math

math. Tracks of a Killer

Introduction:

The body of famous pop music producer Johnathan Wallace was found in his bathtub.  It is our hypothesis that an intruder surprised the victim and drowned him.  The only clue at the crime scene was a set of muddy footprints leading from a nearby window to the bathroom and back again.  The footprints were smeared, so their exact size could not be determined, and the soles of the shoes had no pattern.  It will be difficult to match the footprints to any particular pair of shoes.

You will use data collected from a sample group of people to determine whether there is a correlation between height and either shoe length or stride length.  If there is, you can then use the predictive equation to predict the height of the killer based on the muddy footprint evidence at the crime scene.

Learning objectives:

• Evaluate statistical claims using eight guidelines and an understanding of how statistical studies are created

Before you begin:

• Review the key principles of correlation and causation in unit 5E of your textbook.
• Download the file “Online QR Activity – Tracks of a Killer – Data file.xls” which provides you the data on the sample of people’s heights, shoe lengths, and stride lengths. Save it as “LastName-Tracks of a Killer activity spreadsheet.xls.” You will be submitting this saved spreadsheet through Canvas when it’s complete.
• Locate the resources for “Interpreting correlation coefficients,” “Exploring correlation with Excel,” and “Graphing with Excel” on our Canvas site which you will use to help you complete this Activity.

Procedure:

• Use the data in the “Online QR Activity – Tracks of a Killer – Data file.xls” spreadsheet, to calculate two correlation coefficients in Excel, one for Shoe Length vs. Height and one for Stride Length vs. Height.
• Create two scatter plots in Excel, one for each of the relations listed above. You should insert the trendline, equation for the trendline, and correlation coefficient () on each graph.  Don’t forget to label your axes and include a title for each graph.

• Answer the Analysis questions below in a Word Document which you should save as Save it as “LastName-Tracks of a Killer analysis.” The analysis should be a minimum of 1 page (at least 250-300 words), typed double-spaced in Times New Roman font.
• Submit the completed and saved Excel budget spreadsheet and the analysis Word Document, through this assignment in Canvas.

Crime scene and suspect data

Three suspects were questioned immediately following the murder:

• Penelope Paige, pop star, 5’4”/green eyes/blonde hair. Possible motive:  She is suing Wallace over the failure of her last album.
• Rex Chapman, rock guitarist, 5’8”/brown eyes/brown hair. Possible motive:  He accused Wallace of stealing profits from his hit single “Walk It Off.”
• Dirty Dawg, rapper, 6’0”/brown eyes/black hair. Possible motive:  He wants out of a record contract with Wallace.

Here is the evidence from the crime scene:

Analysis:

1. Based on the data, do you think there is a linear relationship between Stride Length and Height? Explain your answer and incorporate your interpretation of the correlation coefficient and trendline.
2. Based on the data, do you think there is a linear relationship between Shoe Length and Height? Explain your answer and incorporate your interpretation of the correlation coefficient and trendline.
3. Do you think it is possible to infer a person’s height from his or her shoe size? Explain your answer.
4. Do you think it is possible to infer a person’s height from his or her stride length? Explain your answer.
5. Use the relationship between Stride Length and Height to determine the approximate heights of people with the following stride lengths. You should include in your solutions work that shows the unit conversions necessary.
1. 75 m
2. 45 m
3. 50 m
6. Suppose you measure the stride length of a set of footprints, and you predict that the person who made the footprints is 1.75 m tall. Later, you find out that the person who made the footprints is actually only 1.52 m tall.  Give two possible reasons why your prediction was incorrect, and thoroughly explain your reasons.
7. Use the relationships that you calculated and determine which of the three suspects most likely left the footprints to and from Jonathan Wallace’s bathroom. Show all your calculations.  Hint:  Use the axis from your graph to determine which variables are the x and y in your trendline equation.

 Excellent Proficient Satisfactory Needs Improvement Not Evident Graphs Points: 30 Both scatterplots have all 6 required elements present (for a total of 12 required elements). Points: 25 Up to 2 required elements are missing from the scatterplots. Points: 20  Up to 3 required elements are missing and/or the graphs are not scatterplots Points: 18  More than 4 required elements are missing and/or the graphs are not scatterplots Points: 0 Graphs were not submitted Analysis questions Points: 60  All 7 analysis questions were answered thoroughly and completely Points: 53  Most analysis questions were answered thoroughly and completely, but 1-2 were not. Points: 47  Some analysis questions were answered thoroughly and completely, but 3-4 were not. Points: 40 Some analysis questions were answered thoroughly and completely, nut 5-6 were not, OR all analysis questions were answered, but not thoroughly. Points: 0 (0.00%) Not included Writing Points: 10 Writing exhibited complex sentence structure, and was free of spelling and grammatical errors Points: 9 Writing exhibited simple sentence structure, and was free of spelling and grammatical errors Points: 8 Writing exhibited simple sentence structure, and had less than 3 spelling and/or grammatical errors Points: 7 Writing exhibited simple sentence structure, and had 4-5 spelling and/or grammatical errors OR writing had incomplete sentences and no spelling/grammatical errors. Points: 0 Writing exhibited poor sentence structure, and had many spelling and/or grammatical errors 100 87 75 65

Adapted from:  Texas Instruments. (2010). Forensics Case 1 – Tracks of a Killer: Using footprints to estimate height. Retrieved 2010, from Education technology – Classroom Activities: http://education.ti.com/calculators/downloads/US/Activities/Detail?id=6369

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