecting the arrow and then select “More Options.”
Ensure the “Format Trendline” pane has “Trendline Options” selected.
Check the “Display Equation on chart” and “Display R-squared value on chart” checkboxes at the bottom of the pane.
Select the “Linear” radio button to put a linear trendline on the plot and note both the R? value and the appearance of the line.
In turn, select each of the trendline radio buttons and note the appearance of the curve that appears. When you select “Polynomial” also increase the “Order” and note how the curve changes. Do not select the “Moving Average” trendline; its results are not used in this project.
Decide which curve (other than “Linear”) best fits the data points and note its R? value and type. If you select “Polynomial,” also note its order,
Select the right-hand plot and repeat Steps 2-8.
You should now have two types of regression curves for each plot and their associated R? values. One of these types will be Linear and the other will have been chosen by you. For each of the four R? (coefficient of determination) values, take the square root to find the R (correlation coefficient) value.
Part 2
Driver Education Article Analysis
Read “Driver education and teen crashes and traffic violations in the first two years of driving in a graduated licensing system” and write at least two paragraphs describing and analyzing the use of hypothesis testing and regression analysis performed by the authors. A list of some questions your paragraphs should answer follows, but is by no means inclusive.
What is meant by “Hypothesis Testing”?
What is the process of hypothesis testing?
What are the null and alternative hyptheses the authors used?
Does their data support their conclusion?
Do you agree with their conclusion? What specific reported data leads you to your conclusion?
• What statement about their data did you find most interesting? Why?
I suggest using some lined paper and writing at least some short answers to these questions before attempting to complete the essay.
Part 3
Automobile and Bicycle Deaths
Part 3.1
Analysis
You will need some paper to complete this section. Write out the answers to each of the prompts, so that you have them when you start to write the final essay.
The supplied spreadsheets “Motor- Vehicle Deaths and Rates” and “Bicycle-related injury tables” provide several types of data. Use these to do the following analysis:
1. Form and state a hypothesis this data may or may not support. For example,
, “You are more
likely to die from an automobile accident today than you were 10 years ago,” or, “Cycling is more dangerous than riding in an automobile.” This is your claim
2. Use the hypothesis testing process described in the notes to determine the validity of your claim. Choose an appropriate level of significance, but not more than 10%.
State the null and alternative hypotheses and note which contains your claim.
Enter the data and perform the appropriate hypothesis test
Make a decision regarding the null hypothesis.
Interpret this decision in the context of your claim.
The supplied spreadsheet “Project Data” contains a specific portion of the data from the other two spreadsheets. Use this spreadsheet to perform a regression analysis (see Part 1 for details) and answer the following questions:
Should the number of automobile and bicycle deaths be related?
Does the data suggest they may be related? How can you tell?
Although we only discussed linear regression in class, there are many other types of regression analyses that may be done. For example, in the article from Part 2 the authors used Logistic Regression. Conveniently, Excel has several types of regression built in. Is there a regression curve that appears to fit better, and if so, what is it?
For a best fit regression curve, does it matter which set of data is the explanatory variable?Why or why not? Should it matter? Why or why not?
Part 3.2
Essay Prompt
Once you have performed both analyses, write several paragrahs describing them and reporting your results. Your paragraphs should be fairly similar to the article from Part 2.
Be sure to clearly state your claim as well as what hypothesis test you used (T-Test for a population mean or Z-Test for a population proportion) and why that test was the appropriate choice. You should also explicitly state the value of the test statistic and the p-value from the test. Although you should not explicitly state “Reject the null hypothesis” or “Fail to reject the null hypothesis” in your essay, the interpretation of this decision should make it clear what your decision was.
Your regression analysis report should include the data you used and at the very least answer the questions posed above. You will likely want a picture of the “better fit” regression cuive, assuming you found one. Be as specific as you can. Discuss your results and what they mean.
Part 4 Final Thoughts and Prompts
This project is intended to be an essay showing me your ability to describe and apply the primary statistical tools we have learned this semester. These are Regression Analysis and Hypothesis Testing. I am specifically looking for clear and concise statements (effective communication) as well as logical conclusions (critical thinking). If you need assistance with the first, the Writing Lab in the Center for Student Learning in Addlestone Library is a great resource, although my advice is always, “Write how you speak.” For help with the second, you should always be asking yourself,
“Does what I am saying make sense? Are my thoughts in a logical order?”
The final result should be about two to three pages double-spaced (if in MLA) and 1000 to 1500 words, plus space for any pictures/figures. In particular, I expect to see a data table containing the data you used for your regression analysis and a picture showing the best fit regression curve you found.
As always, if you do not understand something, you must ask me about it. That could be a question related to doing the analysis, writing about the analysis, or even what I am looking for from you.
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