Police sometimes measure shoe prints at crime scenes so that they can leam something about criminals. Listed below are shoe print lengths, foot lengths, and heights of males. Construct a scatterplot, find value of the linear correlation coefficient r, and find the P-value of r Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Based on these results, does it appear that police can use a shoe print length to estimate the height of a male? Use a significance level of a =0.05. Shoe Print (cm) 29.3 26.6 181 8 29.3 25 7 173.1 30 4 279 1817 30 9 26.8 D 24 8 168 7 Foot Length (cm) 27 8 179 9 Height (cm) Construct a scatterplot. Choose the correct graph below OA O D. B.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Question
5
**Title: Analyzing Shoe Prints and Heights for Criminal Investigations**

**Introduction**
Police sometimes measure shoe prints at crime scenes to gain insights about criminals. Presented below are data for shoe print lengths, foot lengths, and heights of males. The task is to construct a scatterplot, find the linear correlation coefficient (r), and determine the P-value. The goal is to assess whether there is sufficient evidence to support a claim of linear correlation between shoe print length and height, using a significance level of \( \alpha = 0.05 \).

**Data:**
- **Shoe Print (cm):** 29.3, 29.3, 30.4, 30.9, 26.8
- **Foot Length (cm):** 26.6, 25.7, 27.9, 27.8, 24.8
- **Height (cm):** 181.8, 173.1, 181.7, 179.9, 168.7

**Scatterplot Construction**
A scatterplot is needed to visualize the relationship between the shoe print length (x-axis) and height (y-axis). The correct scatterplot should accurately reflect the data points generated from the pairs of shoe print lengths and heights given above.

**Visual Options Available:**

- **Option A:** This scatterplot graph does not represent the correct correlation pattern.
- **Option B:** This scatterplot graph does not represent the correct correlation pattern.
- **Option C:** This scatterplot is identified as the correct representation of the data points.
- **Option D:** This scatterplot does not indicate the correct relationship.

**Calculation of Linear Correlation**
To determine the correlation, calculate the linear correlation coefficient \( r \). This value indicates the strength and direction of a linear relationship between two variables. Round \( r \) to three decimal places as necessary.

**Analysis and Conclusion**
With the calculated \( r \) and the corresponding P-value, determine if there is sufficient evidence for the claim of a linear correlation between shoe print length and height at \( \alpha = 0.05 \). If the evidence supports it, police can reasonably use shoe print length to estimate a person's height.
Transcribed Image Text:**Title: Analyzing Shoe Prints and Heights for Criminal Investigations** **Introduction** Police sometimes measure shoe prints at crime scenes to gain insights about criminals. Presented below are data for shoe print lengths, foot lengths, and heights of males. The task is to construct a scatterplot, find the linear correlation coefficient (r), and determine the P-value. The goal is to assess whether there is sufficient evidence to support a claim of linear correlation between shoe print length and height, using a significance level of \( \alpha = 0.05 \). **Data:** - **Shoe Print (cm):** 29.3, 29.3, 30.4, 30.9, 26.8 - **Foot Length (cm):** 26.6, 25.7, 27.9, 27.8, 24.8 - **Height (cm):** 181.8, 173.1, 181.7, 179.9, 168.7 **Scatterplot Construction** A scatterplot is needed to visualize the relationship between the shoe print length (x-axis) and height (y-axis). The correct scatterplot should accurately reflect the data points generated from the pairs of shoe print lengths and heights given above. **Visual Options Available:** - **Option A:** This scatterplot graph does not represent the correct correlation pattern. - **Option B:** This scatterplot graph does not represent the correct correlation pattern. - **Option C:** This scatterplot is identified as the correct representation of the data points. - **Option D:** This scatterplot does not indicate the correct relationship. **Calculation of Linear Correlation** To determine the correlation, calculate the linear correlation coefficient \( r \). This value indicates the strength and direction of a linear relationship between two variables. Round \( r \) to three decimal places as necessary. **Analysis and Conclusion** With the calculated \( r \) and the corresponding P-value, determine if there is sufficient evidence for the claim of a linear correlation between shoe print length and height at \( \alpha = 0.05 \). If the evidence supports it, police can reasonably use shoe print length to estimate a person's height.
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