(Round to three decimal places as needed.) (c) Does a linear relation exist between the number of reported cases of Lyme disease and the number of drowning deaths? The variables Lyme disease and drowning deaths are V associated because r is v and the absolute value of the correlation coefficient is than the critical value, (Round to three decimal places as needed.)
(Round to three decimal places as needed.) (c) Does a linear relation exist between the number of reported cases of Lyme disease and the number of drowning deaths? The variables Lyme disease and drowning deaths are V associated because r is v and the absolute value of the correlation coefficient is than the critical value, (Round to three decimal places as needed.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:**Data on Lyme Disease Cases and Drowning Deaths**
The table displays monthly data on the number of Lyme Disease cases and drowning deaths:
| Cases of Lyme Disease | Drowning Deaths | Month |
|-----------------------|-----------------|-------|
| 2 | 0 | J |
| 2 | 1 | F |
| 3 | 2 | M |
| 4 | 1 | A |
| 5 | 2 | M |
| 15 | 9 | J |
| 22 | 17 | J |
| 13 | 5 | A |
| 6 | 3 | S |
| 5 | 3 | O |
| 4 | 1 | N |
| 1 | 0 | D |
**Critical Values for Correlation Coefficient**
The table to the right provides the critical values for correlation coefficients based on sample size \(n\):
| \(n\) | Critical Value |
|-------|----------------|
| 3 | 0.997 |
| 4 | 0.950 |
| 5 | 0.878 |
| 6 | 0.811 |
| 7 | 0.754 |
| 8 | 0.707 |
| 9 | 0.666 |
| 10 | 0.632 |
| 11 | 0.602 |
| 12 | 0.576 |
| 13 | 0.553 |
| 14 | 0.532 |
| 15 | 0.514 |
| 16 | 0.497 |
| 17 | 0.482 |
| 18 | 0.468 |
| 19 | 0.456 |
| 20 | 0.444 |
| 21 | 0.433 |
| 22 | 0.423 |
| 23 | 0.413 |
| 24 | 0.404 |
| 25 | 0.396 |
| 26 | 0.388 |
![**Understanding the Correlation Between Lyme Disease and Drowning Deaths**
Lyme disease is an inflammatory disease that leads to symptoms such as skin rash and flu-like conditions. It is transmitted via the bite of an infected deer tick. This exercise presents data reflecting the number of reported Lyme disease cases and drowning deaths in a rural county. You will work through parts (a) through (c) below:
### Tasks:
1. **Draw a Scatter Diagram of the Data**
- Select the correct graph reflecting the relationship between Lyme disease cases and drowning deaths.
Options for the scatter diagram:
- **A:** Lyme Disease on the x-axis, Drownings on the y-axis
- **B:** Drownings on the x-axis, Lyme Disease on the y-axis
- **C:** Lyme Disease on the x-axis, Drownings on the y-axis (✓ Correct)
- **D:** Drownings on the x-axis, Lyme Disease on the y-axis
The correct scatter plot is option **C**, where Lyme Disease is plotted on the x-axis and Drownings on the y-axis.
2. **Determine the Linear Correlation Coefficient**
- The linear correlation coefficient (\( r \)) quantifies the strength of the relationship between Lyme disease and drowning deaths.
Result: \( r = 0.963 \) (Rounded to three decimal places)
3. **Assess the Linear Relationship**
- Analyze whether there is a significant linear relationship between reported cases of Lyme disease and the number of drowning deaths based on the correlation coefficient.
**Tasks:**
- Determine if the variables Lyme disease and drowning deaths are [positively/negatively] associated because \( r \) is [greater/less] than the critical value.
### Analysis:
- The variable coefficients indicate a positive association since the correlation coefficient is high (close to 1), suggesting a strong positive correlation.
- The absolute value of the correlation coefficient \( r \) is likely greater than the critical value, affirming a significant linear relationship.
In summary, this analysis aims to explore the correlation between Lyme disease cases and drowning incidents in a specified county, helping understand potential direct or indirect associations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5685ce4-d9f8-4c8e-aa78-bd82f1a4dfdc%2F07c3b660-53eb-4120-bef0-e8a65c2f636a%2Fwoltjyj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding the Correlation Between Lyme Disease and Drowning Deaths**
Lyme disease is an inflammatory disease that leads to symptoms such as skin rash and flu-like conditions. It is transmitted via the bite of an infected deer tick. This exercise presents data reflecting the number of reported Lyme disease cases and drowning deaths in a rural county. You will work through parts (a) through (c) below:
### Tasks:
1. **Draw a Scatter Diagram of the Data**
- Select the correct graph reflecting the relationship between Lyme disease cases and drowning deaths.
Options for the scatter diagram:
- **A:** Lyme Disease on the x-axis, Drownings on the y-axis
- **B:** Drownings on the x-axis, Lyme Disease on the y-axis
- **C:** Lyme Disease on the x-axis, Drownings on the y-axis (✓ Correct)
- **D:** Drownings on the x-axis, Lyme Disease on the y-axis
The correct scatter plot is option **C**, where Lyme Disease is plotted on the x-axis and Drownings on the y-axis.
2. **Determine the Linear Correlation Coefficient**
- The linear correlation coefficient (\( r \)) quantifies the strength of the relationship between Lyme disease and drowning deaths.
Result: \( r = 0.963 \) (Rounded to three decimal places)
3. **Assess the Linear Relationship**
- Analyze whether there is a significant linear relationship between reported cases of Lyme disease and the number of drowning deaths based on the correlation coefficient.
**Tasks:**
- Determine if the variables Lyme disease and drowning deaths are [positively/negatively] associated because \( r \) is [greater/less] than the critical value.
### Analysis:
- The variable coefficients indicate a positive association since the correlation coefficient is high (close to 1), suggesting a strong positive correlation.
- The absolute value of the correlation coefficient \( r \) is likely greater than the critical value, affirming a significant linear relationship.
In summary, this analysis aims to explore the correlation between Lyme disease cases and drowning incidents in a specified county, helping understand potential direct or indirect associations.
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